In MIMO communications, it is expensive and some-times impossible to obtain timely channel state information at transmitter (CSIT) when the number of antennas is large. Furthermore, if the carrier frequency is high, the variation of the phases of the channel state information is significant with small movement in the channels. On the other hand, spatial signal path directions and the amplitudes of path gains vary slowly. We propose a beam network methodology for multi-antenna communication using such partial CSIT as directions and amplitudes instead of the conventional approach that employs full CSIT. Three representative problems are presented to demonstrate the simplicity and performance of the methodology. These include the single-user MIMO channel, a MIMO interference channel, and a multicast network via a reconfigurable intelligent surface (RIS). In particular, we see that the usual high complexity of RIS state design can be simplified to choosing states to connect an incoming beam to outgoing beams.1

A novel class of achievable rate regions is obtained for the general$K$-receiver discrete memoryless broadcast channel over which two groupcast messages are to be transmitted, with each message required by an arbitrary group of receivers. The associated achievability schemes are parameterized by an expansion of the message set which then determines how random coding techniques are employed. These techniques include generalized versions of up-set message-splitting, the generation of possibly multiple auxiliary codebooks for certain compositions of split messages using superposition coding with subset inclusion order, partial interference decoding at all receivers in general, joint unique decoding at receivers that desire both messages, and non-unique or indirect decoding at receivers that desire only one of the two messages. The generality of the proposed class of schemes implies new achievable rate regions for problems previously not considered as well as those that were studied before, with specific members of that class having rate regions that coincide with previously found capacity regions for special classes of broadcast channels with two private or two nested groupcast messages, wherein the group of receivers desiring one message is contained in that desiring the other. Moreover, new capacity results are established for certain partially ordered classes of broadcast channels for a class of two non-nested groupcast messages. To further show the strength of the proposed achievable rate regions we consider the so-called combination network as a test case. When specialized to the combination network, some members of the class of inner bounds are shown, via converse results, to result in the capacity region when the two messages are (a) intended for two distinct sets of$K{-}1$receivers each and (b) nested, in which one message is intended for one or two (common) receivers and both messages are intended for all other (private) receivers. In the latter two nested messages cases, we hence recover, in a top-down manner, previous results by Bidokhti, Prabhakaran, and Diggavi, obtained therein using lower complexity network coding schemes based on rate-splitting and linear superposition coding but tailored to the combination network, while in the first case we obtain a new capacity result for a non-nested message set, which was hitherto unknown. Furthermore, we show the achievability of rate pairs in two interesting examples of combination networks, with three and four common receivers each. These examples were proposed in the previous literature to show the sub-optimality of the aforementioned rate-splitting and linear superposition coding scheme, and hence to motivate the additional consideration of a pre-encoding technique and a block-Markov linear superposition coding for the combination network, with the latter then lifted to the general broadcast channel. Our results suggest that the proposed framework here for the general broadcast channel when specialized to the combination network is strong enough to incorporate the enhancements afforded by those two latter techniques, thereby implying that perhaps block-Markov superposition coding is not necessary in the general broadcast channel. Moreover, there is a trade-off between the complexity of the coding scheme within the class of schemes we propose when applied to the combination network and that of the determination of the distribution of the auxiliary random variables and the encoding function that achieve the capacity region. This may have interesting implications for the general broadcast channel as well.

Multiple groupcasting over the broadcast channel (BC) is studied in a special setting. In particular, an inner bound is obtained for the$K$-receiver discrete memoryless (DM) BC for the diamond message set which consists of four groupcast messages: one desired by all receivers, one by all but two receivers, and two more desired by all but each one of those two receivers. The inner bound is based on rate-splitting and superposition coding and is given in explicit form herein as a union over coding distributions of four-dimensional polytopes. This inner bound is then shown to be the capacity for a certain class of partially ordered DM BCs with order defined via the less noisy condition. When specialized to the so- called combination network, which is a class of three-layer (two-hop) broadcast networks parameterized by$2^{K}{-}1$finite-and-arbitrary-capacity noiseless links from the source node in the first layer to as many nodes of the second layer, our top-down approach from the DM BC to the combination network yields an explicit inner bound as a single polytope via the identification of a single coding distribution. This inner bound consists of inequalities which are then identified to be within the class of generalized cut-set outer bounds recently obtained by Salimi et al for broadcast networks. We hence establish the capacity region of the general$K$-user combination network for the diamond message set, and do so in explicit and structured form. Such a result implies a certain strength of our inner bound for the DM BC in that it (a) produces a hitherto unknown capacity region when specialized to the combination network and (b) may capture many combinatorial aspects of the capacity region of the$K$-receiver DM BC itself for the diamond message set. Moreover, we extend that inner bound by adding binning to it. As in the no-binning case, we provide the more general inner bound in explicit form.

A model of device-to-device (D2D) coded caching in which only a subset of users transmit information during the D2D transmission process was recently introduced. Such networks are referred to as partially cooperative D2D networks. Tebbi and Sung proposed a coded caching achievability scheme for such networks that enables all users to obtain their respective file demands. This is done by forming user sets and employing some of the transmitting users to compensate for the non-transmitting users in each such user set. In this paper, we show that this approach is sub-optimal. In particular, we show that by forming groups of such user sets that satisfy certain properties, it is possible to exploit additional coding opportunities across all the user sets in that group that are not exploited in the previously proposed scheme. We also show how to construct such groups and characterize the resulting improvement in the device-to-device transmission rate.

Device-to-device (D2D) coded caching is considered in which there is a server hosting a library of files and a set of users. Each user is equipped with a cache memory of equal size. The system operates in two phases: first, the placement phase, in which the users’ cache memory is filled with data from the file library, followed by the delivery phase, in which each user demands one file from the library. These demands are then satisfied via user-to-user multicast transmissions only, without any involvement from the central server. For such a system, we obtain a novel lower bound on the optimal D2D sum rate. Moreover, the best known achievable D2D sum rate is shown to be within a constant multiplicative factor of 3.17 of our lower bound, improving upon the previously best known lower bound. Hence, the result in this paper further closes the gap between the best known achievable sum rate and the optimal sum rate for D2D coded caching.

A three-server coded caching scheme was presented recently by Luo et al. that extends the single-server coded caching scheme by Maddah-Ali and Niesen. Forming user sets as in the single-server case, Luo et al. show that by "pairing" such user sets that satisfy certain conditions, the rate of the three-server scheme may be reduced to less than two-thirds of the rate of the single-server scheme. Yet, in some cases, the pairing is not perfect (i.e., some of the sets are left unpaired) and the requirements of the unpaired sets must then be satisfied by a sub-optimal scheme. This results in the so-called "pairing loss", leading to a transmission rate greater than one-half of the single-server scheme due to imperfect pairing.In this paper, it is shown that instead of just pairing user sets, groups of 2 and 6 user sets can be formed, enabling a more efficient organization. It is shown that within groups of size 6 (and 2), the user demands can be satisfied at a rate equal to one-half that of the single-server scheme. Then, through a specific example, a grouping algorithm is given that forms all user sets into such groups of size 2 or 6. Hence, the three-server rate may be uniformly reduced to exactly half the single-server rate, eliminating the pairing loss altogether..

This paper investigates the three-receiver (Y1, Y2, Y3) discrete memoryless (DM) broadcast channel (BC) for eight receive message cognition settings in which the weakest receiver Y3knows the message intended for the intermediate receiver Y2, Y2may or may not know the message intended for Y3, and the strongest receiver Y1knows none, one, or both of the messages intended for receivers Y2and Y3. For these eight settings, but for the Gaussian BC, the capacity regions were obtained previously by Asadi et al. In this paper, we establish the capacity regions for all eight cases for the class of less noisy DM BCs, thereby lifting the previously known capacity results from the Gaussian BC to the less noisy BC. To further expand the optimality results to strictly larger classes of broadcast channels, we propose a coding scheme that includes rate-splitting and indirect decoding, techniques not needed for the less noisy or Gaussian BCs, for four of the eight message cognition cases in which receiver Y2knows the message intended for Y3, and show that this more general scheme achieves capacity without requiring that receiver Y2be stronger than Y3in any sense (and when Y1knows the message intended for Y2, Y1is not required to be stronger than Y2either whereas when Y1does not know the message intended for Y2it is assumed that Y1is more capable than Y2) whereas it is assumed that Y1is less noisy than Y3in all four cases. Moreover, the converse proof for the second set of capacity results require both the Nair-Wang information inequality and the Csiszar sum lemma.

Multiple groupcasting over the broadcast channel (BC) is studied in a special setting. In particular, an inner bound is obtained for the K-receiver discrete memoryless (DM) BC for the diamond message set that consists of four groupcast messages: one desired by all receivers, one by all but two receivers, and two more desired by all but each one of those two receivers. The inner bound is based on rate-splitting and superposition coding and is given in explicit form herein as a union over coding distributions of four-dimensional poly-topes. When specialized to the so-called combination network, which is a class of three-layer (two-hop) broadcast networks parameterized by 2K-1 finite-and-arbitrary-capacity noiseless links from the source node in the first layer to as many nodes of the second layer, our top-down approach from the DM BC to the combination network yields an explicit inner bound as a single polytope via the identification of a single coding distribution. This inner bound consists of inequalities which, in a problem that is akin to finding a few needles in a haystack, are then identified to be within the class of a plethora of (indeed, infinitely many) generalized cut-set outer bounds recently obtained by Salimi et al for broadcast networks. We hence establish the capacity region of the general K-user combination network for the diamond message set, and do so in explicit form. Such a result implies a certain strength of our inner bound for the DM BC in that it (a) produces a hitherto unknown capacity region when specialized to the combination network and (b) may capture many, if not all, combinatorial aspects of the capacity region of the K-receiver DM BC itself (for the diamond message set).

The K-receiver discrete memoryless (DM) broadcast channel (BC) is considered in which each receiver is equipped with a cache memory of the same size. We obtain an upper bound on the capacity-memory tradeoff with uncoded pre-fetching, the highest rate of reliable communication for given cache size. This bound holds for the interleavable DM BC, a class of channels that subsumes the K-receiver degraded DM BC and the three-receiver less noisy DM BC. We then specialize our bound to the Gaussian BC, and show that it is tighter than that recently proposed in the literature for coded pre-fetching for a wide range of cache sizes as would be expected, but the two bounds coincide for sufficiently large cache size. In the two-receiver case, our bound is tight in that it is the exact capacity-memory trade-off with uncoded prefetching which implies that, in this case, coded prefetching does not enhance the capacity-memory tradeoff for sufficiently large cache size.

The MAC-IC-MAC is a class of multiple-access interference channels consisting of two multiple-access channels (MACs) that are mutually interfering but in which there is interference only from one transmitter of each MAC to the receiver of the other MAC. Two achievable rate regions that are within a quantifiable gap of the capacity region for the discrete-memoryless semi-deterministic MAC-IC-MAC were obtained in a previous companion work by the authors using inner and outer bounds that are unions of polytopes over admissible random coding distributions. In this paper, we obtain single-distribution-and hence explicit-inner and outer bounds that characterize the capacity region of the MIMO Gaussian MAC-IC-MAC to within a constant gap. We also evaluate and study the generalized degrees of freedom (GDoF) region via multidimensional signal-level partitioning for MIMO networks. Through its lens, the achievability of the key vertices of the GDoF region are examined. This analysis as well as the symmetric GDoF curve reveal that, at high SNR, when the ratio of the interference-to-noise to the signal-to-noise ratios, both taken in dB, is within a certain range, non-interfering transmitters in that cell can fully occupy the receivers' signal partitions in one or more dimensions that cannot otherwise be utilized by the interfering transmitter alone. This extends the same finding in the companion paper which established the results of this work for the scalar Gaussian MAC-IC-MAC.

The K-user discrete memoryless (DM) broadcast channel (BC) with two nested multicast messages is studied in which one common message is to be multicast to all receivers and the second private message to a subset of receivers. The receivers that must decode both messages are referred to as private receivers and the others that must decode only the common message as common receivers. For two nested multicast messages, we establish the capacity region for several classes of partially ordered DM BCs characterized by the respective associated sets of pair-wise relationships between and among the common and private receivers, each described by the well-known pair-wise more capable or less noisy condition. For three classes of partially ordered DM BCs, the capacity region is shown to be simply achieved by two-level superposition coding and the proofs of the converses rely on a recently found information inequality. The rate region achievable by two-level superposition coding is then enhanced through a multi-level superposition coding scheme after splitting the private message into as many parts as there are common receivers and indirect decoding. A closed-form two-dimensional polyhedral (polygonal) description is obtained for it for a given coding distribution in spite of the indeterminate number of split rates via a structured form of Fourier-Motzkin elimination. Through a converse result that relies on the Csiszar sum lemma and that information inequality, a specialization of this region that corresponds to splitting the private message into just two sub-messages is proved to be the capacity region for several classes of partially ordered DM BCs beyond those for which two-level superposition coding is capacity optimal, thereby underscoring the benefit of rate-splitting. All previously known capacity results for partially ordered DM BCs with two nested multicast messages for the two and three-receiver DM BCs as well as DM BCs with one private or one common receiver are subsumed in the general results obtained in this work.

The two-receiver Gaussian broadcast channel (BC) is studied when each receiver has a cache memory. Using a joint cache-channel coding scheme, the exact capacity-memory tradeoff-the highest rate of reliable communication as a function of the cache size-is established for any cache size.

A K-receiver discrete memoryless (DM) broadcast channel (BC) with general message sets is studied. A general message set is one that contains any subset of or all possible 2K-1 groupcast messages, with each such message intended for a distinct subset of receivers. Message merging is a simple idea of bijectively mapping multiple messages into a single message, and hence with a rate that is the sum of the rates of the merged messages. Using a natural form of message merging it is shown that superposition coding of the merged messages and successive decoding of a subset of those messages at each receiver achieves the capacity region of the class of K-receiver interleavable DM BCs for any general message set. The interleavable class of DM BCs subsumes the K-receiver degraded DM BC and the less noisy DM BC in the three-receiver case as special cases. A generalization of that result is also given. For certain classes of message sets, message merging, superposition coding and successive decoding is shown to again achieve the capacity region, but for corresponding classes of channels that are larger than the interleavable DM BC. In each such class, there is a group of receivers that are not constrained to be ordered in strength by any notion of order (i.e., degraded, less noisy or more capable). Most known results on the optimality of superposition coding and successive decoding, including notably, for the interleavable DM BC with private messages, and for the recently found classes of DM BCs for two nested multicast messages with one private or one common receiver, are subsumed by the general -yet simply established -result of this paper.

In this paper, we consider the K-receiver discrete memoryless (DM) broadcast channel (BC) with K private messages of the same rate. Inspired by the decentralized caching problem which has received much interest of late, we consider the case where each message consists of 2Kindependent sub-messages, with each sub-message available at a distinct subset of receivers as side information. We assume that the rates of all the sub-messages available at the same number of receivers are the same. Hence, each receiver has exactly the same amount of information about each message, including its intended message, as side information. For this symmetric side information structure, we establish the symmetric capacity for the interleavable DM BC, a class of channels which subsumes the K-receiver degraded DM BC and the less noisy BC in the three-receiver case. Our coding scheme involves (a) network coding in the form of a bit-wise XOR of two or more messages (b) message merging where multiple messages are bijectively mapped into a single message with a rate that is the sum of the rates of the merged messages (c) superposition coding where the codebooks are generated for the merged messages and (d) successive decoding at each receiver to find its intended message with the aid of the side information.

The generalized degrees of freedom (GDoF) of the two-user multiple-input multiple-output interference channel is studied under the assumption of delayed channel state information at the transmitters. In particular, with M antennas at each transmitter and N antennas at each receiver, and in the non-trivial case when M N (with the case of M N not needing any CSIT), new lower and upper bounds on the symmetric GDoF are obtained that are parameterized by α, which links the interference-to-noise ratio (INR) and the signalto-noise ratio (SNR) at each receiver via INR = SNRα. A new upper bound for the symmetric GDoF is obtained by maximizing abound on the weighted sum rate, which in turn is obtained from a combination of genie-aided side-information and an extremal inequality. The maximum weighted sum rate in the high SNR regime is shown to occur when the transmit covariance matrix at each transmitter is full rank. An achievability scheme is developed that is based on block-Markov encoding and backward decoding, and which incorporates channel statistics through interference quantization and digital multicasting. This symmetric GDoF lower bound is maximized separately for different ranges of α, by optimizing the transmit power levels in the achievability scheme separately in the very weak [0 ≤ α ≤ (1/2)], weak [(1/2) <; α ≤ 1], and strong (α 1) interference regimes. The lower and upper bounds coincide when α ≥ [(r + 1)/(r + 2)], where r = min(2, M/N), thus characterizing the symmetric GDoF completely for strong interference and a range of values of weak interference. It is also shown that treating interference as noise is strictly sub-optimal from a GDoF perspective even when the interference is very weak.

Approximate capacity regions are established for a class of interfering multiple access channels consisting of two multiple-access channels (MACs), each with an arbitrary number of transmitters, with one transmitter in each MAC causing interference to the receiver of the other MAC, a channel we refer to henceforth as the MAC-IC-MAC. For the discrete memory-less (DM) MAC-IC-MAC, two inner bounds are obtained that are generalizations of prior inner bounds for the two-user DM interference channel (IC) due to Chong et al. For the semi-deterministic MAC-IC-MAC, it is shown that single-user coding at the non-interfering transmitters and superposition coding at the interfering transmitter of each MAC achieves a rate region that is within a quantifiable gap of the capacity region, thereby extending such a result for the two-user semi-deterministic IC by Telatar and Tse. For the Gaussian MAC-IC-MAC, an approximate capacity region that is within a constant gap of the capacity region is obtained, generalizing such a result for the two-user Gaussian IC by Etkin et al. On contrary to the aforementioned approximate capacity results for the two-user IC, whose achievability requires the union of all admissible input distributions, our gap results on the semi-deterministic and the Gaussian MAC-IC-MAC are achievable by only a subset and one of all admissible coding distributions, respectively. The symmetric generalized degrees of freedom (GDoFs) of the symmetric Gaussian MAC-IC-MAC with more than one user per cell, which is a function of the interference strength (the ratio of INR to SNR at high SNR, both expressed in dB) and the numbers of users in each cell, are V-shaped with flat shoulders. An analysis based on signal-level partitions shows that the non-interfering transmitters utilize the signal-level partitions at the receiver where they are intended that cannot be accessed by the interfering transmitters (due to the restriction of superposition coding), thereby improving the sum symmetric GDoF of up to one degree of freedom per cell under a range of SINR exponent levels, which in turn becomes wider as the number of transmitters in each cell increases. Consequently, time-sharing between interfering and non-interfering transmitters is GDoF-suboptimal in general, as is time-sharing between the two embedded MAC-Z-MACs.

The one-to-three MIMO interference channel (IC) is a partially connected three-user IC with multiple antenna terminals where one transmitter is heard at all three receivers, thus causing interference at its two unintended receivers, whereas the other two transmitters are heard only at their respective intended receivers. In this paper, we present inner and outer bounds on the capacity region of the one-to-three MIMO IC, quantify the gap between the two bounds, and show that the gap is independent of the SNRs and INRs. In particular, the achievable scheme involves multi-level superposition coding with linear precoding based on the generalized singular value decomposition (GSVD). The outer bound is obtained using various combinations of genie information provided to the receivers.

Using an order-theoretic approach, a novel achievable rate region is obtained for the K-receiver discrete memoryless broadcast channel with two nested messages, one message desired by all receivers and the other desired by a subset of the receivers. When specialized to the combination network this inner bound is shown to achieve the capacity region when all but two receivers desire both messages.

The capacity region of the three-receiver discrete memoryless less noisy broadcast channel with message cognition is established in the case where the weakest receiver knows the message required by the strongest receiver prior to transmission. This problem was previously studied for the scalar Gaussian broadcast channel by Asadi et al but only inner and outer bounds were obtained. The capacity result of this paper can also be seen to augment the theory of the three-receiver discrete memoryless less noisy broadcast channel for which the capacity region was found previously by Nair and Wang but without message cognition.

The K-user multiple-input multiple-output broadcast channel with an arbitrary number of antennas at each node is studied. It is assumed that the transmitter has either perfect or no channel state information from each of the K receivers. The degrees of freedom (DoF) region under the restriction of linear encoding strategies - also known as the linear DoF (LDoF) - is established. In particular, a novel approach is developed to find outer bounds on the LDoF region. First, we discover some key properties of the corner points of the LDoF region. Then, we construct a convex hull of a series of sub-regions which together contains all possible corner points of the LDoF region, and thus the convex hull is an outer bound of the LDoF region. Furthermore, by showing that each of the sub-regions is achievable using linear coding schemes, we prove that the obtained convex hull is the exact LDoF region. We also provide the explicit expressions of the LDoF region polytope for two and three- user special cases, recovering known results.

The generalized degrees of freedom (GDoF) region of the multiple-input multiple-output (MIMO) Gaussian Z-interference channel with an arbitrary number of antennas at each node is established under the assumption of delayed channel state information at transmitters (CSIT). The GDoF region is parameterized by α, which links the interference-to-noise ratio (INR) to the signal-to-noise ratio (SNR) via INR = SNRα. A new outer bound for the GDoF region is established by maximizing a bound on the weighted sum-rate of the two users, which in turn is obtained by using a combination of genie-aided side-information and an extremal inequality. The maximum weighted sum-rate in the high SNR regime is shown to occur when the transmission covariance matrix of the interfering transmitter has full rank. An achievability scheme based on block-Markov encoding and backward decoding is developed which uses interference quantization and digital multicasting to take advantage of the channel statistics of the cross-link, and the scheme is separately shown to be GDoF-optimal in both the weak (α ≤ 1) and strong (α > 1) interference regimes. This is the first complete characterization of the GDoF region of any interference network with delayed CSIT, as well as the first such GDoF characterization of a MIMO network with delayed CSIT and arbitrary number of antennas at each node. For all antenna tuples, the GDoF region is shown to be equal to or larger than the degrees of freedom (DoF) region over the entire range of α, which leads to a V-shaped maximum sum-GDoF as a function of α, with the minimum occurring at α = 1. The delayed CSIT GDoF region and the sum-DoF are compared with their counterparts under perfect CSIT, thereby characterizing all antenna tuples and ranges of α for which delayed CSIT is sufficient to achieve the perfect CSIT GDoF region (or sum-DoF). It is also shown that treating interference as noise is not, in general, GDoF-optimal for the MIMO Z-IC, even in the weak interference regime.

We establish that the capacity regions of the discrete memoryless and vector Gaussian multiple access channels with general message sets are achievable with hierarchical successive group decoding, where groups of messages are successively decoded in accordance with the following rule: for each pair of messages known to nested sets of transmitters, the message known to more transmitters is decoded prior to-and not jointly with-the message known to fewer transmitters. This conclusion requires neither rate-splitting nor time-sharing, and is agnostic to whether or not the messages were encoded dependently. For instance, with private messages, hierarchical successive group decoding includes jointly decoding all messages at once, while for degraded messages, it is successive decoding in only one order. A consequence of our main result is that the capacity region of the multiple access channel with general message sets is achievable by time-sharing between only those successive decoding vertices whose decoding order respects the rule described as earlier.

A general inner bound is given for the discrete memoryless broadcast channel with an arbitrary number of users and general message sets, a setting that accounts for the most general form of concurrent groupcasting, with up to exponentially many messages intended for any set of subsets of receivers. Achievability is based on superposition coding and rate-splitting, where each receiver jointly decodes both its desired messages as well as the partial interference assigned to it via rate-splitting. The proof of achievability builds on the techniques for the description and analysis of superposition coding recently developed by the authors for the multiple access channel with general messages.

The K-user discrete memoryless (DM) broadcast channel (BC) with two degraded messages, with one common message to be decoded by all receivers and a private message by a subset of receivers, is studied. The receivers that must decode both messages are referred to as private receivers and the remaining ones that need only decode the common message as common receivers. We obtain two main results. The first one establishes the capacity region of two classes of DM BCs characterized by the associated sets of pair-wise relationships between and among the common and private receivers, each described by the well-known more capable and less noisy conditions. For both these classes, the capacity region is achieved by superposition coding and joint decoding so that the main contribution herein lies in the proofs of the converses. When specialized to the two previously well-studied cases of a single private receiver and a single common receiver, the two aforementioned classes are respectively as large as or larger than those for which capacity was previously obtained. The second main result is a new inner bound in closed form that involves rate splitting, superposition coding, and indirect decoding and we state its capacity optimality for a new class of four-receiver DM BCs.

Sun and Luo recently showed that if the vector-space single-beam interference alignment problem for a K-user, L-carrier interference channel is feasible, then K ≤ 2L - 2. We prove the converse, that if K ≤ 2L - 2, then the problem is feasible, i.e., that the requisite beamformers do exist.

Two different random coding techniques, both referred to as superposition coding in the literature, have been widely used to obtain inner bounds for the capacity regions of various communication networks. In one, auxiliary codewords are generated independently, and in the other, they are generated in a dependent manner. Using the multiple-access channel with general message sets as a case study, we place the two techniques under a common, order-theoretic framework. The key attribute of this framework is that it explicitly accounts for the acyclic direction and transitivity of the possible auxiliary codeword dependencies, leading to three significant discoveries. First, with respect to a fixed coding distribution, the set of rates achievable by superposition coding with dependent auxiliary codeword generation forms a polymatroid, thereby generalizing the same previously known result for superposition coding with independent auxiliary codewords. Second, we obtain a large class of superposition coding schemes by intermingling dependent and independent auxiliary codeword generation, and demonstrate that the constituent polyhedral achievable rate regions are also polymatroids in each case. The third discovery is that, in the multiple-access channel with general message sets, each associated superposition coding inner bound attains the capacity region. These results demonstrate a tradeoff between the complexity of dependencies in auxiliary codeword generation and that of the function that maps them into transmitted codewords.

The capacity region of the K -user vector Gaussian multiple-access channel with general message sets is established. Furthermore, due to the presence of convexity, both in the discrete and continuous senses, it is shown that this capacity region is efficiently computable. The capacity result is obtained by specializing recent results by the authors for the discrete memoryless multiple-access channel and demonstrating that it suffices to only consider jointly Gaussian input and auxiliary random variables. For this second conclusion, it is shown that jointly Gaussian random variables maximize entropy subject to lattice conditional independence and covariance constraints, a result that is of interest in its own right. Discrete convexity arises since the capacity region is a union of polymatroids. Over each polymatroid, computing the maximal weighted sum rates is simple due to submodularity-a discrete analog of concavity-of the set function associated with the linear inequalities that define the polymatroid. Continuous convexity arises as the set of admissible covariance matrices is convex and the polymatroidal bounds are concave in these covariances.

We establish the degrees of freedom (DoF) region for the multiple-input multiple-output (MIMO) two-transmitter, and two-receiver (2 × 2) interference network with a general message set consisting of nine messages, one for each pair of a subset of transmitters at which that message is known and a subset of receivers where that message is desired. An outer bound on the general nine-message 2 × 2 interference network is obtained and it is shown to be tight, thereby establishing the DoF region for the most general antenna setting wherein the four nodes have an arbitrary number of antennas each. The DoF-optimal scheme is applicable to the MIMO 2 × 2 interference network with constant channel coefficients, and hence, a fortiori, to time/frequency varying channel scenarios. In particular, a linear precoding scheme is proposed that can achieve all the DoF tuples in the DoF region. In it, the precise roles played by transmit zero-forcing, interference alignment, random beamforming, symbol extensions, and asymmetric complex signaling (ACS) are delineated. For instance, we identify a class of antenna settings, in which ACS is required to achieve the fractional-valued corner points. Evidently, the DoF regions of all previously unknown cases of the 2 × 2 interference network with a subset of the nine-messages are newly established as special cases of the general result of this paper. For instance, the DoF region of the well-known four-message (and even three-message) MIMO X channel is newly established. This problem had remained open despite previous studies, which had found inner and outer bounds that were not tight in general. Hence, the DoF regions of all special cases obtained from the general DoF region of the nine-message 2 × 2 interference network of this paper that include at least three of the four X channel messages are new, among many others. This paper sheds light on how the same physical 2 × 2 interference network could be used by a suitable choice of message sets to take most advantage of the channel resource in a flexible and efficient manner.

We establish the degree of freedom (DoF) regions of the two-user multiple-input multiple-output (MIMO) broadcast channel with a general message set (BC-GM), that includes private and common messages, under fast fading. Nine different channel state knowledge assumptions-collectively known as hybrid channel state information at the transmitter (CSIT) models-are considered wherein the transmitter has either perfect/instantaneous, delayed, or no CSI from each of the two receivers. General antenna configurations are addressed wherein the three terminals have arbitrary numbers of antennas. The DoF regions are established for the five hybrid CSIT models in which either both channels are unknown at the transmitter or each of the two channels is known perfectly or with delay. In the four remaining cases in which exactly one of the two channels is unknown at the transmitter, the DoF regions under the restriction of linear encoding strategies-also known as the linear DoF (LDoF) regions-are established. As the key to the converse proofs of the LDoF region of the MIMO BC-GM under such hybrid CSIT assumptions, we show that, when only considering linear encoding strategies, the CSI from the receiver with more antennas does not help if there is no CSI available from the receiver with fewer antennas. This result is conjectured to be true even without the restriction on the encoding strategies to be linear. If true, the LDoF regions obtained for the four hybrid CSIT cases herein will also be the DoF regions for those cases. Many of the results of this paper when specialized to even the two-message problems are new. These include the LDoF regions, when one of the two channels is not known, of the MIMO BC-GM when specialized to the MIMO BC with private messages. They also include the DoF/LDoF regions for all the hybrid CSIT models obtained by specializing the corresponding regions for the MIMO BC-GM to the case with degraded messages.

The degrees of freedom (DoF) region for three users and the sum and symmetric DoF for K users are obtained for the multiple-input multiple-output cyclic Z-interference channel with M transmit antennas and N receive antennas at each user pair under the separate assumptions of perfect and delayed channel state information at the transmitters (CSIT). New communication schemes based on interference alignment are developed and are shown to be DoF-optimal for all choices of the number of antennas. The maximum sum-DoF scales linearly with the number of users for both perfect and delayed CSIT.

We present an inner bound for the combination network based on superposition coding and partial interference decoding. This inner bound is tight in the three-user and K-user symmetric cases, where capacity has been previously characterized. However, unlike previous achievability schemes, the scheme presented herein does not require network coding. By avoiding network coding, our inner bound has fewer extraneous parameters. Moreover, it contains the intersection of polymatroids, one for each receiver, a structure that may be more amenable to further analysis than the previous inner bounds for the combination network.

The degrees of freedom (DoF) region is obtained for the 3-user symmetric multiple-input multiple-output cyclic Z-interference channel with M transmit antennas and N receive antennas at each user-pair under the separate assumptions of perfect and delayed channel state information at the transmitter (CSIT). New communication schemes based on interference alignment are developed and are shown to be DoF-optimal for all choices of the number of antennas. For both perfect and delayed CSIT, the new schemes are shown to outperform those for the 2-user Z-interference channel in terms of sum DoF.

The conditions which govern reliable communication over networks are often given as a union of polyhedra. As increasingly larger networks are considered, these conditions become unwieldy and intractable, unless useful structure can be found in them. An example of a polyhedron with a useful underlying structure is a polymatroid, which despite its exponential number of defining inequalities, has a simple and explicit formula for its vertices. For the multiple access channel with general message sets, we show that each capacity characterization in a large class of capacity characterizations involves polymatroids.

We establish the degrees of freedom (DoF) region for the multiple-input multiple-output (MIMO) two-transmit, two-receive network which has an arbitrary number of antennas at each of its four terminals. General message sets are considered, from which all possible communication scenarios based on two-transmit, two-receive network can be regarded as special cases. An outer bound is given first and then it is shown to be tight. In particular, we propose a linear precoding scheme that can achieve all the DoF tuples in the region. Time extension and asymmetric complex signaling are utilized when necessary. The scheme works for both constant channel as well as time/frequency varying channel scenarios. From our general result, one can obtain the degrees of freedom region and the corresponding DoF-optimal precoding scheme for the two-transmit, two-receive network with any subset of all possible messages. Some of these DoF regions have been found before, but many are new. Our work sheds light on the optimal message sets design that could take the most advantage of channel resources in a flexible and efficient manner.

The generalized diversity-multiplexing tradeoff (GDMT) of the two-user, quasi-static fading, multi-input, multi-output (MIMO) Z interference channel (Z-IC) is established for the general case with an arbitrary number of antennas at each node under the assumptions of full channel state information at the transmitters (CSIT) and a short-term average power constraint. In the GDMT framework, which captures the rate versus reliability tradeoff in the high signal-to-noise ratio (SNR) regime, the direct link SNR and cross-link interference-to-noise ratio (INR) are allowed to be disparate, so that their ratios relative to a nominal SNR in the decibel scale, i.e., the SNR and INR exponents, are arbitrary and fixed. It is shown that a simple Han-Kobayashi message-splitting/partial interference decoding scheme that uses only partial CSIT-in which the second transmitter's signal depends only on its cross-link channel matrix and the first user's transmit signal does not need any CSIT-can achieve the full-CSIT GDMT of the MIMO Z-IC. The GDMT of the MIMO Z-IC under the No-CSIT assumption is also obtained for some range of multiplexing gains. The size of this range depends on the numbers of antennas at the four nodes and the SNR and INR exponents of the direct and cross links, respectively. For certain classes of channels including those in which the interfered receiver has more antennas than do the other nodes, or when the INR exponent is greater than a certain threshold, the GDMT of the MIMO Z-IC under the No-CSIT assumption is also completely characterized.

Two-unicast layered interference networks under the Shannon feedback and limited Shannon feedback settings are studied from a degrees of freedom (DoF) perspective. The main focus is on the archetypal two-hop multiple-input, multiple-output (MIMO) (M,N), × (M,N) × (M,N) network, denoted here as the (M,N)3network, which is a layered two-unicast network with two transmitters, two relays, and two receivers, with the first hop network between the transmitters and the relays, and the second hop network between the relays and the receivers, both being MIMO Gaussian interference channels. In particular, the first transmitter-receiver pair and the first relay have M antennas each and the second transmitter-receiver pair and the second relay having N antennas each. The (full) Shannon feedback setting for the (M,N)3network is one in which the transmitters have delayed knowledge of the first and second hop channel coefficients and the relay and destination outputs and the relays have delayed knowledge of the second hop channel coefficients and destination outputs. The DoF region under this setting is established. A key result in this paper shows that this Shannon feedback DoF region can in fact be achieved with much less side information-under what we refer to as the limited Shannon feedback setting-wherein the transmitters have no channel state or output feedback whatsoever and only the M-antenna relay (assuming M ≥ N) has delayed knowledge of the coefficients of the second-hop channel and of only the received signal of the N-antenna receiver. For this limited Shannon feedback setting, the DoFs region of the (M,N)3network is established by introducing a retro-cooperative interference alignment scheme. These DoF region results for the (M,N)3network with feedback are also extended to more general layered interference networks including the two-unicast l-hop layered networks as well as layered networks with more general numbers of antennas at the various terminals.

The degrees of freedom (DoF) region of the two-user multiple-input multiple-output (MIMO) interference channel is established under hybrid CSIT models in which there is some combination of instantaneous, delayed or no channel state information at the transmitters (CSIT) of each of the four channel matrices. In a standard version of this hybrid CSIT model, there is delayed CSIT at one transmitter and instantaneous CSIT at the other transmitter of incoming channel matrices at their respective unpaired receivers. The DoF regions for this standard model is established and, moreover, it is shown to be applicable to a large class of hybrid CSIT models. In so doing, a new DoF-optimal achievable scheme based on a combination of transmit beamforming and interference alignment is developed. Conditions are obtained on the numbers of antennas at each of the four terminals such that the DoF region under hybrid CSIT is equal to that under (a) instantaneous CSIT and (b) delayed CSIT. It is also demonstrated that by alternating between constituent hybrid CSIT states it is possible to obtain synergistic DoF benefits.

The diversity multiplexing-gain tradeoff (DMT) of a Rayleigh faded relay network (RN) with a single source-destination pair and n half-duplex relay nodes, all with single antennas, is characterized and shown to be equal to the DMT of an (n + 1) × 1 MISO point-to-point channel. Further, it is shown that the quantize map-and-forward (QMF) scheme with fixed, channel independent scheduling for the relays can achieve the fundamental DMT of the RN. An interesting consequence is that the DMT of the RN can be achieved without any channel state information (CSI) at the relay nodes.

The question of whether the degrees of freedom (DoF) of multiuser networks can be enhanced even under isotropic fading and no channel state information or output feedback at the transmitters (CSIT) is investigated. Toward this end, the two-user multiple-input multiple-output (MIMO) broadcast and interference channels are studied with no side-information at the transmitters and with receivers equipped with full-duplex radios. The full-duplex feature allows for receiver cooperation because each receiver, in addition to receiving the signals sent by the transmitters, can also simultaneously transmit a signal in the same band to the other receiver. Unlike the case of MIMO networks with CSIT and full-duplex receivers, for which DoF are known, it is shown that for MIMO networks with no CSIT, full-duplex receiver cooperation is beneficial to such an extent that even the DoF region is enhanced. Indeed, for important classes of two-user MIMO broadcast and interference channels, defined by certain relationships on numbers of antennas at different terminals, the exact DoF regions are established. The key to achieving DoF-optimal performance for such networks are new retro-cooperative interference alignment schemes. Their optimality is established via the DoF analysis of certain genie-aided or enhanced version of those networks. Taken together, the results of this paper show that full-duplex receiver cooperation can recover the DoF lost due to lack of CSIT. In particular, even without CSI and/or output feedback, it has the potential of yielding most, if not all, the gains promised by delayed CSIT, or even Shannon, feedback.

The interference channel with common information (IC-CI) consists of two transmit-receive pairs that communicate over a common noisy medium. Each transmitter has an individual message for its paired receiver, and additionally, both transmitters have a common message to deliver to both receivers. In this paper, through explicit inner and outer bounds on the capacity region, we establish the capacity region of the Gaussian IC-CI to within a bounded gap of one bit, independently of the values of all channel parameters. Using this constant-gap characterization, the generalized degrees of freedom (GDoF) region is determined. It is shown that the introduction of the common message leads to an increase in the GDoF over that achievable over the Gaussian interference channel without a common message, and hence, to an unbounded improvement in the achievable rate. A surprising feature of the capacity-within-one-bit result is that most of the available benefit (i.e., to within one bit of capacity) due to the common message is achieved through a simple and explicit coding scheme that involves independent signaling at the two transmitters so that, in effect, this scheme forgoes the opportunity for transmitter cooperation that is inherently available due to shared knowledge of the common message at both transmitters.

The layered two-hop, two-unicast multi-input, multi-output (MIMO) interference network consists of two transmitters, two relays, and two receivers with the first and the second hop networks between transmitters and relays, and between relays and receivers, respectively, both being Gaussian MIMO interference channels. The degrees of freedom (DoF) region is established in the general case in which there are an arbitrary numbers of antennas at each of the six terminals. It is shown that the DoF region coincides with the min-cut outer bound for both time-varying or fixed-channel coefficients. The min-cut bound is shown to be achievable via a concatenated communication scheme that consists of linear vector space joint beamforming (that includes zero forcing and signal alignment) at all terminals as the inner precoding scheme and point-to-point coding and aligned interference neutralization as the outer precoding scheme.

The capacity region of the two-user multi-input multioutput (MIMO) Gaussian interference channel (IC) is characterized to within a constant gap that is independent of the channel matrices for the general case of the MIMO IC with an arbitrary number of antennas at each node. An achievable rate region and an outer bound to the capacity region of a class of interference channels were obtained in previous work by Telatar and Tse as unions over all possible input distributions. In contrast to that previous work on the MIMO IC, a simple and an explicit achievable coding scheme are obtained here and shown to have the constantgap-to-capacity property and in which the sub-rates of the common and private messages of each user are explicitly specified for each achievable rate pair. The constant-gap-to-capacity results are thus proved in this work by first establishing explicit upper and lower bounds to the capacity region. A reciprocity result is also proved which is that the capacity of the reciprocal MIMO IC is within a constant gap of the capacity region of the forward MIMO IC.

An approximate capacity result is demonstrated for a specific class of interference channels with common information (IC-CI). The class is the semideterministic interference channel of Telatar and Tse, and the outer bound herein generalizes their bound from the case where each transmitter sends only private information to the case where each transmitter sends both private and common information to its corresponding receiver. It is shown that our outer bound is within a quantifiable gap of the inner bound of Jiang-Xin-Garg, a generalization of the Han-Kobayashi region to the IC-CI. Moreover, this result reproduces both the Telatar-Tse result in the case of no common information and a constant-gap-to-capacity result for the Gaussian IC-CI.

The two-user multiple-input multiple-output (MIMO) fast-fading interference channel (IC) with an arbitrary number of antennas at each of the four terminals is studied under the settings of Shannon feedback and output feedback, wherein channel matrices and outputs, or just the channel outputs, respectively, are available to the transmitters with a delay. While for most numbers of antennas at the four terminals, the degree-of-freedom (DoF) regions with Shannon feedback are equal to that with just delayed channel state information (CSIT), it is shown that for the rest of the MIMO ICs, the DoF region with Shannon feedback is strictly larger than the DoF region with just delayed CSIT. To realize these DoF gains with Shannon feedback, a new interference alignment scheme is obtained wherein transmitter cooperation made possible by output feedback (in addition to delayed CSIT) is employed to effect a more efficient form of interference alignment than is feasible with previously known schemes that use just delayed CSIT. The DoF region for output-only feedback is also obtained for all but a class of MIMO ICs that satisfy one of two inequalities involving the numbers of antennas. Moreover, the DoF region for Shannon feedback is shown to be applicable to two limited Shannon feedback settings where the transmitters have knowledge only of certain channel matrices and certain outputs with delay.

The generalized multiplexing gain region (GMGR) of the slow-fading MIMO interference channel is obtained under the assumption of perfect channel state information at the transmitters (CSIT) in the general case where there are an arbitrary number of antennas at each of the four nodes. It is shown that a simple Han-Kobayashi (HK) linear Gaussian superposition coding scheme with a public/private message split at each transmitter can achieve the GMGR of the channel if the covariance matrices associated with the private and public sub-message codewords at each transmitter are certain functions of the null-space of the respective cross-link channel matrix. Moreover, in such a coding scheme, the multiplexing gains of the sub-messages can be chosen without any CSIT. Building on this result, and with Miand Nidenoting the numbers of transmit and receive antennas at the ithtransmitter and receiver, respectively, it is shown that at transmitter i an approximate version of the associated null-space expressed in terms of Nj(Mi-Nj)+log(INRij) bits per channel realization is sufficient to achieve the perfect CSIT GMGR of the channel, where INRijis the interference-to-noise ratio at receiver j. Furthermore, under the assumption of no CSIT, the GMGR is characterized for two sub-classes of MIMO ICs.

The fundamental diversity-multiplexing tradeoff of the three-node, multi-input, multi-output (MIMO), quasi-static, Rayleigh faded, half-duplex relay channel is characterized for an arbitrary number of antennas at each node and in which opportunistic scheduling (or dynamic operation) of the relay is allowed, i.e., the relay can switch between receive and transmit modes at a channel dependent time. In this most general case, the diversity-multiplexing tradeoff is characterized as a solution to a simple, two-variable optimization problem. This problem is then solved in closed form for special classes of channels defined by certain restrictions on the numbers of antennas at the three nodes. The key mathematical tool developed here that enables the explicit characterization of the diversity-multiplexing tradeoff is the joint eigenvalue distribution of three mutually correlated random Wishart matrices. Besides being relevant here, this distribution result is interesting in its own right. Previously, without actually characterizing the diversity-multiplexing tradeoff, the optimality in this tradeoff metric of the dynamic compress-and-forward protocol based on the classical compress-and-forward scheme of Cover and El Gamal was shown by Yuksel and Erkip. However, this scheme requires global channel state information at the relay. In this paper, the so-called quantize-map and forward (QMF) coding scheme is adopted as the achievability scheme with the added benefit that it achieves optimal tradeoff with only the knowledge of the (channel dependent) switching time at the relay node. Moreover, in special classes of the MIMO half-duplex relay channel, the optimal tradeoff is shown to be attainable even without this knowledge. Such a result was previously known only for the half-duplex relay channel with a single antenna at each node, also via the QMF scheme. More generally, the explicit characterization of the tradeoff curve in this study enables the in-depth comparisons herein of full-duplex versus half-duplex relaying as well as static versus dynamic relaying, both as a function of the numbers of antennas at the three nodes.

The generalized degrees of freedom (GDoF) region of the MIMO Gaussian interference channel (IC) is obtained for the general case of an arbitrary number of antennas at each node and where the signal-to-noise ratios (SNRs) and interference-to-noise ratios vary with arbitrary exponents to a nominal SNR. The GDoF-optimal coding scheme involves message splitting and partial interference decoding and consists of linear Gaussian superposition coding of the private and common submessages that can be seen as jointly performing signal-space and signal-level interference alignment. The admissible degree of freedom (DoF)-splits between the private and common messages are also specified. A study of the GDoF region reveals various insights through the joint dependence of optimal interference management techniques at high SNR on the SNR exponents and the numbers of antennas at the four terminals. For instance, it reveals that, unlike in the scalar IC, treating interference as noise is not always GDoF-optimal even in the very weak interference regime. Moreover, while the DoF-optimal strategy that relies just on transmit/receive zero-forcing beamforming and time sharing is not GDoF optimal (and thus has an unbounded gap to capacity), the precise characterization of the very strong interference regime-where single-user DoF performance can be achieved simultaneously for both users-depends on the relative numbers of antennas at the four terminals and thus deviates from what it is in the single-input single-output case. For asymmetric numbers of antennas at the four nodes, the shape of the symmetric GDoF curve can be a “distorted W” curve to the extent that for certain multiple-input multiple-output ICs it is a “V” curve.

The degrees of freedom (DoF) region of the two-user multiple-input multiple-output (MIMO) interference channel (IC) is studied under the assumptions of fast fading and delayed channel state information (CSI) at the transmitters (CSIT). Under our fast fading assumption, the channel matrices vary independently across time, so that delayed CSIT is equivalent to outdated CSIT. In particular, the DoF region under delayed CSIT is established for the general MIMO IC with an arbitrary numbers of antennas at each of the four terminals. Toward this end, a set of outer bounds to the DoF region of the general MIMO IC is derived. These bounds are then shown to be tight by developing DoF-region-optimal interference alignment schemes. A comparison of the DoF region of the MIMO IC under the delayed CSIT assumption with those under the two extremes of instantaneous CSIT and no CSIT assumptions is made. This comparison reveals that there are nonempty classes of MIMO ICs, defined by certain relationships between the numbers of antennas at the four terminals, that correspond to each of the following four scenarios: the no CSIT DoF region is strictly contained by, or is equal to, the delayed CSIT DoF region, which in turn is strictly contained by, or is equal to, the instantaneous CSIT DoF region. It is notable that within the class of MIMO ICs for which the delayed CSIT DoF region is strictly larger than the no CSIT DoF region, there is a subclass for which the interference alignment scheme which uses just delayed CSIT achieves the entire DoF region previously known to be achievable only with instantaneous CSIT.

The degree-of-freedom (DoF) regions are characterized for the multiple-input multiple-output (MIMO) broadcast channel (BC), interference channels (ICs), including X and multihop ICs, and the cognitive radio channel (CRC), when there is no channel state information at the transmitter(s) (CSIT) and for fading distributions in which transmit directions are statistically indistinguishable. For the K-user MIMO BC, the exact DoF region is obtained, which shows that time division is DoF-region optimal. For the two-user MIMO IC and CRC, inner and outer bounds are obtained that coincide for a vast majority of the relative numbers of antennas at the four terminals. Finally, the DoF of the K-user MIMO IC, the CRC, and X networks are obtained for certain classes of these networks. The results herein are derived for fading distributions and additive noises that are more general than those considered in other simultaneous related works. The DoF with and without CSIT are compared and conditions under which a lack of CSIT does, or does not, result in the loss of DoF are identified, thereby 1) providing robust no-CSIT schemes that have the same DoF as their previously found CSIT counterparts and 2) identifying situations where CSI feedback to transmitters would provide gains that are significant enough that even the DoF could be improved.

The two-user multiple-input multiple-output (MIMO) interference and cognitive radio channels are considered, where theith transmitter and theith receiver haveMiandNiantennas, respectively. In particular, the degrees of freedom (DoF) regions of these channels are studied under the assumption of having no channel state information at the transmitters. Making certain assumptions about the distributions of channel matrices of increasing generality respectively, Huang, Zhu and Guo, and the authors of this paper characterized the DoF region of the MIMO interference channel for all values of the four-tuple (M1,M2,N1,N2), except when min(M1,N1) >;N2>;M2or min(M2,N2) >;N1>;M1. More recently, for isotropic fading distributions, Zhu and Guo have solved this latter case by providing a tight outer bound to the DoF region. Here, a simpler and more widely applicable proof of that outer bound is given based on the idea of interference localization. Using the same idea, under Rayleigh fading, the DoF region is then also established for the MIMO cognitive radio channel (when the second transmitter is cognitive) with min(M1+M2,N1) >;N2>;M2-the only class for which the inner and outer bounds previously reported by the authors were not tight-thereby completing the DoF region characterization of this channel under Rayleigh fading for all values of (M1,M2,N1,N2).

The capacity region of the 2-user multi-input multi-output (MIMO) Gaussian interference channel (IC) is characterized to within a constant gap that is independent of the signal-to-noise ratio (SNR) and all channel parameters. The general MIMO IC is considered with an arbitrary number of antennas at each node. For a class of MIMO ICs characterized by the relation between the numbers of antennas at the different nodes this gap is strictly smaller than the gap in a previous result obtained by Telatar and Tse. For instance, the gap for the SIMO IC with single antenna transmitters and N-antenna receivers obtained here is 1 bit, instead of N bits. Moreover, a simple (or universal) and an explicit achievable coding scheme are given here that have the constant-gap-to-capacity property. Consequently, explicit upper and lower bounds to the capacity region are obtained. A reciprocity result is also proved which is that the capacity of the reciprocal MIMO IC is within a constant gap of the capacity region of the forward MIMO IC.

The generalized degrees of freedom (GDoF) region of the MIMO Gaussian interference channel is obtained for the general case with an arbitrary number of antennas at each node and where the SNR and interference-to-noise ratios (INRs) vary with arbitrary exponents to a nominal SNR. The GDoF region reveals various insights through the joint dependence of optimal interference management techniques at high SNR on the SNR exponents that determine the relative strengths of direct-link SNRs and cross-link INRs and the numbers of antennas at the four terminals. For instance, it permits an in-depth look at the issue of rate-splitting and partial decoding at high SNR and it reveals that, unlike in the SISO case, treating interference as noise is not GDoF optimal always even in the very weak interference regime. Moreover, while the DoF-optimal strategy that relies just on transmit/receive zero-forcing beam-forming and time-sharing is not GDoF optimal (and thus has an unbounded gap to capacity) the precise characterization of the very strong interference regime, where single-user DoF performance can be achieved simultaneously for both users, depends on the relative numbers of antennas at the four terminals and thus deviates from what it is in the SISO case. For asymmetric numbers of antennas at the four nodes the shape of the symmetric GDoF curve can be a “distorted W” curve to the extent that for certain MIMO ICs it is a “V” curve.

We study the finite-rate feedback of optimal input covariance matrices from the channel-aware receiver to the transmitter in a multi-antenna single-user setup. Under a block fading model for the channel matrix, the receiver computes the covariance matrix corresponding to the current channel realization and feeds back information about it using a finite, say Nf, number of bits per block. Our finite-rate feedback analysis is based on a novel geometric paradigm whereby the feedback information is modeled as a source distributed over a new Riemannian surface called the Pn manifold. For a given system strategy, the gap between the achievable rates in the infinite and finite-rate feedback cases is shown to be O(2- Nf/N), where N is the dimension of the Pn manifold used for quantization.

The generalized degrees of freedom region (GDoF) of the multiple-input multiple-output (MIMO) interference channel (IC) is studied under the “no CSIT” assumption under which there is perfect channel state information (CSI) at the receivers and no CSI at the transmitters (CSIT). In the very weak interference regime, where the ratio of channel gains (in dB) of the interfering and direct links, α, is ≤ 0.5, the GDoF regions are characterized for the two classes of the MIMO ICs defined by (a) M1= N1>; M2≥ N2and (b) M1= N1>; N2>; M2(where Miis the number of antennas at transmitter i and Niis the number of antennas at receiver i, i ∈ {1, 2}). In particular, inner-bounds are obtained by developing CSI-independent coding schemes using which it is shown that for each of the two classes a significant portion of the perfect-CSIT GDoF region can be achieved even without CSIT. Furthermore, tight outer-bounds to the no-CSIT GDoF regions are obtained that simultaneously account for the interference encountered by both the receivers. These bounds are thus fundamentally different from those derived in earlier works which deal with the case of α = 1, i.e., the degrees of freedom (DoF) regions. Interestingly, it is found that the loss of DoFs due to lack of CSIT is much less pronounced for the α ≤ 1 over 2 than it is for α = 1.

The degrees of freedom (DoF) region of the K-user MIMO (multiple-input multiple-output) Gaussian broadcast channel (BC) is studied under i.i.d. fading when there is delayed channel state information at the transmitter (CSIT). The general case of the MIMO BC is considered where each terminal has an arbitrary number of antennas. The delayed CSIT assumption is that the transmitter has perfect knowledge of `stale' channel states (i.e., with some delay) but no knowledge of current CSI. An outer-bound to the DoF region is derived. This bound is shown to be tight in the 2-user case via an interference alignment scheme that optimally accounts for multiple and possibly distinct number of antennas at the two receivers.

The two-user multi-input, multi-output (MIMO) interference and cognitive radio channels are studied under the assumption of no channel state information at the transmitter (CSIT) from the degrees of freedom (DoF) region perspective. With Miand Nidenoting the number of antennas at transmitter i and receiver i respectively, the DoF region of the MIMO interference channel was recently characterized by Huang et al., Zhu and Guo, and by the authors of this paper for all values of the 4-tuple (M1,M2,N1,N2), except when min(M1,N1) >; N2>; M2(or min(M2,N2) >; N1>; M1). This latter case was solved more recently by Zhu and Guo, who provided a tight outer-bound. Here, a simpler and more widely applicable proof of that outer-bound is given based on the idea of interference localization. Using it, the DoF region is also established for the class of MIMO cognitive radio channels (under certain restrictions on the fading distributions) when min(M1+ M2,N1) >; N2>; M2(with the second transmitter cognitive) - the only class for which the inner and outer bounds previously obtained by the authors were not tight.

The interference channel with common information (IC-CI) is studied. In an IC-CI, each transmitter has an individual message for its paired receiver, and additionally, both transmitters collaboratively must deliver a common message to both the receivers. For the symmetric Gaussian IC-CI, the capacity region is characterized to within a gap of 3 bits independently of the values of the channel parameters. Further, using this constant-gap characterization, the generalized degrees of freedom region is also determined. Insight is provided on how the common message helps in markedly improving the achievable rates over that in an IC without a common message.

The degrees of freedom (DoF) region of the 2-user MIMO interference channel (IC) is studied under fast fading and the assumption of delayed channel state information at transmitters (CSIT) wherein the receivers know all channel matrices perfectly and the transmitters acquire this knowledge with a certain delay. An outer bound to the DoF region is first derived. This bound is then shown to be tight for all possible values of the number of antennas at the four terminals. This is done by developing interference alignment based achievability schemes. A comparison of the DoF region under the delayed CSIT assumption is made with that of the idealistic perfect CSIT assumption where perfect and global channel knowledge (without delay) is available at the transmitters (and receivers) on the one hand and with the DoF region of the conservative no CSI assumption on the other, where CSI is available at the receivers but not at all at the transmitters.

This paper presents an in-depth analysis of the zero forcing (ZF) and minimum mean squared error (MMSE) equalizers applied to wireless multiinput multioutput (MIMO) systems with no fewer receive than transmit antennas. In spite of much prior work on this subject, we reveal several new and surprising analytical results in terms of output signal-to-noise ratio (SNR), uncoded error and outage probabilities, diversity-multiplexing (D-M) gain tradeoff and coding gain. Contrary to the common perception that ZF and MMSE are asymptotically equivalent at high SNR, we show that the output SNR of the MMSE equalizer (conditioned on the channel realization) is$\rho_{\rm mmse} = \rho_{\rm zf}+\eta_{\ssr snr}$, where$\rho_{\rm zf}$is the output SNR of the ZF equalizer and that the gap$\eta_{\ssr snr}$is statistically independent of$\rho_{\rm zf}$and is a nondecreasing function of input SNR. Furthermore, as${\ssr snr}\ura{} \infty$,$\eta_{\ssr snr}$converges with probability one to a scaled${\cal F}$random variable. It is also shown that at the output of the MMSE equalizer, the interference-to-noise ratio (INR) is tightly upper bounded by${{\eta_{\ssr snr}}\over {\rho_{\rm zf}}}$. Using the decomposition of the output SNR of MMSE, we can approximate its uncoded error, as well as outage probabilities through a numerical integral which accurately reflects the respective SNR gains of the MMSE equalizer relative to its ZF counterpart. The$\epsilon$-outage capacities of the two equalizers, however, coincide in the asymptotically high SNR regime. We also provide the solution to a long-standing open problem: applying optimal detection ordering does not improve the D-M tradeoff of the vertical Bell Labs layered Space-Time (V-BLAST) architecture. It is shown that optimal ordering yields a SNR gain of$10\log_{10}N$dB in the ZF-V-BLAST architecture (where$N$is the number of transmit antennas) whereas for the MMSE-V-BLAST architecture, the SNR gain due to ordered detection is even better and significantly so.

The diversity-multiplexing tradeoff of the dynamic decode-and-forward protocol is characterized for the half-duplex three-terminal (m,k,n)-relay channel where the source, relay and the destination terminals havem,kandnantennas, respectively. The tradeoff curve is obtained as a solution to a simple, two-variable, convex optimization problem which is explicitly solved in closed-form for certain special classes of relay channels, namely, the (1,k, 1) relay channel, the (n, 1,n) relay channel and the (2,k, 2) relay channel. Moreover, the tradeoff curves for a certain class of relay channels, such as the (m,k,n>;k) channels, are found to be identical to those for the decode-and-forward protocol for the full duplex channel while for other classes of channels they are marginally lower at high multiplexing gains. Our results also show that for some classes of relay channels and at low multiplexing gains the diversity orders of the dynamic decode-and-forward protocol are greater than those of the static compress-and-forward protocol which in turn is known to be tradeoff optimal over all static half duplex protocols. In general, the dynamic decode-and-forward protocol has a performance that is comparable to that of the static compress-and-forward protocol which, unlike the dynamic decode-and-forward protocol, requires global channel state information at the relay node. Its performance is also close to that of the decode-and-forward protocol over the full-duplex relay channel thereby indicating that the half-duplex constraint can be compensated for by the dynamic operation of the relay wherein the relay switches from the receive to the transmit mode based on the source-relay channel quality.

The problem of user scheduling in a Gaussian i.i.d. Rayleigh faded multiple-access channel (MAC) is considered, whereby the receiver uses perfect knowledge of the channels of all the transmitters to select and schedule two-out-of-M users. The transmitters are assumed to have one antenna each and the two selected users are allocated equal rates. The receiver is equipped with Nrantennas. For user selection that is based on minimizing outage probability (say via an exhaustive search over (2M)possibilities), the diversity-multiplexing tradeoff (DMT) of the corresponding outage probability is computed. Moreover, a novel user-selection algorithmis proposed that achieves the same DMT as does the minimum outage probability method, but with only a O(M) complexity instead of O(M2) required for an exhaustive search to minimize outage probability. The DMT optimality of the proposed algorithm is also proved for 2-user scheduling in the dual M-user Gaussian broadcast channel assuming availability of global channel state information. Simulation results are presented which demonstrate that the proposed algorithm achieves an outage probability close to that of the exhaustive search.

The diversity-multiplexing tradeoff (DMT) is obtained for the symmetric MIMO half-duplex (HD) relay channel where the source and the destination have n antennas each and the relay node has m antennas (hereafter, such a channel is referred to as an (n, m)-relay channel). The characterization of the DMT requires the joint eigenvalue distribution of three specially correlated central Wishart random matrices, which is derived using a related result in. The explicit characterization of the DMT, besides providing the theoretical benchmark for evaluating performance of practical cooperative protocols on this channel, reveals several interesting facts such as: a) the HD operation of the relay fundamentally limits relay channel performance in the sense that the DMT of the full-duplex (FD) relay channel can be strictly greater than that of the HD relay channel; b) an extra antenna at the relay node on a HD relay channel does not always improve the achievable diversity order, unlike that on an FD relay channel. While the fundamental DMTs of the two channels (FD and HD) coincide for a range of low multiplexing gains (MG), this range becomes smaller and the gap between the two (HD and FD) at higher MGs become larger with increasing number of antennas at the relay node, thus potentially justifying the extra cost of an FD relay. It is also proved that the DMTs of the HD and FD (n, 1)-relay channels are the same. Finally, it is shown that the DMT of the (1, m) relay channel can be achieved over different ranges of multiplexing gains by the dynamic decode-and-forward (DDF) and the quantize-and-forward (QF) protocols.

The fundamental diversity-multiplexing tradeoff (DMT) of the quasi-static fading, MIMO Z interference channel (ZIC), with M1and M2antennas at the transmitters and N1and N2antennas at the corresponding receivers, respectively, is derived. Channel state information at the transmitters (CSIT) and a short-term average power constraint is assumed. The achievability of the DMT is proved by showing that a simple Gaussian superposition coding scheme can achieve a rate region which is within a constant (independent of signal-to-noise ratio (SNR)) number of bits from an upper bound to the capacity region of the ZIC. We also characterize an achievable DMT of the ZIC with No-CSIT and show that in a small region of multiplexing gains (MG), the full CSIT DMT of the ZIC can be achieved with no CSIT at all. The size of this MG region depends on the system parameters such as the number of antennas at the four nodes (referred to hereafter as “antenna configuration”), SNRs and interference-to-noise ratio (INR) of the direct and cross links. Interestingly, for some antenna configurations this MG region covers the entire MG region of the ZIC. Thus, under these circumstances, the optimal DMT of the MIMO ZIC with F-CSIT is same as that of a corresponding ZIC with No-CSIT and availability of CSIT can not further improve the DMT. Finally, we identify a class of ZICs with M1= M2= M ≤ N1over 2, N1≤ N2and SNR ≤ INR where the achievable DMT with No-CSIT coincides with the optimal DMT with F-CSIT.

The fundamental diversity-multiplexing tradeoff (DMT) of the quasi-static fading, symmetric 2-user MIMO interference channel (IC) with channel state information at the transmitters (CSIT) and a short term average power constraint is obtained. The general case is considered where the interference-to-noise ratio (INR) at each receiver scales differently from the signal-to-noise ratio (SNR) at the receivers. The achievability of the DMT is proved by showing that a simple Han-Kobayashi coding scheme can achieve a rate region which is within a constant (independent of SNR) number of bits from a set of upper bounds to the capacity region of the IC. In general, only part of the DMT curve with CSIT can be achieved by coding schemes which do not use any CSIT (No-CSIT). A result in this paper establishes a threshold for the INR beyond which the DMT with CSIT coincides with that with No-CSIT. Our result also settles one of the conjectures made in. Furthermore, the fundamental DMT of a class of non-symmetric ICs with No-CSIT is also obtained wherein the two receivers have different numbers of antennas.

While interference alignment schemes have been employed to realize the full multiplexing gain of K-user interference channels, the analyses performed so far have predominantly focused on the case when global channel knowledge is available at each node of the network. This paper considers the problem where each receiver knows its channels from all the transmitters and feeds back this information using a limited number of bits to all other terminals. In particular, channel quantization over the composite Grassmann manifold is proposed and analyzed. It is shown, for K-user multiple-input, multiple-output (MIMO) interference channels, that when the transmitters use an interference alignment strategy as if the quantized channel estimates obtained via this limited feedback are perfect, the full sum degrees of freedom of the interference channel can be achieved as long as the feedback bit rate scales sufficiently fast with the signal-to-noise ratio. Moreover, this is only one extreme point of a continuous tradeoff between the achievable degrees of freedom region and user feedback rate scalings which are allowed to be non-identical. It is seen that a slower scaling of feedback rate for any one user leads to commensurately fewer degrees of freedom for that user alone.

We analyze feedback of the optimal input covariance matrix Q from a channel-aware multi-antenna receiver to a multi-antenna transmitter using Nfbits per block. The matrix Q is allowed to have real or complex entries and its rank is allowed to be either fixed or variable. By unravelling the geometry of the quantization spaces involved, we obtain the normalized volume of geodesic balls and use these to evaluate the distortion suffered in quantizing information using different code books. The difference in ergodic capacity between the finite and infinite rate feedback cases is bounded as O(2-Nf/N) where N is the dimension of the quantization manifold. The results apply to both the MIMO link and the MIMO MAC channels, and do not depend on the specific distribution of the channel matrix.

The cognitive interference channel (C-IC) is defined as the interference channel that consists of two transmitter-receiver pairs and in which any one or more of the four terminals is cognitive. The degrees of freedom (dof) region of the C-IC is studied for the case in which there is perfect and no channel state information at the receivers and the transmitters, respectively. The proposed inner and outer-bounds yield the precise characterization of dof region, except for a few cases of cognition in which for certain values of the number of antennas at the four terminals, the bounds are not tight. Finally, an example on the feasibility of interference alignment without transmitter knowledge of the channel realizations is shown.

The operation of the multiple input multiple output (MIMO) Gaussian broadcast channel (BC) with K transmit antennas and K over r users with r receive antennas each is analyzed when channel state information (CSI) is obtained at the transmitter from the ithuser via finite-rate feedback link of capacity Bibits. It is proved that if Biis scaled at the rate of αir(K - r) log2P, where P is the transmit power and α ∈ [0, 1], then using dirty paper coding (DPC), the multiplexing gain of αir can be achieved for user i. This result on the feedback scaling rate rests on an elegant achievability scheme, the construction of which brings to light several new insights on the manner in which DPC achieves the complete multiplexing gain in the perfect-CSIT case.

Two novel communication protocols for the quasistatic coherent fading relay channel are proposed and analyzed under the diversity-multiplexing tradeoff framework. Both these protocols satisfy the half-duplex constraint and fall under the class of decode and forward (DF) protocols, wherein the relay node attempts to decode the source signal and if successful transmits the re-encoded signal. The first protocol is a static DF protocol where the relay waits for a fixed, channel independent duration before attempting to decode. It is shown that it achieves a tradeoff curve that uniformly improves upon those of the previously best known static half-duplex protocols, which are the NAF protocol and the STC3 protocol. Our second protocol is a dynamic DF protocol where the relay waits for a dynamic, channel dependent duration before attempting to decode and it is shown to achieve a tradeoff curve that uniformly improves upon the previously proposed half-duplex dynamic DF protocol.

We compute the diversity-multiplexing tradeoff (DMT) curve for a three node multi-input-multi-output (MIMO) half-duplex (HD) relay network, operating in the dynamic decode-and-forward (DDF) mode. We consider the case where the source and the destination have n antennas each and the single relay node has m antennas. Denoting such a channel as a (n, m)-relay channel, we provide an analytical characterization of the DMT curve for certain simple configurations such as (n, 1), (1, m) and (2, 2). We employ a numerical method to compute the DMT for more general channel configurations. Interestingly, for low multiplexing gains the achievable diversity orders of the HD-DDF protocol coincides with the diversity orders achieved by the full-duplex decode-and-forward (FDDF) protocol analyzed in. In fact, the HD-DDF and FDDF protocols achieve the same diversity orders for all integer multiplexing gains. Thus, the half duplex constraint does not significantly affect the achievable DMT for the DF protocol when the source and the destination have the same number of antennas.

To model the benefit accrued due to limited rate feedback on the information transfer of optimal `input covariance matrices' from a channel-aware receiver to the transmitting users in a multiple-access channel, we study the distortion-rate tradeoff of a source uniformly distributed over multivariate generalizations of PF(n,p2) (the set of positive semi-definite matrices with a trace constraint) and Vn,k¿(the classical Stiefel surface) manifolds. Using sphere-packing and random coding arguments, the distortion-rate function is bounded within asymptotically tight limits.

A dirty paper coding (DPC) based transmission scheme for the Gaussian multiple-input multiple-output (MIMO) cognitive radio channel (CRC) is studied when there is imperfect and perfect channel knowledge at the transmitters (CSIT) and the receivers, respectively. In particular, the problem of optimizing the sum-rate of the MIMO CRC over the transmit covariance matrices is dealt with. Such an optimization, under the DPC-based transmission strategy, needs to be performed jointly with an optimization over the inflation factor. To this end, first the problem of determination of inflation factor over the MIMO channel Y = H1X + H2S + Z with imperfect CSIT is investigated. For this problem, two iterative algorithms, which generalize the corresponding algorithms proposed for the channel Y = H(X + S) + Z, are developed. Later, the necessary conditions for maximizing the sum-rate of the MIMO CRC over the transmit covariances for a given choice of inflation factor are derived. Using these necessary conditions and the algorithms for the determination of the inflation factor, an iterative, numerical algorithm for the joint optimization is proposed. Some interesting observations are made from the numerical results obtained from the algorithm. Furthermore, the high-SNR sum-rate scaling factor achievable over the CRC with imperfect CSIT is obtained.

Reliable communication over the discrete-input/continuous-output noncoherent multiple-input multiple-output (MIMO) Rayleigh block-fading channel is considered when the signal-to-noise ratio (SNR) per degree of freedom is low. Two key problems are posed and solved to obtain the optimum discrete input. In both problems, the average and peak power per space-time slot of the input constellation are constrained. In the first one, the peak power to average power ratio (PPAPR) of the input constellation is held fixed, while in the second problem, the peak power is fixed independently of the average power. In the firstPPAPR-constrainedproblem, the mutual information, which grows asO(SNR2), is maximized up to second order in SNR. In the secondpeak-constrainedproblem, where the mutual information behaves asO(SNR), the structure of constellations that are optimal up to first order, or equivalently, that minimize energy per bit, are explicitly characterized. Furthermore, among constellations that are first-order optimal, those that maximize the mutual information up to second order, or equivalently, the wideband slope, are characterized. In both PPAPR-constrained and peak-constrained problems, the optimal constellations are obtained in closed form as solutions to nonconvex optimizations, and interestingly, they are found to be identical. Due to its special structure, the common solution is referred to as space-time orthogonal rank one modulation, or STORM. In both problems, it is seen that STORM provides a sharp characterization of the behavior of noncoherent MIMO capacity.

The large gain promised by the multi-input multioutput (MIMO) technology comes with a cost. In particular, multiple analog radio frequency (RF) chains, which are expensive and power consuming, are required at both the transmitter and receiver sides. On the other hand, the antennas connecting to the RF chains are less expensive. Hence, one engineering compromise is to implement more antennas than RF chains and to use only a subset of them based on some antenna selection (AS) algorithm. An interesting question therefore arises: given a RF chain limited MIMO system, what is the fundamental performance gain by adding more antennas? In this two-part paper, we answer this question by using the diversity-multiplexing (D-M) gain tradeoff metric. Consider a Rayleigh fading channel with Mt) antennas and Lt(Lt⩽ Mt) RF chains at the transmitter while Mrantennas and Lr(Lr⩽ Mr) RF chains at the receiver. We obtain the fundamental D-M tradeoff as a function of Mt, Mr, and min(Lr, Lt). Referring to the special case where Lt= Mt) and Lr= Mras the RF unlimited system (or full system) and RF limited system (or pruned system) otherwise, we prove that the pruned system with optimal channel-dependent AS has the same D-M tradeoff as the full system if the multiplexing gain is less than some integer threshold P, while it suffers from some diversity gain loss for multiplexing gains larger than P. In particular, if min(Lr, Lt) = K = min(Mr, Mt), then P = K, i.e. the D-M tradeoffs of the pruned system and the full system are the same. Moreover, this result can be extended to more general fading channels such as Nakagami channel. A fast and D-M tradeoff-optimal AS algorithm is proposed as a byproduct of our analysis. Index Terms?Antenna selection, diversity gain, fast algorithm, MIMO, Nakagami fading, outage probability, Rayleigh fading, spatial multiplexing gain, tradeoff.

The low decoding complexity structure of Linear Dispersion Space Time Block Codes (LDSTBCs) with unitary weight matrices is analyzed. It is shown that given n = 2alpha, the maximum number of groups in which the information symbols can be separated and decoded independently is (2a + 2), and as we lower the number of different groups to (2k + 2), 0 les k les alpha, we get higher rate codes. We also find the analytic expression for rates that such codes can achieve for any chosen group number, thus completely characterizing the rate-ML-decoding-complexity tradeoff for this class of codes. The proof of the result also includes a method for constructing such optimal rate achieving codes. Interestingly, this analysis produces some low decoding complexity codes with rate greater than one.

We propose a simple power scheduling algorithm for relay channels with multiple antennas. The algorithm combines seamlessly with a low complexity communication protocol that employs rateless coding for the relay channel. The goal of the algorithm is to achieve a target average total transmission power. It requires little signaling and can be used whenever the destination node can predict future channel states. The scheduling works by a power on/off control of the source and relay nodes. It has about 1 dB gain in low SNR. It has little gain in moderate to high SNR due to the very small amount of signaling, but can be used to achieve a range of target average total transmission power without adjusting the on-power.

A parallel channel with random but ordered gains is considered. A sufficient condition on the code-book (with unit block length codewords) for this channel is derived, so that the fundamental D-M tradeoff of this channel is achieved, irrespective of the distribution of the gains. This condition suggests to construct codes so that the magnitudes of elements of each codeword difference vector are ordered, and the minimum Euclidean distance is maximized. Moreover, an average power constraint on the codewords is sufficient, rather than a constraint on every codeword required for approximate universality [1] if the gains are not ordered. For a 2-parallel channel (i.e. having 2 sub-channels) with ordered gains, a simple explicit code, referred to as the Zig Zag code, is proposed, which achieves the highest diversity order at a fixed rate. For a multiple-input multiple-output (MIMO) block fading channel, a novel low-complexity D-M tradeoff optimal space-time (ST) architecture, referred to as the ordered D-BLAST-ZF, is proposed, which effectively decomposes the MIMO channel into a parallel channel with ordered gains. This architecture uses a few bits of feedback, containing information of the antenna strength order, as determined by a careful choice of mapping between channel matrices and permutation matrices. Numerical simulations show that, over a parallel channel obtained via the ordered D-BLAST-ZF in a 2 times 2 MIMO channel, a Zig Zag code gives comparable gain over the permutation code of [1] as the latter gives overQAMcodeused over only the stronger sub-channel.

Distributed space–time block coding schemes based on quadrature amplitude modulation (QAM) symbols are introduced that enable users in a wireless multiple-access relay channel to cooperate with each other in order to improve the reliability of their information in a fair, rate-efficient manner. The distributed coding schemes are designed for a system that consists of$m$users that need to send their information to a common destination. Each user is equipped with only one antenna and a half-duplex transceiver so that it can transmit to the destination or any other user at one time and also receive signals from any other user at another time. The destination is equipped with one or more receive antennas. The goal is to design cooperative schemes which achieve the maximum diversity order (which is equal to the diversity order of the outage probability) while being fair to the users in terms of rate allocation. Two cooperative coding schemes are proposed that meet these requirements—a two-phase cooperative scheme and a single-phase self-information canceling linear (SCL) scheme. The two-phase scheme is of lower decoding complexity and it requires the users to only transmit QAM symbols. The SCL scheme is of higher complexity with the users transmitting linear combination of QAM symbols but it also achieves better performance. Both schemes incorporate new classes of cooperation rules for deciding whether or not a user acts as a relay for another user. The usual “outage-based” cooperation rule, whereby a user cooperates with another user provided the mutual information of the channel between them is greater than the rate, is sufficient for deriving information-theoretic limits but it cannot be used directly for analysis of a particular coding scheme. Even though the decoder used by the destination in the proposed coding schemes assumes that the inter-user communication is always successful, our performance analysis does not make this assumption. In fact, it rigorously accounts for the decoding errors arising from the information exchange between users. Consequently, it sheds light on precisely what cooperation rules (among the class of rules analyzed) lead to maximal diversity.

Embodiments of the diagonal Bell Laboratories layered space-time (D-BLAST) architecture for multiple-input-multiple-output (MIMO) communication are developed wherein information symbol vectors are encoded using codewords from a lattice code [called a diagonally layered lattice (DLL) code], which are formatted onto the diagonals of a space-time frame. Decoding is done using a sphere decoder for each diagonal based on soft statistics obtained after zero forcing (ZF) or minimum-mean-square-error (MMSE) filtering and decision feedback. These operations give rise to an effective parallel channel model with channel gains with nonidentical statistics and additive noise which is Gaussian in the ZF-filtering case and non-Gaussian in the MMSE-filtering case. The so-called full modulation diversity (FMD) property is nevertheless shown to yield the maximum achievable diversity orders over the MIMO channel for both the ZF- and the MMSE-filtering-based decoders respectively, for any arbitrary fading distribution. In the case of the independent, identically distributed (i.i.d.) Rayleigh fading MIMO channel withK-transmit andN-receive antennas (withNgesK), these diversity orders areNK-K(K-1)/2 andNKfor ZF- and MMSE-filtering-based decoding, respectively. The error probability analysis also yields a design criterion for optimizing transmit power allocations. Several lattice design methods are proposed for the effective parallel channel models. Two methods are proposed to achieve high coding gain in the Rayleigh fading MIMO channel; a third method is proposed that minimizes the exact symbol error probability (SEP) and can be tailored for any given fading distribution. A novel soft decision feedback decoder is also proposed based on the list sphere decoder to mitigate error propagation due to hard decision feedback. The salient feature of the proposed DLL schemes is that they have nearly full rate and full (or high) diversity order and yet a much lower decoding complexity than other existing full rate, full diversity space-time block codes (STBCs). The frame error probability (FEP) performance of the optimized DLL schemes for moderate-to-high spectral efficiencies and a wide range of signal-to-noise ratios (SNRs) can be quite close to the performance of the best performing, but more complex to decode, STBCs. Moreover, the proposed DLL schemes significantly outperform other existing MIMO systems of comparable decoding complexity.

We consider space-time transceiver architectures for space-division multiple-access (SDMA) fading channels with simultaneous transmissions from multiple users. Each user has up to four transmit antennas and employs a space-time orthogonal or a quasi-orthogonal design as an inner code. At the multiple-antenna receiver, efficient successive group interference cancellation strategies based on zero-forcing or minimum mean-square error (MMSE) filtering are employed in some fixed or channel-dependent order. These strategies are efficient in the sense that they exploit the special structure of the inner codes to yield much higher diversity orders than would be otherwise possible, while at the same time preserving what we call thedecouplingpropertyof the constituent inner codes which enables the use of low-complexity outer encoders/decoders for each user. Motivated by the special structure of the effective channel matrix induced by the inner codes, we obtain several new distribution results on the QR and eigenvalue decompositions of certain structured random matrices. These results are the key to a comprehensive performance analysis of the proposed multiuser transceiver architectures including the characterization of diversity-multiplexing tradeoff (DMT) curves and exact per-user bit-error rates (BERs) without making simplifying assumptions about error propagation.

We consider a slow-fading narrowband multiple-input multiple-output (MIMO) multiple-access channel (MAC) in which multiple users, each equipped with multiple transmit antennas, communicate to a receiver equipped with multiple receive antennas. The users are unaware of the channel state information (CSI) whereas the receiver has perfect CSI and employs a successive group decoder (SGD). We obtain achievable outage probabilities for the case where an outage must be declared simultaneously for all users (common outage) as well as the case where outages can be declared individually for each user (individual outage). We then derive the optimum successive group decoder (OSGD) that simultaneously minimizes the common outage probability and the individual outage probability of each user, over all SGDs of permissible decoding complexity. For each channel realization, the OSGD is also shown to maximize the error exponent of the decodable set of users. An adaptive SGD is derived which not only retains the outage optimality of the OSGD but also minimizes the expected decoding complexity. Asymptotically tight (in the limit of high signal-to-noise ratio (SNR)) affine approximations are then obtained for the weighted sum common and individual outage capacities and the symmetric outage capacity yielded by the OSGD. Limiting expressions for the relevant capacities as the number of users and the number of receive antennas approach infinity are also obtained and it is shown that the OSGD yields symmetric capacity gains commensurate with the decoding complexity allowed. Simulation results with practical low-density parity-check (LDPC) outer codes show that the OSGD offers significantly improved performance at low decoding complexity.

The V-BLAST (vertical Bell Labs layered Space- Time) architecture involves independent coding/decoding per antenna (layer) with equal rate and power per antenna and a fixed order of nulling/canceling decoding but is known to suffer from poor performance; for example, in a multi-input multioutput (MIMO) Rayleigh fading channel with Mt transmit and Mr receive antennas (Mr⩾ Mt), the diversity-multiplexing gain (D-M) tradeoff is just (Mr- Mt+1)(1 - r/Mt) for r ε [0,Mt]. There are two remedies available, namely, (i) channel-dependent ordered decoding at the receiver and (ii) allocation of rates and powers across the transmit antennas. However, the former doesn't improve the D-M tradeoff curve and while the latter does (with maximum diversity gain Mr and maximum multiplexing gain Mt), its tradeoff curve is still significantly inferior compared to the D-M tradeoff curve of the optimum (unconstrained) MIMO architecture. In this two-part paper, it is shown that a dramatically better D-M tradeoff and error (e.g. outage) probability can be obtained if the two remedies, i.e., ordered BLAST decoding and rate/power allocation, are judiciously combined. Indeed, a framework is developed for jointly designing channel-dependent ordered decoding at the receiver and decoding order-dependent rate/power allocation at the transmitter. The framework encompasses a large class of new spatial multiplexing architectures (SMAs). In this part, an upper bound to the D-M tradeoff for this class is obtained and found to be quite close to the optimal D-M tradeoff of the MIMO channel. Two special SMAs are proposed corresponding to two different decoding orderings. One is called the Norm ordering Rate Tailored SMA (NRT-SMA), and the other is called the Greedy ordering Rate Tailored SMA (GRT-SMA).

The study of the class of new spatial multiplexing architectures (SMAs) is continued. As introduced in Part I of this paper, the SMAs consist of joint design of rate and power allocation to the spatially-multiplexed substreams at the transmitter and ordered nulling/canceling detection/decoding at the receiver. This was studied in Part I under the diversitymultiplexing tradeoff framework. Here the more detailed and practical problem of allocating rates and powers across the transmit antennas is investigated to minimize the overall system (uncoded or outage) error probability. Since the layer gains are unavailable to the transmitter, the rates and powers must be allocated based on the statistics of the layer gains. However, the channel dependent ordering rules make the precise distributions of the layer gains complicated or intractable. To solve this problem, a simple, yet effective, four-parameter hyperbola model is proposed to closely approximate the error probability of each layer. With this approximation, the computation of rate and power allocation according to the criterion of minimizing the maximal error probability of all the substreams is given. Simulation results validate the superior performance of the proposed SMAs, especially that of the Greedy ordering Rate Tailored SMA (GRT-SMA). Although the rate and power allocation method is obtained under the assumption of iid Rayleigh fading channel, the proposed SMAs also work well in other types of fading channels (such as in correlated and Rician channels).

A new technique is proposed for designing decision feedback detectors (DFDs) wherein the per-symbol decision rules are obtained by exploiting modulation constraints. It is presented in the context of the multi-input, multi-output (MIMO) fading channel with K transmit and N receive antennas. Three cases are considered to illustrate the technique where all the transmitters employ real-valued pulse-amplitude modulation (PAM), or phaseshift keying (PSK), or complex quadrature amplitude modulation (QAM). In each case, the corresponding per-symbol decision rules are obtained by imposing the modulation constraints on a likelihood function maximization problem. When all transmitters employ PAM, it is shown that the resulting DFD (the PAM-DFD) is equivalent to the decorrelating decision feedback detector (DDFD) when the latter is used on a modified received statistic. Two DFDs are then derived (the PSK-DFDs and the QAMDFDs) for the cases when all transmitters employ PSK and QAM, respectively. To illustrate the performance benefit, we consider the Rayleigh fading channel and derive the exact joint error probability (JEP) of the PAM-DFD and show that the (possibly fractional) diversity order of the JEP is equal to N - K-1/ 2 . This greatly improves on the diversity order of N - K + 1 of the JEP obtained by the D-DFD without exploiting the real modulation constraint. Through simulations, it is shown that the PSK-DFDs and the QAM-DFDs result in significant performance improvements over the D-DFD as well. It is conjectured that one of the PSK-DFD achieves the improved diversity order of N - K-1/ 2 as well and the QAM-DFDs result in an improvement in effective SNR gain.

The decision feedback detector (DFD) can achieve the high spectral efficiency of a MIMO channel in that it converts the MIMO channel into multiple parallel layers, through which independently coded data substreams may be spatially multiplexed and be transmitted over the same time and frequency slot. Because of independent coding/decoding, the DFD may apply arbitrarily ordered detection. In this paper, we analyze the effect of detection ordering on the diversity gain per layer of the DFD in a MIMO Rayleigh-fading channel. For a MIMO channel withMttransmit andMr(MrgesMt) receive antennas, we derive an upper bound to the diversity gain per layer for any detection ordering, i.e.,Diles (Mr-i+ 1)(Mt-i+ 1) for 1 lesilesMt. We show that the DFD using the so-called greedy ordering rule can achieve the diversity gain upper bound. We further study the diversity-multiplexing (D-M) gain tradeoff of DFD in a pruned MIMO channel whereLt(Ltles Mt) transmit andLr(LtlesLrlesMr) receive antennas are selected out of the full system. It is shown that the D-M tradeoff of DFD in an optimally pruned channel isddfd,opt(r) = (Mr-Lt+ 1)(Mt-Lt+ 1)(1 -r/Lt). Such a tradeoff-optimally pruned system can be obtained by a fast antenna selection algorithm. This result has interesting implications to the multi-access communications with user selection. The theoretical analysis is validated by the numerical examples.

The diversity-multiplexing (D-M) gain tradeoff is a popular benchmark for measuring the performance of multi-input multi-output (MIMO) systems. This paper studies the fundamental D-M gain tradeoff of a pruned MIMO system where Lttransmit and Lrreceive antennas are selected out of the full system with Mttransmit and Mrreceive antennas (Lt≤ Mtand Lr≤ Mr). It is shown that a MIMO system with the optimal antenna selection (AS) has the same D-M tradeoff as the full system if the multiplexing gain is less than some threshold P, although it suffers from some diversity gain loss for the multiplexing gain larger than P. On the other hand, this paper quantifies, in terms of the D-M tradeoff, the gain of introducing additional transmit/receive antennas without increasing the number of RF chains and coding complexity. We also propose a fast and D-M tradeoff-optimal AS algorithm as a byproduct of our analysis.

Reliable communication over the discrete input and continuous output noncoherent multiple-input multiple-output (MIMO) Rayleigh fading channel is considered when the SNR per degree of freedom is low. The input constellations are required to satisfy peak and average power constraints. When the peak-to- average power ratio of the input constellation is limited (PAPR- limited) and in the low SNR regime, the mutual information up to second order in SNR is maximized jointly over input signal matrices and their respective probabilities, over all T + 1 point constellations (where T is the coherence length). Even though the problem considered is a finite dimensional non-convex optimization, it admits an elegant solution in closed form. The constellation obtained is referred to as Space Time Orthogonal Rank one Modulation (STORM), and it provides new insights into noncoherent MIMO comunications in the low SNR regime. By deriving an appropriate upper bound, it is shown that in most cases with even moderate values for PAPR and T, STORM is near-optimal with respect to the maximum mutual information achievable with unconstrained cardinality. For the case when the peak-power constraint is a fixed constant (peak-constrained), STORM achieves the capacity per unit energy, while having a wideband slope T times that of the conventional approach of MIMO ON-OFF signaling. This translates to increased bandwidth efficiency or PAPR reduction by a factor of T in the wideband regime.

Constellation design for the noncoherent multiple-input-multiple-output (MIMO) block Rayleigh-fading channel is considered. For general signal-to-noise ratios (SNRs), starting from a given base unitary constellation of finite cardinality, and using the cutoff rate expression as the design criterion, input probabilities and per-antenna amplitudes for the constellation points are obtained via a difference of convex programming formulation. Using the mutual information as a performance metric, it is shown that the optimized constellations significantly outperform the base unitary designs from which they are obtained in the low-medium SNR regime, and indeed they also similarly outperform the mutual information achieved by isotropically distributed unitary inputs for the continuous input channel [i.e., the so-called unitary space-time capacity (USTC)]. At sufficiently high SNRs, the resulting mutual information coincides with that of the base unitary designs. Thus the optimum constellation design technique works over the entire range of SNRs. The bit energy/spectral efficiency tradeoff of the optimized constellations are also obtained, and these provide valuable insights on modulation and coding, which are especially useful for wideband channels where the SNR per degree of freedom is low

Uplink communication in a cellular radio network is considered where the base station in each cell employs linear or decision feedback multiuser receivers. We address the problem of minimizing the total of the user transmit powers over all linear or decision feedback multiuser receivers, such that all the users achieve their signal-to-interference ratio (SIR) targets. A distributed algorithm is obtained that is shown to converge, both in the deterministic and stochastic formulations, to the jointly optimal pair of power allocations and multiuser receivers.

The problem of signal design for bandwidth-efficient multiple access (BEMA) over additive white Gaussian noise (AWGN) channels is addressed under quality of service (QoS) requirements specified by asymptotic effective energies (AEEs). The AEE characterizes the bit error rate (BER) in the low-noise regime, but in contrast to BER, it is tractable and amenable to analysis and signal design. We adopt the BEMA strategy of bandwidth conservation where users are detected successively using minimum mean-squared error decision feedback (MMSE-DF) detection and where signals are designed in a greedy fashion for one user at a time, in the reverse order in which the users are detected. The signal design method proposed here is based on an exact characterization of how a signal update for one user affects the issue of preserving bandwidth with the addition of signals for subsequent users. A geometric insight in the construction of good signal sets and significant improvements in bandwidth over full-rank or orthogonal signaling are obtained. The main result of this paper can hence be seen as providing a tight upper bound on the minimum signature sequence dimension or rank (and hence bandwidth) needed to satisfy individual, possibly distinct user QoS constraints specified in terms of the AEE measure.

The behavior in terms of information theoretic metrics of the discrete-input, continuous-output noncoherent MIMO Rayleigh fading channel is studied as a function of spatial correlations. In the low SNR regime, the mutual information metric is considered, while at higher SNR regimes the cutoff rate expression is employed. For any fixed input constellation and at sufficiently low SNR, a fully correlated channel matrix is shown to maximize the mutual information. In contrast, at high SNR, a fully uncorrelated channel matrix (with independent identically distributed elements) is shown to be optimal, under a condition on the constellation which ensures full diversity. In the special case of the separable correlation model, it is shown that as a function of the receive correlation eigenvalues, the cutoff rate expression is a Schur-convex function at low SNR and a Schur-concave function at high SNR, and as a function of transmit correlation eigenvalues, the cutoff rate expression is Schur-concave at high SNR for full diversity constellations. Moreover, at sufficiently low SNR, the fully correlated transmit correlation matrix is optimal. Finally, for the general model, it is shown that the optimal correlation matrices at a general SNR can be obtained using a difference of convex programming formulation.

We propose two novel communication protocols for the quasi-static coherent fading relay channel and analyze them under the diversity-multiplexing tradeoff framework. Both these protocols satisfy the half-duplex constraint and fall under the class of decode and forward (DF) protocols, wherein the relay node attempts to decode the source signal and if successful transmits the re-encoded signal. Our first protocol is a static DF protocol where the relay waits for a fixed (channel independent) duration before attempting to decode. We show that it achieves a tradeoff curve that uniformly improves upon those of the previous best known static half-duplex protocols, which are the NAF protocol and the STC3 protocol. Our second protocol is a dynamic DF protocol where the relay waits for a dynamic (channel dependent) duration before attempting to decode and it is shown to achieve a tradeoff curve that uniformly improves upon those of all previously proposed half-duplex protocols, including the dynamic DF protocol.

Outage capacity and throughput are the two key metrics through which the fundamental limits of delay-sensitive wireless MIMO links can be studied. In this paper, we show that these metrics are intimately related, and consequently, as in the case of outage capacity, the growth rate of throughput with SNR rho is t log rho for a general class of fading channels (with channel state information at the receiver (CSIR) and with or without CSI at the transmitter (CSIT)) whose channel matrix is of rank t with probability one. However, while asymptotically tight affine lower bounds of the form t log rho + 0(1) were recently derived for outage capacity for such channels, in the sense that the limit as rho rarr infin of the difference between the outage capacity and the lower bound is zero, such affine lower bounds are not possible in general for the throughput. Using the t log rho + O(1) bounds on outage capacity however, lower bounds on throughput are specified where the high SNR limit of the ratio of the throughput and its lower bound is unity. These bounds reveal that the throughput optimal outage probability approaches zero as rho rarr infin. An important exception is the scenario where both the transmitter and receiver have CSI under the long-term power constraint (LTPC), for which we obtain a lower bound of the form t log rho + O(1) which is asymptotically tight (in the stronger sense) and interestingly, this lower bound is identical to the asymptotic delay-limited capacity. The throughputs of MISO and SIMO fading channels are extensively analyzed and it is shown that asymptotically, isotropic Gaussian input is throughput optimal, correlation is detrimental whereas increase in the Rice factor is beneficial and that throughput is schur-concave in the correlation eigenvalues

Constellation design for the noncoherent multi-input, multi-output (MIMO) block Rayleigh fading channel is considered. For general SNRs, starting from a given base unitary constellation of finite cardinality, and using the cutoff rate expression as the design criterion, we obtain input probabilities and per-antenna amplitudes for the constellation points via a global optimization formulation. Using the mutual information as a performance metric we obtain numerical results that show that the optimized constellations significantly outperform the base unitary designs from which they are obtained in the low-medium SNR regime, and indeed they also similarly outperform the mutual information achieved by isotropically distributed inputs for the continuous input channel (i.e., the so-called unitary space-time capacity (USTC)). At sufficiently high SNRs, the resulting mutual information coincides with that of the base unitary designs. Thus we have an optimum constellation design technique that works over the entire range of SNRs. The bit-energy/spectral-efficiency tradeoff of the optimized constellations are also obtained, and these provide valuable insights on modulation and coding, which are especially useful for wideband channels where the SNR per degree of freedom is low

The connection between the average codeword or frame error probability (FEP) of space-time codes and the outage probability over general block-fading multiple-input multiple-output (MIMO) channels is established. Three archetypal problems are considered under general fading distributions in a single framework wherein the receiver has channel state information whereas the transmitter knows a) the fading distribution but not the channel realization b) the channel realization but must follow a short term (per codeword) average power constraint, and c) the channel realization but is constrained only by a long-term average power constraint. Three telescoping sets of space-time codes are defined for a given rate and it is shown that average FEPs arbitrarily close to the respective outage probabilities for each of the three cases a)-c) can be achieved by codes in each set for sufficiently large frame lengths. For the smallest set among the three which contains codes with a spectral norm constraint that is stricter than the average or maximum energy constraints commonly assumed, firm sphere-packing lower bounds on the FEP are obtained, and, consequently, strong converse theorems are proved which assert that the respective outage probabilities also represent the best achievable FEP in the large frame-length limit. Moreover, the set of spectral norm constrained codes are also shown to be large enough to contain universal codes that can communicate reliably over any channel realization for which the mutual information exceeds the information rate of the code

This correspondence highlights the performance limitation of linear minimum mean-squared error (mmse) detection in underdetermined vector Gaussian channels (as in overloaded code-division multiple-access (CDMA) systems) where the number of symbols (users) exceeds the signal space dimension (spread factor). It is shown that for such a simple receiver it is not possible to construct signal sets (or spreading codes) to even satisfy the basic requirement that every user's symbol error probability decays exponentially as noise power vanishes. This result holds for arbitrary received energies, modulation schemes, and any strictly underdetermined system with a finite signal space dimension and a finite number of users

A unified framework for coherent multiple antenna communications is presented leading to a general space-time code design criterion valid for arbitrary spatial and temporal fading correlations. This framework provides insights into the effect of each of spatial and temporal correlations on space-time code design. The single code design expression applies to quasi-static, fast fading and multiple block fading channels and more generally also to channels with arbitrary correlations in the temporal dimension as well as in the spatial dimension with arbitrary rank. The general coding strategy proposed consists of precoding a space-time code with its size determined by the rank of transmit correlation, the structure determined by the Cholesky factorization of the temporal correlation, and the precoding matrix obtained from the eigenvectors of the transmit correlation matrix

We consider a multi-input multi-output (MIMO) fading channel with coherent reception and provide a sharp characterization of the outage capacity in the form of an asymptotically tight (in the limit of high signal-to-noise ratio) affine lower bound, under only mild assumptions on the fading distribution. The bound is simpler to compute than the original capacity and succinctly captures the various features particular to the channel. For systems where both the transmitter and the receiver have perfect channel state information, we derive asymptotically tight affine lower bounds on the outage capacities under a long-term and a short-term power constraint as well as on the delay-limited capacity. Further, when only the receiver has perfect channel state information, and when the rank of the channel matrix is equal to the number of transmit antennas with probability one, we show that an isotropic Gaussian input is asymptotically optimal. Moreover, for Ricean channels the asymptotic effect of the Rice factor on the delay-limited capacity is also characterized

Code design for the low SNR MIMO noncoherent correlated Rayleigh fading channel is considered. Design rules which exploit the correlations in the transmit antennas in the MIMO case, to provide gains over the corresponding SIMO case are presented. The Chernoff bound on the average pairwise error probability (APEP) is used to study the effect of the receive correlation matrix on system performance at different SNR regimes. Based on a lower bound on the APEP, which is related to the Bhattacharya coefficient, a technique is proposed to design codes for use with transmit beamforming, with codewords having unequal prior probabilities. The motivation for such codes with unequal priors arises from recent information theoretic results on the low SNR channel. Such constellations are shown to perform substantially better than constellations designed assuming equal priors, at low SNRs

The design requirements for space-time coding typically involves achieving the goals of good performance, high rates, and low decoding complexity. In this paper, we introduce a further constraint on space-time code design in that the code should also lead to low values of the peak-to-mean envelope power ratio (PMEPR) for each antenna. Towards that end, we propose a new class of space-time codes called the "low PMEPR space-time" (LPST) codes. The LPST codes are obtained using the properties of certain cyclotomic number fields. The LPST codes achieve a performance identical to that of the threaded algebraic space-time (TAST) codes but at a much smaller PMEPR. With M antennas and a rate of one symbol per channel use, the LPST codes lead to a decrease in PMEPR by at least a factor of M relative to a Hadamard spread version of the TAST code. For rates beyond one symbol per channel use and up to a guaranteed amount, the LPST codes have provably smaller PMEPR than the corresponding TAST codes. Additionally, with the concept of punctured LPST codes proposed in this paper, significant performance improvement is obtained over the full diversity TAST schemes of comparable complexity. Numerical examples are provided to illustrate the advantage of the proposed codes in terms of PMEPR reduction and performance improvement for very high rate wireless communications.

A new approach is presented for the design of full modulation diversity (FMD) complex lattices for the Rayleigh-fading channel. The FMD lattice design problem essentially consists of maximizing a parameter called the normalized minimum product distance d/sub p//sup 2/ of the finite signal set carved out of the lattice. We approach the problem of maximizing d/sub p//sup 2/ by minimizing the average energy of the signal constellation obtained from a new family of FMD lattices. The unnormalized minimum product distance for every lattice in the proposed family is lower-bounded by a nonzero constant. Minimizing the average energy of the signal set translates to minimizing the Frobenius norm of the generator matrices within the proposed family. The two strategies proposed for the Frobenius norm reduction are based on the concepts of successive minima (SM) and basis reduction of an equivalent real lattice. The lattice constructions in this paper provide significantly larger normalized minimum product distances compared to the existing lattices in certain dimensions. The proposed construction is general and works for any dimension as long as a list of number fields of the same degree is available.

A space-time code is proposed that exhibits the highest coding gain among competing full-rate full transmit diversity space-time codes for the two transmit and receive antenna coherent quasi-static fading channel. The proposed code is derived from a layered architecture with real rotation of quadrature amplitude modulation (QAM) information symbols in two dimensions. The existing codes of similar architecture concentrate on application of complex full modulation diversity rotations or asymmetric real rotations. An analytic evaluation illustrates the significant improvement in coding gain achieved with the proposed code. Moreover, the coding gain of the proposed code is independent of its rate. This implies that the proposed code achieves the optimal diversity-multiplexing tradeoff curve for the two transmit antenna system. A stacked extension of the proposed code offers a reduced complexity capacity optimal alternative to the full diversity codes for larger number of transmit antennas. Performance enhancement in several scenarios is verified through simulations.

A framework is presented that allows a number of known results relating feedback equalization, linear prediction, and mutual information to be easily understood. A lossless, additive decomposition of mutual information in a general class of Gaussian channels is introduced and shown to produce an information-preserving canonical decision-feedback receiver. The approach is applied to intersymbol interference (ISI) channels to derive the well-known minimum mean-square error (MMSE) decision-feedback equalizer (DFE). When applied to the synchronous code-division multiple-access (CDMA) channel, the result is the MMSE (or signal-to-interference ratio (SIR) maximizing) decision-feedback detector, which is shown to achieve the channel sum-capacity at the vertices of the capacity region. Finally, in the case of the asynchronous CDMA channel we are able to give new connections between information theory, decision-feedback receivers, and structured factorizations of multivariate spectra.

This correspondence characterizes the performance limitation of the well-acclaimed generalized Welch-bound equality (WBE) signals under linear minimum mean-squared error (MMSE) detection. It is analytically proven, and experimentally verified, that when users in an overloaded but finite-size code-division multiple-access (CDMA) system are allocated such signals, the error rate of at least one user "floors" (i.e., it cannot be driven to zero even in the absence of additive noise), independently of the symbol energies. If, in addition, all users are received with equal energy, then the error rate of every user "floors".

The problem of bandwidth constrained space-time signal design for the noncoherent Rayleigh block-fading channel is addressed. Existing design techniques for this channel subdivide the coherence interval into smaller time blocks and use repetitions of a basic waveform to signal in each subblock. When the coherence time of the channel is short this access technique becomes questionable, due to the inverse relationship between bandwidth and time support. In particular, there may not be sufficient time support to allow matched filtered reception with finite (or nearly finite) Shannon bandwidth waveforms. To address this problem, we consider other notions of bandwidth, such as the root-mean square (RMS) bandwidth and fractional out of band energy (FOBE), which are appropriate for signals with finite time support. We extend our previous work on unconstrained signal designs for the block fading channel to incorporate such bandwidth constraints. The resulting signal constellations can be used 1) as a comparison point for any signal design procedure and 2) to conclude that there is a performance advantage to be had when signals are properly matched to the finite time support of the channel.

A general class of training-based space-time codes is considered for the noncoherent block correlated Rayleigh fading channel. Such codes can be efficiently decoded by first forming the MMSE estimate of the channel and then decoding the underlying coherent space-time code using the channel estimate as if it were perfect. The diversity order of this (in general, suboptimal) estimator-decoder is obtained, and it is shown that under certain conditions on the channel correlation matrix, training codes inherit the diversity order of the underlying coherent code.

The max-min fairness idea is applied to optimize the CDMA capacity region. For any given signal set, a fair rate-allocation algorithm is specified. The notion of fair capacity is introduced and a signal design algorithm is proposed that produces signal sets with near-maximum fair capacity under (a) optimum decoding and (b) suboptimal decoding based on MMSE filtering and successive decoding, when there is sufficient bandwidth.

We consider a wireless network with multiple terminals (m/spl ges/2) as well as multiple receive antennas at the destination (N/spl ges/1) and obtain diversity multiplexing tradeoff upper bounds for some recently proposed cooperative diversity protocols. The results obtained show that irrespective of the coding scheme employed none of these protocols can yield a diversity order greater than N+m-1. Further, the tradeoff bounds indicate that the protocol yielding the best diversity order may change with the multiplexing gain. Using these bounds we propose a switching strategy that yields the best tradeoff bound which also significantly outperforms the optimal tradeoff curve for the baseline noncooperative system at all possible multiplexing gains.

Practical space-time coding strategies are proposed for multiple users cooperating to communicate to a destination in a wireless channel. For a system with m single antenna users and a destination with N receive antennas, a two-phase cooperative scheme is proposed that achieves a diversity order of m - 1 + N for the error probability. This effectively proves the achievability of the diversity order implied by the outage probability for this model. This two-phase scheme employs a short full diversity space-time block code over QAM symbols. Even though the suboptimum decoder used by the destination assumes that the inter-user communication is successful, the corresponding analysis does account for the decoding errors in the inter-user communications phase. The key to the diversity order analysis is an appropriate modification of the rule for deciding whether or not a user acts as a relay for another user. The performance analysis technique presented here also extends to another practical cooperation strategy, proposed specifically for the case of m = 2 and N = 1, that is inspired from an optimal diversity-multiplexing tradeoff curve achieving protocol.

This paper considers non-ergodic multi-input multi-output (MIMO) fading channels. We compare the outage capacities yielded by the optimal unconstrained system and some recently proposed space-time architectures for i.i.d. Gaussian inputs. All the systems considered here are known to yield outage capacities having the same (maximum) rate of growth with the signal-to-noise ratio (SNR). For each system, an asymptotically tight lower bound on the outage capacity is derived. The analysis reveals that the diagonal BLAST architecture with the zero-forcing front end is asymptotically optimal with respect to the outage capacity. Another space-time architecture is shown to be optimal at all SNR with respect to the outage capacity.

This paper addresses blind multiuser detection in a direct-sequence code-division multiple-access (DS-CDMA) network in presence of both multiple-access interference and intersymbol interference. In particular, it considers a DS-CDMA system where K out of N users are transmitting; the N admissible spreading codes are known, and so is the code of the user to be demodulated. The number of interferers, the signatures of a certain number, possibly all, of the interferers, and the channel impulse response of each active user are unknown. The spreading codes of the unknown interferers are determined via a procedure that exploits the knowledge of the set of admissible transmitted codes and of the known active codes. The procedure applies to both single and multiple receiving antennas. The performance assessment of a blind decorrelating detector, implemented by resorting to the proposed identification procedure, shows that it outperforms a plain subspace-based blind decorrelator for small sizes of the estimation sample.

A theory of noncoherent decision feedback multiuser detection for nonorthogonal binary modulation is developed that parallels that of coherent decision feedback multiuser detection for single-pulse modulation. In particular, an optimum noncoherent decision feedback detector is obtained that maximizes symmetric energy over a newly defined class of decision feedback detectors. Unlike the usual per-user performance metrics such as asymptotic efficiency or near-far resistance, the symmetric energy measure captures, with a single number, the asymptotic (high signal-to-noise ratio (SNR)) bit-error performance of all users at once. Several properties of the optimum decision feedback detector are established, one of which is that it outperforms the decision feedback generalized-likelihood ratio (GLR) detector in symmetric energy. It is also shown that, regardless of the order in which users are detected, the optimum noncoherent decision feedback detector outperforms its non-decision feedback counterpart in symmetric energy. Furthermore, two simple rules are obtained for determining the order in which users must be detected to guarantee that the optimum decision feedback detector outperforms its non-decision feedback counterpart (which in turn, is superior to the decorrelative GLR detector presented earlier) in terms of asymptotic effective energy for every user. In fact, one of the two (greedy) ordering rules also maximizes symmetric energy among all possible orderings. Such ordering rules are not available for the noncoherent decision feedback GLR detector in earlier work of the authors. Feasible sets of received energies are characterized in which it is possible, with power control, to achieve quality-of-service objectives for each user. None of the results in this paper make simplifying assumptions about the effects of error propagation. The term "noncoherent" in this work is used to denote that the receiver has no knowledge of the carrier phases and received signal energies of any of the users.

Training codes are introduced for the multiple-antenna, noncoherent, multiple block-Rayleigh-fading channel in which the fading coefficients, which are constant over a fixed number of dimensions (coherence interval) for each block and then change independently to a new realization, are known neither at the transmitter nor at the receiver. Each codeword of a training code consists of a part known to the receiver-used to form a minimum mean-squared error (MMSE) estimate of the channel-and a part that contains codeword(s) of a space-time block or trellis code designed for the coherent channel (in which the receiver has perfect knowledge of the channel). The channel estimate is used as if it were error-free for decoding the information-bearing part of the training codeword. Training codes are hence easily designed to have high rate and low decoding complexity by choosing the underlying coherent code to have high rate and to be efficiently decodable. Conditions for which the estimator-detector (E-D) receiver is equivalent to the optimal noncoherent receiver are established. A key performance analysis result of this paper is that the training codes when decoded with the E-D receiver achieve a diversity order of the error probability that is equal to the diversity order of the underlying coherent code. In some cases, the performance of training codes can be measured relative to coherent reception via "training efficiency," which is then optimized over the energy allocation between the training and data phases. In the limit of increasing block lengths, training codes always achieve the performance of coherent reception. The examples of training codes provided in this work have polynomial complexity in rate but an error rate comparable to the best performing unitary designs available, even though the latter require exponential decoding complexity.

For an uncoded, K-transmit, N-receive antenna coherent narrow-band communication system employing a decorrelating decision feedback detector (D-DFD), the exact average (over channel realizations) joint error probability (JEP) as well as the average per-symbol error probabilities (SEPs) are derived without making any simplifying assumptions on error propagation. It is proved that the diversity orders of the JEP and the SEP (of every symbol) is limited by error propagation to N-K+1. Based on our exact error probability analysis, however, we suggest an optimization of JEP over nonnegative quadrature amplitude modulation (QAM) constellation sizes (rates) and average powers across transmitters which yield significant improvements over the usual equal power and equal rate assignment. In fact, the JEP of such an optimized design has the much improved diversity order of N (which is also the diversity order obtained through the optimum maximum-likelihood (ML) detector). Moreover, it is seen that these simple optimized designs can achieve a significant fraction of the /spl epsi/-outage capacity even without outer codes. It is also known-but only through simulations-that when the symbols are detected in certain channel realization-dependent orders it is possible to improve substantially over fixed-order detection in the case of the equal rate and equal power assignment. We provide an analysis for a recently proposed channel-dependent ordering rule and show that it does not provide an improvement of the diversity order of the JEP beyond N-K+1. Another ordering rule that was proposed earlier to maximize the worst case post-detection signal-to-noise ratio (SNR) under the perfect feedback assumption is shown to be optimal under a more compelling criterion that does not involve that simplifying assumption. While efficiently computable, this ordering rule is seen to perform almost as well as the optimal channel-dependent ordering rule that minimizes the conditional JEP (and hence the JEP). Nevertheless, a multiple-input multiple-output (MIMO) system with an optimized rate and power allocation and a fixed order of detection is not only less complex but also has a significantly lower JEP than that of the equal-power, equal-rate system, where transmitters are detected in a channel-dependent order, optimal or otherwise.

A new class of full diversity space-time codes is proposed that leads to a significantly smaller peak-to-mean envelope power ratio (PMEPR) compared to the recently invented diagonal algebraic space-time (DAST) and threaded algebraic space-time (TAST) codes. Moreover, the proposed "low PMEPR space-time" (LPST) codes exhibit identical performance and decoding complexity compared to the TAST codes. Additionally, unlike the TAST codes, the LPST codes meet an upper bound known as the singleton bound on the maximum achievable rate by a space-time code. The key to the construction of the LPST codes is an improved spreading scheme that outperforms the originally suggested Hadamard spreading scheme for the PMEPR reduction of DAST codes. Several properties of the LPST codes in relation to PMEPR are studied. Numerical results are presented to support the significant advantage of the proposed codes in terms of reduced PMEPR for high rate wireless communications.

We propose a stacked orthogonal space-time architecture for the quasi-static, MIMO Rayleigh fading channel where the K transmit antennas are divided into K/2 groups. Each group employs the Alamouti design as the inner code with the indeterminates being uncoded symbols or symbols from some outer code. Successive group interference suppression strategies based on decorrelating and MMSE filters are used to decode the component codes in some fixed or channel dependent order. These strategies exploit the specific structure of the inner codes to yield high diversity orders while preserving the decoupling property, thereby enabling the use of single-input, single-output (SISO) outer codes. The problems of finding the exact frame error probability (FEP) or outage probability of the interference suppression schemes are challenging. Nevertheless, these analysis problems are solved for the decorrelating case. Alternatively, the outage probability is minimized over channel dependent ordering rules via a greedy algorithm for any given rate and power tuples. We also demonstrate the intimate connection between outage probability and the achievable FEP for long frame-lengths. In the case of the optimized stacked space-time systems with (SISO) outer coding, we show that much better diversity orders and frame error probabilities (of about 4 dB in one example) are obtained relative to the codes of V. Tarokh et al. (1999) and these improvements are also obtained with a lower decoding complexity.

The problem of signal design for bandwidth efficient multiple access is addressed under quality of service (QoS) constraints specified by (possibly different) BER. Indeed, BER more accurately measures the performance than the signal-to-interference ratio (SIR) for uncoded communication. Furthermore, we argue that the asymptotic effective energy (AEE) faithfully characterizes BER, and we translate the BER-specified QoS into AEE-specified ones. We then propose a recursive, greedy algorithm for joint signal design to minimize the system bandwidth while ensuring that each user achieves its desired AEE (and hence BER). This algorithm successfully converts excess power into bandwidth savings under reliability constraints, and significantly improves spectral efficiency over full-rank (e.g. orthogonal) signaling and SIR-based approaches.

The problem of optimizing signals for the Gaussian multiple access channel under a quality of service (QoS) constraint is addressed. In particular, the bandwidth efficient multiple access (BEMA) approach (Varanasi, M.K. and Guess, T., IEEE Trans. Commun., vol.49,no.5, p.844-54, 2001) is considered, wherein signals are designed at the base station and fed back to, and for use by, uplink transmitters, in order to minimize a strict bandwidth while ensuring that each user meets a rate-specified QoS constraint. A new recursive, greedy algorithm for signal design is proposed that exactly meets the QoS requirements. Preliminary analysis and numerical examples suggest it is optimal.

We consider M-ary communication with K users over a space diversity channel, consisting of a single transmit antenna for each user and multiple receive antennas. We examine two different flat fading models, namely, phase coherent wavefront fading and noncoherent element-to-element fading. In the case of wavefront fading, the fade is constant across the face of the receive antenna and we can associate an angle of arrival to the signal. We present a variation of the MUSIC algorithm for estimating this parameter and use it to form a spatial beam. In the case of noncoherent element-to-element fading, the fading path to each sensor is different (although possibly correlated) and no angle of arrival can be exploited for conventional beamforming. For each channel model, we develop several detection strategies which assume various amounts of prior information about the fading. We then consider blind extensions of these detectors based on subspace tracking, which do not require a prior model for the interfering users' signals.

The jointly optimum receiver is obtained for multi- user communications in a frequency nonselective Rayleigh-fading channel with N/sub T/ transmit antennas per user and N/sub R/ receive antennas. Based on a general analysis of quadratic receivers in zero-mean complex Gaussian vectors, asymptotically tight expressions (for high signal-to-noise ratio (SNR)) for the pairwise error probabilities are derived. Subsequently, it is shown that N/sub T/-dimensional single-user signaling suffices to provide full diversity order N=N/sub T/N/sub R/ for all the users. In other words, the presence of other users does not increase the minimum dimension required beyond what is needed for the single-user space-time channel. For the special case of low-rank "code-division multiple-access (CDMA)" signaling with N/sub T/=1 and provided the signatures of any two users are linearly independent, it is shown that the error probability of a K-user system asymptotically approaches single-user-like performance for every user. Remarkably, therefore, an increase in the number of users, and hence an increase in the aggregate spectral efficiency, does not require the users to transmit with more power to achieve single-user-like performance asymptotically. A signal design algorithm is proposed to illustrate this point and examples are given. These results are then generalized to the multiple transmit antenna case. A new (N/sub T/+1)-dimensional signaling strategy is proposed for the multiuser channel that leverages existing single-user space-time signal designs while ensuring full diversity order and single-user-like performance asymptotically for every user.

The jointly optimum multiuser noncoherent detector for differential phase-shift keying (DPSK) modulation over the generalized diversity Rayleigh-fading (GDRF) channel is derived and analyzed. The GDRF channel includes time/frequency/receiver antenna diversity and allows fading correlations between the various diversity branches of each user. Noncoherent detection here refers to the case where the receiver has neither knowledge of the instantaneous phases nor of the envelopes of the users' channels. Upper and lower bounds on the bit-error probability of the optimum detector are derived for a given user. For fast fading, when the fading coefficients vary from one symbol interval to the next (but are still essentially constant over one symbol interval), the detector asymptotically (for high signal-to-noise ratios (SNRs)) reaches an error floor, which is bounded from below and above for different fast fading scenarios. For slow fading, when the channel is constant for at least two consecutive symbol intervals, the upper bound is shown to converge asymptotically to the lower bound. Thus, the asymptotic efficiency of optimum multiuser DPSK detection can be determined and is found to be positive. In contrast to coherent detection, however, it is smaller than unity in general. Since the asymptotic efficiency is independent of the interfering users' signal strengths, the optimum detector is near-far resistant. While optimum multiuser detection is exponentially complex in the number of users, its performance provides the benchmark for suboptimal detectors. In particular, it is seen that the previously suggested post-decorrelative detectors can be far from satisfactory.

There have been several papers in the literature that deal with the design of signature waveforms for use by the transmitters in uplink, single-cell, multiple-access communications. In particular, we consider the approach introduced by Guess and Varanasi (1996, 1997), where the signature waveforms are specifically designed for the centralized multiuser receiver at the base so that each transmitter can be guaranteed a preassigned quality-of-service (QoS) requirement in terms of the received signal-to-interference ratio (SIR). The resulting strategy is called bandwidth-efficient multiple access (BEMA). When all users employ pulse amplitude modulation (PAM) and a common signaling rate, the key question in BEMA is how the waveforms must be designed to occupy as little bandwidth as possible and still meet the QoS objectives. For a strict measure of bandwidth, and for a given set of received powers, this question was addressed by the authors for the maximum SIR decision-feedback (MSIR-DF) receiver of Varanasi and Guess (1998). A similar question was addressed by Viswanath, Anantharam and Tse (see ibid., vol.45, p.1968-1983, Sept. 1999) where, for a sum constraint on the received powers, optimal signature signals and transmit powers were obtained for the linear MSIR receiver (without decision feedback). A somewhat different but related non-QoS approach proposes the design of signature signals that maximize the total capacity of the multiple-access channel under a spreading-gain constraint. This article undertakes a comparison of the minimum bandwidth required (to achieve the QoS requirements) for the signals designed for the MSIR-DF receiver, for the linear MSIR receiver, and for sum-capacity maximization as shown by Viswanath and Anantharam (see ibid., vol. 45, p.1984-1991, Sept. 1999). We show that the bandwidth required for multiuser receivers with decision feedback can be significantly less than that required for linear receivers or for sum-capacity maximization when the MSIR-DF receiver is used.

Multiuser detection for overloaded code-division multiple-access (CDMA) systems, in which the number of users is larger than the dimension of the signal space, is of particular interest when bandwidth is at a premium. In this paper, certain fundamental questions are answered regarding the asymptotic forms and performance of suboptimum multiuser detectors for cases where the desired and/or interfering signal subspaces are of reduced rank and/or have a nontrivial intersection. In the process, two new suboptimum detectors are proposed that are especially well suited to overloaded systems, namely, the group pseudo-decorrelator and the group minimum mean-squared error (MMSE) detector. The former is seen to be the correct extension of the group decorrelator in the sense that it is the limiting form (in the low-noise regime) of the group MMSE detector. Pseudo-decorrelation is also used as a feedforward filter in a new decision feedback scheme. For the particular case of real-valued modulation, it is shown that the proposals of the so-called "improved" linear (also known as "linear-conjugate" or "widely linear") detectors were more simply derived earlier using the idea of minimal sufficiency, which we also apply to the new detectors of this paper.

We consider blind adaptive multiuser detection in correlated waveform multiple-access-based cellular radio networks. A common stochastic approximation (SA)-based framework is proposed from which three blind adaptive algorithms for linear minimum mean squared error detection are obtained. Two of them coincide with previously proposed algorithms and the third is shown to be best suited for implementation at a base station. The work here also improves these SA-based adaptation algorithms in the context of cellular radio networks, in terms of the convergence properties by using the results on the SA technique with averaging. Convergence issues of the different adaptations are investigated and numerical examples are presented to demonstrate the performance improvement due to averaging.

Three noncoherent minimum mean-squared error (NMSE)-based multiuser receivers are proposed for multipulse modulation. These receivers have a common MMSE prefilter and are followed by one of three phase-independent decision rules. The simplest decision rule selects the maximum magnitude of the MMSE filter outputs, and the other two account for the second-order statistics of the residual multiple-access interference that remains after MMSE filtering. Blind adaptive algorithms are then proposed for the three noncoherent MMSE receivers. The common adaptive algorithm for the MMSE prefilter, which is based on the stochastic approximation method, is shown to converge in the mean-squared error sense to the nonblind NMSE prefilter. Our convergence analysis yields new insight into the tradeoff between the rate of convergence and the residual mean-squared error. The noncoherent blind receivers obtained here do not require the knowledge of the received signals of any of the interfering users, and are hence well-suited for distributed implementation in cellular wireless networks or in communication systems that must operate in noncooperative environments.

Previous results on blind multiuser detection apply in situations where the signal parameters of the users of interest are known, and those of the interferers; are unknown. In this paper, we consider the new paradigm of an N-user system, in which K users are active, and the problem is to detect G users of interest out of those K active users when the signal parameters (codes, amplitudes) of the G users of interest are known, as are the codes of all N users. What is not known at the receiver, however, is K - G, the number of active interferers, and the identity of these interferers. A solution to such a problem could be to ignore the knowledge of the remaining N - G codes, and apply known blind multiuser detectors based on stochastic approximation or subspace tracking techniques. However, it is shown here that the additional knowledge of those codes can be used to obtain an interference-identification-based blind multiuser receiver that has much faster convergence properties. We illustrate the underlying principle in the context of blind group detection in synchronous direct-sequence/code-division multiple-access (DS/CDMA) systems operating in channels that exhibit frequency-selective fading.

The optimum noncoherent multiuser detector is obtained for generalized diversity symbol-synchronous communication systems that employ nonorthogonal multipulse modulation. A unified approach is adopted to simultaneously address various forms of diversity such as time, frequency, multipath, and/or receiver-amenna diversity. Upper and lower bounds on the average bit-error probability of the optimum noncoherent detector are derived. While these bounds are numerically computable, they are too complicated to give insights about the relative influence of system parameters on the essential behavior of the bit-error rate. To address this issue, an asymptotic (low noise) analysis of the bit-error probability is undertaken. It is shown that the upper and lower bounds are indeed asymptotically convergent. A formula for the asymptotic efficiency of the optimum noncoherent detector is thereby derived. Interestingly, the asymptotic efficiency is found to be positive, and independent of the signal strengths of the interfering users.

Uplink communication in a cellular radio network is considered where the base station in each cell employs linear or nonlinear (decision feedback) multiuser receivers. For any such receiver, the problem of interest is that of minimizing the total transmit power under the constraint that all the users of the network achieve their quality-of-service objective in terms of signal-to-interference ratio (SIR). When the solution is feasible for the desired SIR requirements, the optimum powers are computed with a distributed iterative power control strategy suitable for implementation at each base station. While the deterministic algorithm requires both in-cell and out-of-cell user information, the stochastic algorithm proposed in this paper can be implemented at the base stations in a truly distributed manner requiring knowledge of only in-cell parameters. Such an algorithm was proposed previously for the case where base stations use linear (single user) matched filter (MF) receivers. However, the feasibility region in terms of attainable SIRs for a well-designed multiuser receiver, particularly for a nonlinear receiver that employs decision feedback, is generally much larger than it is for the linear MF receiver. The stochastic power control algorithm in this paper, for linear or nonlinear multiuser receivers, converges in the mean-square sense to the minimal powers when the target SIRs are feasible. The second major focus of this paper is to improve the convergence properties of the conventional stochastic approximation based power control strategy by using the more recent results on averaging. Convergence issues of both the "nonaveraged" and "averaged" algorithms are investigated, and numerical examples are presented to demonstrate the performance improvement due to averaging.

We consider the problem of designing signal constellations for the multiple transmit-multiple receive antenna Rayleigh-fading communication channel, when neither the transmitter nor the receiver know the fading. In particular, by employing the asymptotic union bound (AUB) on the probability of error, we give a new formulation of the problem of signal design for the noncoherent fading channel. Since unitary signals are optimal for this channel (in the limit of large signal-to-noise ratios SNRs), the problem can be posed in terms of packings on the Grassmanian manifold. A key difference in our approach from that of other authors is that we use a notion of distance on this manifold that is suggested by the union bound. As a consequence of our use of this distance measure, we obtain signal designs that are guaranteed to achieve the full diversity order of the channel, a result that does not hold when the chordal distance is used. We introduce a new method of recursively designing signals, termed successive updates, to approximately optimize this performance measure. We then examine the use of our signals with several convolutional codes over the fading channel. An upper bound on the bit error probability of the maximum-likelihood decoder is presented together with an asymptotic analysis of that bound.

In a previous paper we proposed a multiuser space-time modulation scheme that leverages single-user space-time constellations and guarantees both, a full diversity order, as well as an asymptotic (high SNR) single-user like performance for every user. This is achieved by multiplying each user's space-time information matrix symbol by a low-dimensional "spreading matrix." For instance, for N/sub T/-transmit antennas per user and if the single-user space-time constellation employed requires only the minimum dimension N/sub T/, no more than N/sub T/+1 dimensions are required for the common signal space of all users, i.e., each user's spreading matrix is of size (N/sub T/+1)/spl times/N/sub T/, independent of the number of users. In this paper, we present a simplified design criterion to obtain these spreading matrices by numerical optimization. Since the columns of each user's spreading matrix are constrained to be orthonormal, we propose to perform the optimization using a parameterization of the Grassmann manifold. A special feature of the simplified criterion, and thus of the resulting spreading matrices, is that they are independent of the particular single-user space-time constellations (of a given dimension), so that different spectral efficiencies can be attained without changing or redesigning the spreading matrices.

We propose the new group metric (GM) soft-decision decoder for convolutionally coded synchronous multiple-access channels. The GM decoder exploits the independently operating encoders of the multiuser channel by making decoding decisions for a subset of the users, but incorporating all the multiuser information in its metrics. For a single user, this decoder will have a reduced complexity that is exponential in the sum of encoder memory and the number of users. The soft-decision maximum-likelihood (ML) joint decoder is well known. This optimal decoder suffers from a high complexity requirement that is exponential in the product of encoder memory and the number of users. The size of the decoded subset is a design parameter which allows a tradeoff between complexity and performance. The performance of the GM decoder, once properly characterized, can be analyzed using standard techniques. In addition, a new analysis technique is presented which considers decomposable sequences for the fading channel. With this analysis, we have a new tool for bounding error probabilities for multiuser decoders. Applying this technique to the GM decoder, we can directly identify sequences that are decomposable some fraction of the time, and obtain a new upper bound. Further, this improved bound can be expressed in closed form. Numerical results show that the actual performance gap between the GM and ML decoders can be quite small.

This paper considers the design of signature waveforms for successive-decoding-type multiuser receivers (including the optimum successive decoder (OSD)) in a correlated-waveform multiple-access channel. The problem is to obtain signature waveforms that require as little bandwidth as possible while allowing the receiver to meet a given set of quality-of-service (QoS) objectives. The QoS objectives are specified for each user in terms of capacity, or equivalently, the signal-to-interference ratio. A (generally unachievable) lower bound is obtained on the minimum bandwidth required to achieve these QoS constraints. Moreover, a simple algorithm is proposed for obtaining signal sets that meet the QoS constraints when used with the OSD, and which, while not optimal, require a bandwidth that can be very close to the minimum required bandwidth. It is also shown that such signal sets allow for a significantly more efficient use of bandwidth than do orthogonal signals used in time- or frequency-division multiple access (TDMA/FDMA). Based on our signal design approach, we propose a new multiple-access strategy that we refer to as bandwidth-efficient multiple access (BEMA). While BEMA is more bandwidth efficient than TDMA or FDMA, it retains their desirable feature of needing only single-user coding (and decoding) for each user.

A general, asymptotic (high signal-to-noise (SNR)) error analysis is introduced for quadratic receivers in frequency-flat and multipath Rayleigh-fading channels with multiple transmit and receive antennas. Asymptotically tight expressions for the pairwise error probabilities are obtained for coherent, noncoherent, and differentially coherent space-time receivers. Not only is our unified analysis applicable to more general modulation schemes and/or channel models than previously considered, but it also reveals a hitherto unrecognized eigenvalue structure that is common to all of these problems. In addition to providing an easy recipe for computing the asymptotic pairwise error rates, we make some conclusions regarding criteria for the design of signal constellations and codes such as (a) the same design criteria apply for both correlated and independent and identically distributed (i.i.d.) fading processes and (b) for noncoherent communications, unitary signals are optimal in the sense that they minimize the asymptotic union bound.

The jointly optimum noncoherent multiuser detector is obtained for nonlinear nonorthogonal modulation over the frequency nonselective Rayleigh-fading multiple-access channel. Upper and lower bounds on the average bit-error probability are derived. While these bounds are numerically computable, they are too complicated to give insight into the relative influence of the system parameters on the essential behavior of the bit-error rate. Hence this paper develops an asymptotic analysis of the average bit-error probability. In particular, it is shown that the upper and lower bounds are asymptotically convergent. An exact formula for the asymptotic efficiency of the optimum noncoherent detector is derived. Interestingly, the asymptotic efficiency is found to be positive and independent of the signal strengths of the interfering users. In contrast, the noncoherent detector which would be optimal in a single-user channel (the "conventional detector"), when used over the multiuser channel, has an asymptotic efficiency that is identically equal to zero no matter what the powers of the interferers may be. While the performance analysis of the optimum detector provides the fundamental limit on achievable error rate, the implementational complexity of the optimum detector is exponential in the number of users. As a low-complexity alternative, a decorrelative energy detector is also proposed and analyzed in terms of error probability and asymptotic efficiency.

The jointly optimum noncoherent multiuser detector for DPSK modulation in generalized diversity Rayleigh fading channels (GDRF) was presented previously (Varanasi and Brehler, 1998) and bounds on the error probability were obtained. In the numerical examples these bounds were seen to converge. This paper examines analytically the behavior of the bounds for high signal-to-noise ratio (SNR) scenarios. Slowly fading channels, where the fading coefficients are essentially constant over two successive symbol intervals, and fast fading channels, where the fading coefficients can vary from one symbol interval to the next, are considered. For slow fading, the asymptotic convergence of the upper bound to the lower bound is proved. The asymptote that is reached for high values of the SNR does not depend on the interfering users' energies, establishing thereby the near-far resistance of the optimum multiuser DPSK detector. For fast fading the error floor reached for high SNRs is bounded from below and above.

Noncoherent multiuser detection for nonlinear modulation was previously studied and the idea of phase-independent noncoherent decorrelation was introduced and three post-decorrelative detectors were obtained and analyzed. However, their implementation requires the knowledge of the signature waveforms of all the users, which may be available only for centralized implementation. In this paper, we obtain a blind adaptive noncoherent decorrelative detector for nonlinear modulation that is suitable for distributed implementation with the knowledge of only the normalized signals of the desired user and the additive noise variance. This detector is based on the stochastic approximation method and does not require the overhead of any kind of "training." Two adaptive algorithms are developed, one guided by every signal in the desired user's signal set individually, and the other by the user's entire signal space. While this paper focuses on the particular problem of blind adaptive noncoherent decorrelative detection, it addresses a more general adaptation issue, namely, that of improving the convergence properties of an adaptive scheme by effectively using all the information that is known, and adapting only to the part of the desired solution that is truly unknown. Convergence is shown in the mean squared error sense for both the fixed step-size and time-varying step-size versions of the two algorithms.

In narrow-band multiuser communication systems with fading diversity, it is shown that pre-combining group detection can bridge the diversity-order gap in performance between the optimum and linear detectors. For a system with M diversity channels, the group detector diversity order is M-|G|, where |G| is the interfering group size, a design parameter. Group detection thus provides a more substantial improvement in performance in narrow-band channels over linear detection than in wide-band channels in which the diversity orders of the optimal and linear detectors are equal. Here, the complexity of the receiver is a new parameter which, in addition to the number of antennas, can be used to control the diversity order. Exact formulas for the pairwise-error probabilities and bounds for the bit-error rate are obtained, and numerical results are shown.

The problem of noncoherent multiuser detection for multipulse modulation over the Gaussian multiuser channel is studied. It is assumed that neither the energies nor the carrier phases of the signals of any of the users are available at the receiver. Previously, a post-decorrelative generalized likelihood ratio test (GLRT) based detector was proposed as a solution to this problem. In this paper, we introduce the concept of noncoherent decision feedback (DF) that forms the basis for an improved solution to the same problem. The users are detected sequentially in some fixed order, and the decision for a particular user takes advantage of the reduction of uncertainty associated with the signal space resulting from decisions already made for previous users. In contrast to coherent DF, therefore, the feedforward and feedback transformations in the noncoherent case are themselves functions of the matched filter outputs. An efficient implementation of the noncoherent DF detector for M-ary modulation and /spl rho/-dimensional signal space requires O(M/sub /spl rho//) computational complexity per user. Upper and lower bounds on its symbol error probability are obtained. It is shown that significant improvements over the post-decorrelative GLRT-based detector are often possible. Sufficient conditions are obtained which guarantee, without ignoring error-propagation effects, that the high signal-to-noise performance of the DF strategy can be as good as its genie-aided version in which perfect past users' decisions are used.

Random-coding error exponents are derived for the Gaussian code-division multiple-access (CDMA) channel for the maximum-likelihood and optimum successive decoders. Error exponents not only specify the capacity region of the channel, which is known, but also give lower bounds on the rate of exponential decay of the average probability of error as a function of the block length of random codes. A comparison of the two decoders in terms of their error exponents is included.

Bandwidth-efficient multiple access (BEMA) is a strategy where transmitter pulses are continually designed at the base station and are dynamically allocated to the transmitters via a feedback channel. Such pulses (or "signature waveforms") are designed to conserve bandwidth while simultaneously enabling the receiver at the base station to meet a quality-of-service (QoS) specification for each transmitter. The key technical problem in BEMA communication is therefore the design of the transmitter pulses for the base station receiver. In an earlier paper, we presented solutions to this problem that were shown to be superior (in terms of strict bandwidth) to common signaling schemes such as time-, frequency-, and code-division multiple access (TDMA, FDMA, and CDMA). This paper uses the framework developed earlier, but considers strictly time-limited transmitter pulses and the root-mean squared (RMS) bandwidth measure. As in the earlier paper, significant bandwidth savings over the traditional multiple-access strategies are obtained. However, in contrast to the rank-conserving approach, the bandwidth gains of this paper are realized by tailoring the signature waveform design to conserve RMS bandwidth via eigenvalue optimization problems.

A generalized diversity channel is introduced that models a variety of wireless communication systems that use time, frequency, multipath, and/or antenna diversity with various interbranch correlations between signaling waveforms and the fading and additive noise processes. In the context of this general model, a systematic approach to the design and analysis of optimum noncoherent differential phase-shift keying (DPSK) receivers is introduced. In particular, it is shown how the minimum error probability (MEP) and the generalized likelihood ratio tests (GLRT) can be applied to obtain optimal noncoherent combining rules. A comparative error-rate analysis of the GLRT and MEP detectors and an ad hoc equal-gain combiner is provided for binary signaling, and the suitability of the three schemes is determined as a function of fading characteristics. The asymptotic bit-error-rate analysis is undertaken for the MEP detector for slow and fast fading channels. An estimator-detector decomposition of the noncoherent MEP rule is obtained which allows an insightful comparative study of the fundamental limits of binary phase-shift keying and DPSK modulation-detection methods for both slow and fast fading. The results of this paper are also applicable to postdecorrelative receivers in multiuser channels.

A systematic approach to decision feedback multiuser detection is introduced for the joint detection of symbols of K simultaneously transmitting users of a synchronous correlated waveform multiple-access (CWMA) channel with Gaussian noise. A new performance criterion called symmetric energy is defined which is a low-noise indicator of the joint error rate that at least one user is detected erroneously. Even the best linear detectors can perform poorly in terms of symmetric energy compared to the maximum-likelihood detector. A general class of decision feedback detectors (DFDs) is defined with O(K) implementational complexity per user. The symmetric energy of arbitrary DFD and bounds on their asymptotic effective energy (AEE) performance are obtained along with an exact bit-error rate and AEE analysis for the decorrelating DFD. The optimum DFD that maximizes symmetric energy is obtained. Each one of the K! optimum, decorrelating, and conventional DFDs, that correspond to the K! orders in which the users can be detected, are shown to outperform the linear optimum, decorrelating, and conventional detectors, respectively, in terms of symmetric energy. Moreover, algorithms are obtained for determining the choice of order of detection for the three DFDs which guarantee that they uniformly (user-wise) outperform their linear counterparts. In addition to optimality in symmetric energy, it is also shown that under certain conditions, the optimum DFD achieves the AEE performance of the exponentially complex maximum-likelihood detector for all users simultaneously. None of the results of this paper make the perfect feedback assumption. The implications of our work on power control for multiuser detection are also discussed.

Noncoherent equalization of inter-symbol interference (ISI) channels for nonorthogonal multipulse modulation (NMM) is introduced. Multipulse modulation (a simple example of which is FSK) is usually seen as a nonlinear modulation technique, so that equalization for such modulation schemes is described as being difficult by Lee and Messerschmitt (1994). However, Varanasi (see Proc. IEEE Intl. Conf. Personal Wireless Communications (ICPWC97), Mumbai (Bombay), India, 1997) showed that ISI can indeed be effectively mitigated in baseband channels, such as with the linear and decision feedback, zero-forcing, multi-input, multi-output (MIMO) equalizers proposed in that work. One of the advantages of multipulse modulation is of course the option of noncoherent reception in bandpass communications. In this paper, we obtain a carrier phase-independent MIMO zero-forcing equalizer. Detection at the output of the zero-forcing equalizer is equivalent to M-ary noncoherent one-shot detection of nonorthogonal signals with unequal energies, a problem that was solved previously by the author and Russ (see Proc. IEEE ICC'97, Montreal, Canada, 1997). Any one of the three noncoherent detection rules obtained therein can be used as post-equalizer units depending on whether the energies of the transmitted waveforms are known or unknown at the receiver.

This paper introduces the problem of noncoherent detection for nonorthogonal multipulse modulation in the context of the synchronous multiuser Gaussian channel. Each user sends an M-ary information symbol by transmitting one of M possibly nonorthogonal waveforms. Furthermore, the M signals of one user are allowed to be correlated with the signals of all other users. A key idea proposed here is that of a noncoherent decorrelative receiver front end. Like its counterpart in single-pulse modulation, this front end eliminates multiuser interference. It therefore reduces the multiuser detection problem into decoupled single-user problems over equivalent noise-enhanced single-user channels. Each equivalent single-user channel is rather general and can be described as one where the waveforms employed are not only correlated, but are also of unequal energies. Several new results pertaining to the design and analysis of optimum and suboptimum noncoherent detectors for this single-user channel are obtained. In the multiuser channel, these detectors constitute the post-decorrelative processing units for each user.

Coherent multiuser detection for linear modulation has been the subject of intense research in the past decade. Noncoherent detection for linear differentially phase shift keyed modulation has also received considerable attention in recent years. This paper considers for the first time the problem of noncoherent multiuser detection for M-ary nonlinear nonorthogonal modulation in the synchronous Gaussian channel. A key idea proposed here is that of a noncoherent decorrelative front end for nonlinear modulation. Like its counterpart in linear modulation, that front-end eliminates multiuser interference and reduces the multiuser detection problem into that of single-user detection over an equivalent (noise-enhanced) single-user channel. However, the M effective signals of the equivalent single-user channel are correlated and of unequal energy. Noncoherent detection even in this single-user channel has been an open problem until now. We derive the optimum detector for this channel. It is unfortunately too complicated to implement or analyze. Two suboptimal detectors are hence proposed depending on whether the energies of the M signals are known or unknown at the receiver. For unknown energies, the generalised likelihood ratio test leads to a detector which is easy to implement. Error probability bounds are obtained for this detector. It is shown to be near-far resistant (in contrast to the conventional detector). For known energies, an asymptotic series expansion of a special function involved in the optimum noncoherent decision rule leads to the other suboptimum detector. Its analysis is more difficult but we nevertheless obtain exact expressions for error probability for binary modulation and bounds on error probability in the M-ary case. This detector can outperform the GLRT detector by a significant margin. Both detectors far outperform the conventional single-user detector.

Coherent multiuser detection for linear modulation has been the subject of much research. Noncoherent detection for linear differentially phase shift keyed modulation has also received considerable attention, whereas research in the field of noncoherent detection for nonlinear modulation in correlated-waveform multiple access channels has been far more limited. This paper considers for the first time the problem of noncoherent multiuser detection for binary, nonlinear, nonorthogonal signaling over a synchronous, frequency-nonselective Rayleigh fading channel. A minimum error probability multiuser detector is derived and analyzed through asymptotically convergent upper and lower bounds on error probability. This detector has an exponential (in the number of users) time complexity. Consequently, a suboptimum noncoherent decorrelative energy detector (NDED) is proposed, whose complexity is linear in the number of users. The NDED is analyzed exactly in terms of error probability. An asymptotic performance analysis is undertaken for the NDED and, to serve as a comparison, for the conventional detector. It is shown that the former is near-far resistant, the latter, however, near-far limited.

Optimum time-limited signal sets of equal and unequal energies are obtained under root mean square (RMS) bandwidth constraints. The total capacity and the total asymptotic efficiency of the PAM synchronous Gaussian CDMA (PSG-CDMA) channel are considered as the optimality criteria. The latter measure is monotonic with the determinant of the correlation matrix, R, and the former is monotonic with det(I+/spl sigma//sup -2/R), where /spl sigma//sup 2/ represents the noise level. Average as well as maximum RMS bandwidth constraints are considered in the equal-energy case, and the energy-weighted RMS bandwidth constraint is considered for unequal energy signals. For the equal-energy problem, signal sets are found that simultaneously optimize the total asymptotic efficiency under both average and maximum RMS bandwidth constraints. For the total capacity measure, such simultaneously optimal signal sets are also obtained, albeit under the restriction that the number of signals n be a Hadamard matrix dimension. When the Hadamard dimension is in particular a power of two, we obtain optimum signal sets that are shown to yield equal optimum multiuser detector asymptotic efficiencies for all users of an uncoded PSG-CDMA channel. Unequal energy signal sets are also found under an energy-weighted RMS bandwidth constraint for both optimality criteria.

We study multiuser receiver design and analysis for synchronous code-division multiple-access (CDMA) channels with time-varying Rayleigh fading. Starting from an error probability criterion, we first derive a near-optimum receiver for this channel that admits a detector-estimator decomposition, has certain asymptotic optimality properties and a complexity which is independent of the length of the observation interval. The performance of this detector is analytically characterized and contrasted with that of the optimal multiuser detector for the time-invariant (or static) CDMA Rayleigh-fading channel when it is implemented over the time-varying channel. Notable among our conclusions is the fact that, unlike the static channel multiuser detector, the time-varying channel detector is able to withstand not only the estimated interference from the other system users, but also, the residual interference (that cannot be estimated) arising out of imperfect estimation of the interferer fading parameters. Using estimation error covariance information, this detector shows flexibility in accommodating a wide range of interferer fading conditions.

A group detector jointly detects a group of users, and a parallel group detection scheme is a bank of J independently operating group detectors, one for each group of a J group partition of the K transmitting users of a code-division multiple-access (CDMA) channel. In this paper, two group detectors are introduced for the frequency-selective Rayleigh fading (FSRF) CDMA channel. While the optimum multiuser detector has a time complexity per symbol (TCS) of O(M/sup K//K) for M-ary signaling, each of the two group detectors has a TCS of O(M(|G|)/|G|) where |G| is the group size. Hence, there are parallel group detection schemes, based on each of the two group detectors, that satisfy a wide range of complexity constraints that result from the choice of partition. Each of the two group detectors is minimax optimal in the corresponding conditional group near-far resistance measure. Furthermore, a succinct indicator of the average BER over high SNR regions is defined via the asymptotic efficiency. A lower bound and an exact formula for the asymptotic efficiency are derived for the first and second group detectors, respectively. The group detection approach for the FSRF-CDMA channel generalizes previous approaches to the complexity-performance tradeoff problem. It yields the optimum detector when the group size is K. When the group size is equal to one, the first group detector results in a new optimum linear detector and the second reduces to a recently proposed suboptimum linear detector. All other nontrivial partitions yield new multiuser detectors whose performances are commensurate with their complexities.

The concept of group detection Is introduced to address the design of suboptimum multiuser detectors for code-division multiple-access (CDMA) channels. A group detection scheme consists of a bank of P group detectors, one each for detecting the information symbols of users in each group of a P group partition of the K simultaneously transmitting users. In a parallel group detection scheme, these group detectors operate independently, whereas in a sequential scheme, each group detector. Uses the decisions of the previous group detectors to successively cancel the interference from those users. Group detectors based on the generalized likelihood ratio test (GLRT) are obtained for the synchronous Gaussian CDMA channel. The complexity of these detectors is exponential in the group size, whereas that of the optimum detector is exponential in K. Since the partition of users is a design parameter, group sizes can be chosen to satisfy a wide range of complexity constraints. A key performance result is that the GLRT group detectors are optimally group near-far resistant. Furthermore, upper and lower bounds on the asymptotic efficiency of the sequential group detectors are derived. These bounds reveal that the sequential group detectors can, under certain conditions, perform as well as GLRT group detectors of much larger group sizes. Group detection provides a unifying approach to multiuser detection. When the users are partitioned into K single-user groups, the GLRT, a modified form of GLRT, and the sequential group detectors reduce to previously proposed suboptimal detectors; namely, the decorrelator, the two-stage detector, and the decorrelating decision-feedback detector, respectively. For the other nontrivial partitions, the group detectors are new and have a performance that is commensurate with their complexity.>

Multiuser detection for asynchronous code division multiple access (CDMA) data transmission over the time-dispersive two-path Rician fading channel is considered. The multiuser maximum likelihood sequence detector (MLSD) is derived, and an equivalence of the fading channel to an asynchronous Gaussian intersymbol interference (AGISI) CDMA channel is established. However, the MLSD is found to be implementationally infeasible and this motivates the derivation of the optimum linear detector with near/far resistance as the performance criterion. The optimally near/far resistant linear time-invariant K-user detector is shown to consist of a cascade of a 2 K input/K output linear multiuser diversity combining filter followed by a K input/K output decorrelator that is designed for the equivalent AGISI/CDMA channel. This detector solves the near/far problem and also supports significantly higher bandwidth efficiencies for CDMA communication over the fading channel than does the conventional near/far limited single-user diversity combiner. The performance penalties incurred by multiuser detectors designed for the Gaussian channel when used over the Rician fading channel are also analytically characterized. It is shown that these penalties can be significant, making the case for the use of multiuser detectors optimized for this fading channel, particularly the optimum linear detector due to its relative implementational simplicity.>

Synchronous code division multiple access (CDMA) data transmission over a non-selective Rician fading channel is considered, where the faded signal components arrive at the receiver in synchronism with the specular signal component. Under the assumption that the fading parameters are uncorrelated, this fading CDMA channel is shown to be equivalent to a Gaussian CDMA channel over which a modified signal set is employed. A fading counterpart of the multiuser asymptotic efficiency performance measure is defined. The asymptotic efficiencies of the optimum, decorrelating, and conventional detectors designed for the fading channel are derived. The conventional detector, which has low complexity, is shown to degrade rapidly in near-far environments. The optimal detector for the fading channel exhibits a significant improvement in performance but at the price of a computational complexity that increases exponentially with the number of users. The linear decorrelating detector for the fading case is optimally near-far resistant. The asymptotic efficiencies of multiuser detectors designed for the Gaussian channel when employed over the Rician fading channel are also obtained, thereby quantifying the loss in performance incurred by these mismatched detectors.>

The noncoherent demodulation of multiple differentially phase-shift-keyed signals transmitted simultaneously over an asynchronous code-division multiple-access (CDMA) channel with white Gaussian background noise is considered. A class of bilinear detectors is defined with the objective of obtaining the optimal bilinear detector. The optimality criterion considered is near-far resistance that denotes worst-case asymptotic efficiency over the signal energies and phases which are unknown at the receiver. The optimal bilinear detector is therefore obtained by solving a minimax optimization problem. In the finite packet length case, this detector is shown to be a time-varying multiinput multioutput linear decorrelating filter followed by differential decision logic. In the limit as packet lengths go to infinity, the time-varying decorrelating detector is replaced by a time-invariant multiinput multioutput decorrelating filter. Several properties of the optimally near-far resistant detector are established.>

Communication networks using code division multiple access (CDMA) include applications where several packets of information are transmitted synchronously and simultaneously over a common channel. Consideration is given to the problem of simultaneously demodulating every packet from such a transmission. A nonlinear detection scheme based on a linear complexity multistage multiple-access interference rejection algorithm is studied. A class of linear detectors is considered as constituting the first stage for the multistage detector. A bit-error probability comparison of the linear and multistage detectors is undertaken. It is shown that the multistage detectors are capable of achieving considerable improvements over the linear detectors, particularly in near-far situations, i.e., in the demodulation of weak signals in the presence of strong interfering signals. This problem has been of primary concern for currently operational CDMA systems.>

The noncoherent demodulation of differentially phase-shift keyed signals transmitted simultaneously via a synchronous code-division multiple-access (CDMA) channel is studied under the assumption of white Gaussian background noise. A class of noncoherent linear detectors is defined with the objective of obtaining the optimal one. The performance criterion considered is near-far resistance that denotes worst-case multiuser asymptotic efficiency over near-far environments. It is shown that the optimal linear detector is a noncoherent decorrelating detector. The commonality between the properties of the decorrelating detectors for coherent and noncoherent channels is established. In particular, it is shown that no other differential phase-shift keying (DPSK), multiuser detector achieves a higher near-far resistance than does the noncoherent decorrelator.>