This paper investigates the downlink spectral efficiency of low Earth orbit (LEO) satellite constellations, where spectral efficiency refers to the entire network's total data rate per unit spectrum per unit area on the Earth's surface. For practicality, all links employ single-user codebooks and treat interference as noise. A key finding is that, unlike terrestrial networks, the spectral efficiency of LEO constellations does not increase indefinitely with satellite density. Under typical assumptions about antenna array beam widths, this study explores the satellite density that maximizes spectral efficiency. As a special case, a regular deployment of satellites and ground terminals is analyzed across various densities. Simulation results reveal that regular configurations achieve higher spectral efficiency compared to random configurations. Furthermore, while the total downlink capacity of any LEO constellation remains significantly lower than that of terrestrial networks, there is substantial potential for growth-up to a few orders of magnitude-compared to current capacity levels.

We present distributed methods for jointly optimizing Intelligent Reflecting Surface (IRS) phase-shifts and beamformers in a cellular network. The proposed schemes require knowledge of only the intra-cell training sequences and corresponding received signals without explicit channel estimation. Instead, an achievable sum-rate objective is estimated via sample means and maximized directly. This automatically includes and mitigates both intra- and inter-cell interference provided that the uplink training is synchronized across cells. Different schemes are considered that limit the set of known training sequences from interferers. With MIMO links an iterative synchronous bi-directional training scheme jointly optimizes the IRS parameters with the beamformers and combiners. Simulation results show that the proposed distributed methods show a modest performance degradation compared to centralized channel estimation schemes, which estimate all channels including all cross-channels, and perform significantly better than decentralized channel estimation schemes which ignore the inter-cell interference.

We study distributed algorithms for joint adaptation of precoding and combining filters in frequency division duplex (FDD) multiple-input multiple-output (MIMO) cellular systems. Our approach extends bi-directional training (BiT), designed for time division duplex (TDD) systems, to FDD systems where uplink/downlink reciprocity may not apply. An analysis of the performance loss due to different uplink-downlink frequencies in a point-to-point scenario, shows that a direct application of BiT gives mismatched precoders with substantial performance degradation. We first propose an algorithm assuming each base transceiver station (BTS) knows the uplink and downlink channels of mobiles within the cell. We then consider the scenario where neither the BTSs nor the mobiles have a priori channel state information. Our proposed approaches assume angular reciprocity characterized by angles of arrival/departure that vary predictably with frequency. Hence spatial beams corresponding to angles of arrival can be turned around to the corresponding angles of departure in the paired band. We present three methods, differing in how the angular decomposition is applied and used, namely, to reconstruct the combiner directly, or to reconstruct the received signal. Simulation results indicate that when the multipath is sufficiently sparse, most of achievable gain with channel reciprocity and TDD can be recovered.

Small-cells in licensed spectrum and unlicensed access via Wi-Fi are two commonly used options to reduce the demand for conventional macro-cellular networks and to provide expanded wireless services to low mobility users. The mix of these technologies depends on both the decisions made by wireless service providers (SPs) that seek to maximize revenue, and the allocation of licensed and unlicensed spectrum by regulators. In this paper, we study these interactions and consider heterogeneous cellular networks together with unlicensed access. Both a single monopoly SP and multiple competing SPs are investigated. The SPs split any available licensed spectrum into two separate bands for macro- and small-cells, which are then used to serve two types of users: mobile and fixed. Mobile users must be served by macro-cells only, whereas fixed users can be served by either macro- or small-cells, or alternatively by unlicensed access service. While the providers charge a (different) price per unit rate for licensed access services (macro- or small-cell), unlicensed access is free. We formulate a sequential game in which the users choose a service that yields the highest payoff, and the providers allocate bandwidth across macro-/small-cells. In general, the competition from unlicensed access results in inefficient (albeit unique) market equilibria, and in many cases all or some SPs allocate no resources to small-cell deployment. We conclude by showing how our framework can also be used to optimize the fraction of unlicensed spectrum when new bandwidth becomes available.

Small-cells deployed in licensed spectrum can expand wireless service to low mobility users, which potentially reduces the demand for macro-cellular networks with wide-area coverage. Introducing such heterogeneity also makes network resource allocation more complicated. To understand these challenges and tradeoffs we present a two-tier heterogeneous wireless network model with two types of users: mobile users that can only connect to macro-cells; and fixed users that can associate with either macro-cells or small-cells. We study pricing strategies and bandwidth allocation across macro- and small-cells, assuming both monopoly and competitive Service Providers (SPs). For a monopoly SP, we characterize the revenue-maximizing prices and bandwidth allocations. We then consider a competitive scenario, and we show the existence of a unique Nash equilibrium. The possible Nash equilibria for different system parameters are sorted into four categories corresponding to whether or not different SPs assign bandwidth to the macro- and/or small-cells. We also study the allocations that maximize social welfare. For the competitive scenario, we characterize the conditions under which the optimal social welfare is obtained in equilibria as the number of SPs tends to infinity. Case study examples and numerical results illustrate the corresponding pricing and bandwidth allocations.

We study distributed rank selection in a multi-cell wideband cellular network with multiple antennas per node. The rank for a particular mobile is the number of independent data streams across all sub-carriers and antennas. Rank selection then involves both spatial multiplexing and sub-carrier allocations. We propose assigning frequency-space signatures across the data streams to unify the rank assignment over those two dimensions. A sum rate maximization problem is formulated for allocating the signatures and is solved using distributed bi-directional training. Starting with full-rank transmission, the precoders are iteratively updated, and the optimized rank for a mobile is the number of signatures assigned significant power after convergence. For systems with a large number of antennas and sub-carriers, it may take many iterations to converge. To reduce the training period, we propose using deep learning for estimating the ranks across mobiles before the precoder optimization phase. With a trained Deep Neural Network (DNN), each mobile estimates its own transmission rank directly from its local channel information and locations of neighboring mobiles. Simulation results show that the DNNs can significantly reduce the training period for precoder adaptation while achieving performance close to that with jointly optimized precoders and ranks. This is illustrated with different system parameters and mobile distributions.

We study distributed algorithms for joint adaptation of precoding and combining filters in frequency-division duplex (FDD) multiple-input multiple-output (MIMO) cellular systems. Neither the base stations nor the mobiles have a priori channel state information, and the transmit/receive filters are directly adapted through training. We propose extensions of bi- directional training (BiT), designed for time- division duplex (TDD) systems, to FDD systems where uplink-downlink reciprocity may not apply. A direct application of BiT can give mismatched precoders with substantial performance degradation. Our approach assumes angular reciprocity, that is, the channel multipath, which causes the frequency selectivity, is characterized by angles of arrival/departure that vary predictably with frequency. Hence spatial beams corresponding to angles of arrival can be turned around to point towards the corresponding angles of departure in the paired band. We present three methods based on this general approach with different complexity for angular estimation and selection. Simulation results indicate that when the multipath is sufficiently sparse, most of the achievable gain with channel reciprocity and TDD can be recovered.

This paper studies initial beam acquisition in a millimeter wave network consisting of multiple access points (APs) and mobile devices. A training protocol for joint estimation of transmit and receive beams is presented with a general frame structure consisting of an initial access sub-frame followed by data transmission sub-frames. During the initial subframe, APs and mobiles sweep through a set of beams and determine the best transmit and receive beams via a handshake. All pilot signals are narrowband (tones), and the mobiles are distinguished by their assigned pilot frequencies. Both non-coherent and coherent beam estimation methods based on, respectively, power detection and maximum likelihood (ML) are presented. To avoid exchanging information about beamforming vectors between APs and mobiles, a local maximum likelihood (LML) algorithm is also presented. An efficient fast Fourier transform implementation is proposed for ML and LML to achieve high-resolution. A system-level optimization is performed in which the frame length, training time, and training bandwidth are selected to maximize a rate objective taking into account blockage and mobility. Simulation results based on a realistic network topology are presented to compare the performance of different estimation methods and training codebooks, and demonstrate the effectiveness of the proposed protocol.

Mobile collaborative Internet access (MCA) enables mobile users to share their Internet through flexible tethering arrangements. This can potentially make better use of network resources. However, from a mobile network operator's (MNO's) viewpoint, it can either reduce revenue or increase congestion, and thus has been blocked by some MNOs in practice. We propose a hybrid pricing framework for MNOs who charge users separately for access and tethering. This scheme serves to coordinate the tethering decisions of mobile users with MNO network management objectives. We analyze the MNOs' equilibrium pricing strategies in both cooperative and competitive scenarios. In the cooperative scenario, at the equilibrium, each user's cost is independent of any chosen tethering links. We then characterize the optimal hybrid pricing strategies of MNOs in this scenario. For the competitive scenario, we formulate the MNOs' competitive interactions as a pricing game, and we show that MNO competition leads to equalized prices for users if an equilibrium exists but does not guarantee its existence. Both insights motivate a quantity competition game, which is shown to guarantee equilibrium. Simulation results show that in scenarios of interest the proposed hybrid pricing schemes can double both MNOs' profit and users' payoff and such improvements increase with the degree of network heterogeneity.

Hybrid beamforming (BF) is a promising solution for massive MIMO with limited RF chains. To reduce the amount of pilot overhead for channel estimation, compressed sensing techniques that exploit channel sparsity have been proposed. One key issue is how to design the RF (analog) training vectors to achieve higher BF gain with fewer pilots. Specifically, narrow-beam RF training requires large pilot overhead for finding strongest paths, and random RF training suffers from low BF gain. We propose to use a mixture of narrow-beam and random RF training vectors, and optimize the fraction of the two sets of RF training vectors based on channel support side information (CSSI) at the BS. We show that this optimized fraction exhibits a phase transition: when the CSSI accuracy exceeds a certain threshold, the maximum number of narrow-beam RF training vectors should be used to focus beams in all directions indicated by the CSSI. Otherwise, only random RF training vectors should be used to explore the unknown channel support. Moreover, we derive closed-form bounds on the channel estimation error. Both the analysis and simulations show that the proposed method can achieve substantial gains over various baseline methods.

Downlink weighted sum rate maximizing beamformer design is considered for joint processing (JP) coordinated multi-point (CoMP) transmission. Global channel state information exchange, required by the centralized JP CoMP processing, is in many scenarios impractical due to the backhaul latency and capacity requirements. Low overhead decentralized processing enables JP even with limited backhaul capacity. The proposed best response (BR) design also takes into account the possibly non-orthogonal pilot design and noisy pilot estimation. By allowing spatially overlapping pilot sequences, the transceiver processing requires only the channel state information of locally served users. This enables more flexible pilot design and makes the proposed approach realizable in practical time correlated and noisy channel conditions. Furthermore, the proposed BR algorithm provides low signaling overhead for systems with limited backhaul capacity. Robustness for fading channel conditions and limited pilot resources is shown by numerical examples.

Recently, compressive channel estimation (CE) has been proposed to reduce the pilot overhead for massive MIMO with limited RF chains. One key issue is how to design the RF (analog) training vectors to achieve higher beamforming (BF) gain with fewer pilots. Specifically, narrow-beam RF training requires large pilot overhead for finding strongest paths, and random RF training suffers from low BF gain. We propose to use a mixture of narrow-beam and random RF training vectors, and exploit the channel support side information (CSSI) at the BS to do joint RF training and compressive CE. The narrow-beam RF training vectors are used to achieve a high BF gain, and the random RF training vectors are used to explore the unknown channel support to reduce the pilot overhead. Moreover, we derive closed-form bounds on the CE error. Both the analysis and simulations show that the proposed method can achieve substantial gains over various baseline methods.

Mobile Crowdsourced Access (MCA) enables mobile users (MUs) to share their Internet connections by serving as tethers to other MUs, hence can improve the quality of service of MUs as well as the overall utilization of network resources. However, MCA can also reduce the revenue-generating mobile traffic and increase the network congestion for mobile network operators (MNOs), and thus has been blocked by some MNOs in practice. In this work, we reconcile the conflicting objectives of MNOs and MUs by introducing a pricing framework for MCA, where the direct traffic and tethering traffic are charged independently according to a data price and a tethering price, respectively. We derive the optimal data and tethering prices systematically for MUs with the α-fair utility in two scenarios with cooperative and competitive MNOs, respectively. We show that the optimal tethering prices are zero and the optimal usage-based data prices are identical for all MUs, in both the cooperative and competitive scenarios. Such optimal pricing schemes will lead to mutually beneficial results for MNOs and MUs. Our simulation results show that the proposed pricing scheme approximately triples both the MNOs' profit and the MUs' payoff when the MNOs cooperate, comparing to the case where MCA is blocked. Moreover, competition among MNOs will decrease MNOs' profit and further increase the MUs' payoff.

Joint allocation of spectrum and user association is considered for a large cellular network. The objective is to optimize a network utility function such as average delay given traffic statistics collected over a slow timescale. A key challenge is scalability: given n access points (APs), there are O(2n) ways in which the APs can share the spectrum. The number of variables is reduced from O(2n) to O(nk), where k is the number of users, by optimizing over local overlapping neighborhoods, defined by interference conditions, and by exploiting the existence of sparse solutions in which the spectrum is divided into k+1 segments. We reformulate the problem by optimizing the assignment of subsets of active APs to those segments. An ℓoconstraint enforces a one-to-one mapping of subsets to spectrum segments, and an iterative (reweighted ℓ1) algorithm is used to find an approximate solution. Numerical results for a network with 100 APs serving several hundred users show the proposed method achieves a substantial increase in total throughput relative to benchmark schemes.

Gradient based downlink beamforming with low computational complexity and training overhead is proposed for joint processing (JP) coordinated multi-point transmission (CoMP). Pilot contamination and estimation noise are taken into account in the pilot based transceiver training process. The proposed designs enable decentralized JP when the backhaul and computational limitations do not allow centralized processing. The impact of backhaul quantization is also considered. The stochastic gradient based designs are shown to be more robust to feedback quantization when compared to more complex methods. The trade-off between the implementation complexity and performance is established for the proposed algorithms. The results show that low complexity decentralized JP CoMP is feasible even with limited backhaul capacity.

In massive multiple-input multiple-output (MIMO) systems, acquisition of the channel state information at the transmitter side (CSIT) is crucial. In this paper, a practical CSIT estimation scheme is proposed for frequency division duplexing (FDD) massive MIMO systems. Specifically, each received pilot symbol is first quantized to one bit per dimension at the receiver side and then the quantized bits are fed back to the transmitter. A joint one-bit compressed sensing algorithm is implemented at the transmitter to recover the channel matrices. The algorithm leverages the hidden joint sparsity structure in the user channel matrices to minimize the training and feedback overhead, which is considered to be a major challenge for FDD systems. Moreover, the one-bit compressed sensing algorithm accurately recovers the channel directions for beamforming. The one-bit feedback mechanism can be implemented in practical systems using the uplink control channel. Simulation results show that the proposed scheme nearly achieves the maximum output signal-to-noise-ratio for beamforming based on the estimated CSIT.

Facing the challenge of meeting ever-increasing demand for wireless data, the industry is striving to exploit large swaths of unlicensed spectrum, which supports open access. Major standards bodies are currently considering a proposal to retool and deploy long term evolution (LTE) technologies in unlicensed bands. This paper studies the fundamental question of how the unlicensed spectrum can be shared by strategic operators to mitigate suffering from the tragedy of the commons. A class of general utility functions is considered. The spectrum sharing problem is formulated as a repeated game over a sequence of time slots. It is first shown that a simple static sharing scheme allows a given set of operators to reach a subgame perfect Nash equilibrium for mutually beneficial sharing. The question of how many operators will choose to enter the market is also addressed by studying an entry game. A sharing scheme, which allows dynamic spectrum borrowing and lending between operators, is then proposed to address time-varying traffic and proved to achieve perfect Bayesian equilibrium. Numerical results show that the proposed dynamic sharing scheme outperforms static sharing, which in turn achieves much higher revenue than uncoordinated full-spectrum sharing. Implications of the results for the standardization and deployment of LTE in unlicensed bands (LTE-U) are also discussed.

In future networks, an operator may employ a wide range of access points using diverse radio access technologies (RATs) over multiple licensed and unlicensed frequency bands. This paper studies centralized user association and spectrum allocation across many access points in such a heterogeneous network. Such centralized control is on a relatively slow timescale to allow information exchange and joint optimization over multiple cells. This is in contrast and complementary to distributed scheduling on a fast timescale. A queueing model is introduced to capture the lower spectral efficiency, reliability, and additional delays of data transmission over the unlicensed bands due to contention and/or listen-before-talk requirements. Two optimization-based spectrum allocation schemes are proposed along with efficient algorithms for computing the allocations. The proposed solutions take into account traffic loads, network topology, as well as external interference levels in the unlicensed bands. Packet-level simulation results show that the proposed schemes significantly outperform orthogonal and full-frequency-reuse allocations under all traffic conditions.

A scalable framework is developed to allocate radio resources across a large number of densely deployed small cells with given traffic statistics on a slow timescale. Joint user association and spectrum allocation is first formulated as a convex optimization problem by dividing the spectrum among all possible transmission patterns of active access points (APs). To improve scalability with the number of APs, the problem is reformulated using local patterns of interfering APs. To maintain global consistency among local patterns, inter-cluster interaction is characterized as hyper-edges in a hyper-graph with nodes corresponding to subcarriers allocated to APs. A scalable solution is obtained by iteratively solving a convex optimization problem for bandwidth allocation with reduced complexity and followed by a global spectrum allocation using hyper-graph coloring. Numerical results demonstrate the proposed solution for a network with 100 APs and several hundred user equipment. For a given quality of service, the proposed scheme can often increase the network capacity severalfold compared with assigning each user to the strongest AP with full-spectrum reuse.

Small cells deployed in licensed spectrum and unlicensed access via WiFi provide different ways of expanding wireless services to low mobility users. That reduces the demand for conventional macro-cellular networks, which are better suited for wide-area mobile coverage. The mix of these technologies seen in practice depends in part on the decisions made by wireless service providers that seek to maximize revenue, and allocations of licensed and unlicensed spectrum by regulators. To understand these interactions we present a model in which a service provider allocates available licensed spectrum across two separate bands, one for macro- and one for small-cells, in order to serve two types of users: mobile and fixed. We assume a service model in which the providers can charge a (different) price per unit rate for each type of service (macro- or small-cell); unlicensed access is free. With this setup we study how the addition of unlicensed spectrum affects prices and the optimal allocation of bandwidth across macro-/small-cells. We also characterize the optimal fraction of unlicensed spectrum when new bandwidth becomes available.

Next generation (5G) cellular networks are expected to be supported by an extensive infrastructure with many-fold increase in the number of cells per unit area compared to today. The total energy consumption of base transceiver stations (BTSs) is an important issue for both economic and environmental reasons. In this paper, an optimization-based framework is proposed for energy-efficient global radio resource management in heterogeneous wireless networks. Specifically, with stochastic arrivals of known rates intended for users, the smallest set of BTSs is activated with jointly optimized user association and spectrum allocation to stabilize the network. The average delay is subsequently minimized. The scheme can be carried out periodically on a relatively slow timescale to adapt to aggregate traffic variations and average channel conditions. Numerical results show that the proposed scheme significantly reduces energy consumption and increases quality of service compared to existing schemes.

A distributed interference cancellation scheme for cellular networks is considered, in which a subset of receivers forward their decoded messages to another subset of receivers. The messages can then be used to cancel interference with estimated cross-channel gains. A distributed power control algorithm is presented that harnesses the gain of interference cancellation and that considers channel estimation error. The algorithm is based on the exchange of interference prices, but in this case, the local power updates are not concave due to nonlinear terms introduced by channel estimation errors. A partial cancellation scheme is then presented, where the power updates are derived in closed form. We show that the algorithm converges to a local optimum of the weighted sum-rate maximization problem. Two methods for sorting users into the two groups that, respectively, forward and receive the decoded messages are presented. The first is sequential and is shown to converge to a local optimum. The second is a simple heuristic that is based on a stochastic geometric approach. Numerical results show that power control and adaptive partitioning of the users can add substantial gains to interference cancellation.

Decentralized downlink beamformer design for coherent coordinated multi-point transmission is proposed with weighted sum rate maximization system performance objective. The weighted sum rate is maximized by successive convex approximation of the corresponding weighted mean-squared error minimization problem. Decentralized beam coordination is achieved by employing a best response design, where each base station designs its own precoders in parallel assuming fixed transmission from the adjacent cells. After each beamformer update, the fixed terms are updated according to the solutions of the cooperating transmitters. The proposed design incorporates a bi-directional beamformer signaling scheme to improve the convergence properties. This scheme exploits the time division duplexing frame structure and is shown to improve the training latency of the iterative transceiver design. Furthermore, the improved transceiver convergence rate enables periodic beamformer reinitialization, which greatly improves the achieved system performance in dense networks.

We address the problem of uplink co-operative reception with constraints on both backhaul bandwidth and the receiver aperture, or number of antenna signals that can be processed. The problem is cast as a network utility (weighted sum rate) maximization subject to computational complexity and architectural bandwidth sharing constraints. We show that a relaxed version of the problem is convex, and can be solved via a dual-decomposition. The proposed solution is distributed in that each cell broadcasts a set of demand prices based on the data sharing requests they receive. Given the demand prices, the algorithm determines an antenna/cell ordering and antenna-selection for each scheduled user in a cell. This algorithm, referred to as LiquidMAAS, iterates between the preceding two steps. Simulations of realistic network scenarios show that the algorithm exhibits fast convergence even for systems with large number of cells.

Next generation cellular networks will be heterogeneous with dense deployment of small cells in order to deliver high data rate per unit area. Traffic variations are more pronounced in a small cell, which in turn lead to more dynamic interference to other cells. It is crucial to adapt radio resource management to traffic conditions in such a heterogeneous network (HetNet). This paper studies the optimization of spectrum allocation in HetNets on a relatively slow timescale based on average traffic and channel conditions (typically over seconds or minutes). Specifically, in a cluster with n base transceiver stations (BTSs), the optimal partition of the spectrum into 2n segments is determined, corresponding to all possible spectrum reuse patterns in the downlink. Each BTS's traffic is modeled using a queue with Poisson arrivals, the service rate of which is a linear function of the combined bandwidth of all assigned spectrum segments. With the system average packet sojourn time as the objective, a convex optimization problem is first formulated, where it is shown that the optimal allocation divides the spectrum into at most n segments. A second, refined model is then proposed to address queue interactions due to interference, where the corresponding optimal allocation problem admits an efficient suboptimal solution. Both allocation schemes attain the entire throughput region of a given network. Simulation results show the two schemes perform similarly in the heavy-traffic regime, in which case they significantly outperform both the orthogonal allocation and the full-frequency-reuse allocation. The refined allocation shows the best performance under all traffic conditions.

Most work on wireless network resource allocation use physical layer performance such as sum rate and outage probability as the figure of merit. These metrics may not reflect the true user QoS in future heterogenous networks (HetNets) with many small cells, due to large traffic variations in overlapping cells with complicated interference conditions. This paper studies the spectrum allocation problem in HetNets using the average packet sojourn time as the performance metric. To be specific, in a HetNet with K base terminal stations (BTS's), we determine the optimal partition of the spectrum into 2Kpossible spectrum sharing combinations. We use an interactive queueing model to characterize the flow level performance, where the service rates are decided by the spectrum partition. The spectrum allocation problem is formulated using a conservative approximation, which makes the optimization problem convex. We prove that in the optimal solution the spectrum is divided into at most K pieces. A numerical algorithm is provided to solve the spectrum allocation problem on a slow timescale with aggregate traffic and service information. Simulation results show that the proposed solution achieves significant gains compared to both orthogonal and full spectrum reuse allocations with moderate to heavy traffic.

Two decentralized minimum mean-squared error downlink beamformer designs are proposed for multiple-input single-output coherent coordinated multi-point transmission. We propose a parallel beamformer design with a fast initial rate of convergence for systems with relatively few cooperative base stations (BSs). An alternating direction method of multipliers based design is provided for more complex systems with a large number of cooperating BSs. Support for data sharing among the serving BSs is assumed over limited back-haul connectivity. Channel state information (CSI) is not shared among the cooperating transmitters, and, thus, only local CSI is available at each BS via uplink pilot signaling.

This paper considers a one-dimensional model for a cellular network in which neighboring base stations may cooperatively transmit to users located between them. A distributed algorithm is given for deciding on the power allocation of each base station as well as on which users to serve either cooperatively or individually. The algorithm is proven to converge monotonically and the sum rate performance of different limit points is illustrated. Numerical results are presented that illustrate the performance of the algorithm in terms of sum rate, convergence speed and a fairness metric.

In a limited form cellular providers have long shared spectrum in the form of roaming agreements. The primary motivation for this has been to extend the coverage of a wireless carrier's network into regions where it has no infrastructure. As devices and infrastructure become more agile, such sharing could be done on a much faster time-scale and have advantages even when two providers both have coverage in a given area, e.g., by enabling one provider to acquire “overflow” capacity from another provider during periods of high demand. This may provide carriers with an attractive means to better meet their rapidly increasing bandwidth demands. On the other hand, the presence of such a sharing agreement could encourage providers to underinvest in their networks, resulting in poorer performance. We adapt the newsvendor model from the operations management literature to model such a situation and to gain insight into these trade-offs. In particular, we analyze the structure of revenue-sharing contracts that incentivize both capacity sharing and increased access for end-users.

We analyze the achievable sum rate of the Gaussian MIMO broadcast channel. We first consider Multiple-Input Single-Output (MISO) channels and derive the large system limit of the sum capacity as the number of users and transmit antennas go to infinity with a fixed ratio. We then consider Multiple-Input Multiple-Output (MIMO) broadcast channels and fix the number of users and let the number of transmit and receive antennas tend to infinity with fixed ratio. As in this case an asymptotic expression for sum capacity is hard to obtain, we evaluate the large system sum rate corresponding to successive zero-forcing beamforming with Dirty-Paper Coding. The analysis gives a lower bound on the large system sum capacity, which is numerically observed to be quite close. In addition, large system analysis is applied to estimate the relatively small performance losses with respect to sum capacity of successive zero-forcing beamforming with and without Dirty-Paper Coding in finite MISO systems.

Markets are often viewed as a key ingredient in facilitating more efficient dynamic spectrum access. In this paper we consider how such spectrum markets are influenced by a key property of the wireless medium: interference. Interference can result in "complementarities" among the "spectrum goods" being traded, which complicates the design of an efficient market mechanism. We consider several alternative models for defining such spectrum goods, and explore the impact of these choices on the complexity of the resulting market.

This paper studies the error exponent of block coding over an additive white Gaussian noise channel where a fraction ($f$) of the channel output symbols are revealed to the transmitter through noiseless feedback. If the code rate exceeds$fC$, where$C$is the channel capacity, then the probability of decoding error cannot decay faster than exponentially with block length. However, if the code rate is below$fC$, the error probability can decrease faster than exponentially with the block length, as with full feedback ($f=1$). This is achieved by combining a feedback code and a forward error control code, and jointly decoding them at the receiver. This scheme can attain higher reliability than rate splitting in which feedback and forward codes independently encode separate source messages.

This paper studies the optimal use of limited-rate feedback of channel state information (CSI) in the case of a wideband multicarrier channel with multiple transmit antennas and a single receive antenna. With full knowledge of the CSI, the receiver should compute the optimal beamforming vectors, jointly quantize them, and feed them back to the transmitter. The achievable forward data rate depends on the rate of the feedback link. The optimal tradeoff between the forward and feedback rates is characterized using rate distortion theory in the limit of infinite number of subcarriers with fixed amount of feedback per subcarrier. The distortion metric is the difference between the forward rate achieved with limited feedback and the capacity with perfect CSI at the transmitter. The rate distortion function gives the forward rate as a function of the feedback rate. Numerical results show that to achieve a target forward rate, the required feedback rate can be substantially reduced by joint quantization of the beamformers across subcarriers. A simple quantizer amenable to practical implementation is shown to approach the rate distortion bound with near-linear computational complexity.

Multicell joint processing can mitigate inter-cell interference and thereby increase the spectral efficiency of cellular systems. Most previous work has assumed phase-aligned (coherent) transmissions from different base transceiver stations (BTSs) so that the signals superpose coherently at each receiver, which is difficult to achieve in practice. In this work, a noncoherent cooperative transmission scheme for the downlink is studied, which does not require phase alignment. The focus is on jointly serving two users in adjacent cells sharing the same resource block. The two BTSs partially share their messages through a backhaul link, and each BTS can transmit a superposition of two codewords, one for each receiver. Each receiver decodes its own message, and treats the signals for the other receiver as background noise. With narrowband transmissions the achievable rate region and maximum achievable weighted sum rate are characterized by optimizing the power allocation (and the beamforming vectors in the case of multiple transmit antennas) at each BTS between its two codewords. For a wideband (multicarrier) system, a dual formulation of the optimal power allocation problem across sub-carriers is presented, which can be efficiently solved by numerical methods. Results show that the proposed cooperation scheme can improve the sum rate substantially in the low to moderate signal-to-noise ratio (SNR) range.

Alternative wireless topologies, e.g., an underlay network of Pico-cells, are increasingly seen as being necessary to enhance capacity and coverage in next generation wireless systems. Such networks of closely-spaced base-sites have to contend with high interference issues, wherein interference mitigation via power control or interference co-ordination may not be sufficient. Capacity can be significantly enhanced by Co-ordinated Multi-Point (CoMP) techniques, which allow co-operative signal processing to jointly decode user's signals, especially given fast communication links between the nodes. In this paper, we present a cooperative system design for the uplink of LTE for providing high capacity solutions in dense deployments. We propose non-linear receiver algorithms for inter-cell interference suppression and cancellation based on a decentralized multistage cancellation architecture using user-specific clustered Pico-cell antennas. An interference cancellation method acting on post-antenna combined signal is proposed to reduce the computational complexity of the receiver. The decoding latency inherent in multistage receivers is another key bottleneck, which is addressed in this paper by a method to predict the ACK/NACK status at the output of the multistage receiver before actually doing the cancellation. Simulation results for a dense stadium deployment of Pico-cells are presented that show significant capacity gains with the proposed approaches.

Pico-cell clusters have been proposed for providing high capacities to dense sets of users in next generation networks. We consider the uplink channel and analyze the sum-rate performance of two interfering pico-cell clusters with cooperative multi-cell joint decoding (MJD). The performance of a linear receiver is compared with that of non-linear receivers which allow message passing between the clusters in order to cancel the associated interference. The receiver, in all the above cases, jointly processes all signals across a single cluster. However we consider different message passing schemes, and maximize the sum rate over system parameters, including the load in each cell. Our results are valid in the large-system limit as the number of cells and antennas per cluster each tend to infinity with fixed ratio. Numerical results show that the nonlinear receivers provide significantly larger capacities than linear receivers, especially at high SNRs.

Two users at the two ends of a bidirectional channel wish to estimate the common state of the channel. The problem is usually treated as two separate one-way channel estimation problems: User 1 sends deterministic pilots to assist user 2 in estimating the channel, and vice versa. This paper questions whether such separation is optimal. In other words, is it beneficial to let a user choose pilots that adapt to what the user has learned about the channel? Two concrete models are studied and it is found that using adaptive pilots often improves the channel estimate. In the special case of a Gaussian channel with colored additive interference, an iterative bidirectional estimation scheme is proposed, which achieves significantly better performance than separate one-way estimation.

Interference mitigation approaches in the presence of multiple receive antennas in the uplink of a multi-cell wireless communications system are studied in this paper. A formulation based on interference pricing is proposed, where it is shown that a single price per base-station can be computed and exchanged, in order to set the mobile transmit powers per cell. The work is premised on a decentralized network architecture where schedulers make decisions on users connected to their cell, and there is a low-rate inter-cell communication link to enable distributed interference mitigation. The proposed utility maximization approach provides a general framework for multi-user multiple-input multiple-output (MIMO) systems on the uplink and accommodates both optimal (MMSE) and sub-optimal (MRC) multi-antenna receivers.

We consider data transmission through a time-selective, correlated (first-order Markov) Rayleigh fading channel subject to an average power constraint. The channel is estimated at the receiver with a pilot signal, and the estimate is fed back to the transmitter. The estimate is used for coherent demodulation, and to adapt the data and pilot powers. We derive the Hamilton--Jacobi--Bellman (HJB) equation for the optimal policy in a continuous-time limit where the channel state evolves as an Ornstein--Uhlenbeck diffusion process, and is estimated by a Kalman filter at the receiver. Finding an explicit solution to the HJB equation, as well as proving that a (twice-differentiable) solution exists, appears to be quite challenging. However, assuming that such a solution does exist, we explicitly determine the optimal pilot and data power control policies. The optimal pilot policy switches between zero and the maximum (peak-constrained) value (“bang-bang” control), and approximates the optimal discrete-time policy at low signal-to-noise ratios (SNRs) (equivalently, large bandwidths). The switching boundary is defined in terms of the system state (estimated channel mean and associated error variance), and can be explicitly computed. Under the optimal policy, the transmitter conserves power by decreasing the training power when the channel is faded, thereby increasing the data rate. Numerical results show a significant increase in achievable rate due to the adaptive training scheme with feedback, relative to constant (nonadaptive) training, which does not require feedback. The gain is more pronounced at relatively low SNRs and with fast fading. Results are further verified through Monte Carlo simulations.

We explore the feasibility of linear interference alignment (IA) in MIMO cellular networks. Each base station (BTS) has Nttransmit antennas, each mobile has Nrreceive antennas, and a BTS transmits a single beam to each active user. We present a necessary Zero-Forcing (ZF) condition for zero interference in terms of the number of users, the number of cells, Ntand Nr. We then examine the performance of iterative (forward-backward) algorithms for jointly optimizing the transmit precoders with linear receivers. Modifications of the max-SINR and minimum leakage algorithms are presented, which are observed to converge to a ZF solution whenever the necessary conditions are satisfied. In contrast, convergence of the (original) max-SINR algorithm is problematic when the necessary conditions are satisfied with (near) equality. A more restrictive ZF condition is presented, which predicts when these convergence problems are unlikely to occur.

We consider an interference network with multi-carrier transmission over M parallel sub-channels. There are K transmitter-receiver pairs, each transmitter transmits a single data stream with a rank-one precoding matrix, and the receivers are assumed to be linear. We show that a necessary condition for zero interference (alignment across sub-channels) is K ≤ 2M-2. In contrast, for a Multi-Input Multi-Output (MIMO) interference network with M×M spatial channels (full channel matrices) the corresponding condition is known to be K ≤ 2M - 1. We also characterize the sum rate at high Signal-to-Noise Ratios (SNR) by bounding the SNR offset (x-intercept) of the asymptote of the sum rate vs SNR curve. For a randomly chosen aligned solution as M increases, this offset shifts to the right as logM. In contrast, the SNR offset for a MIMO interference network does not increase with M. An approximation for the performance of sampling the best out of L aligned solutions is also presented. Numerical results show the analytical asymptotes accurately predict the sum rate curves at moderate to high SNRs.

Extensive spectrum markets have the potential to enable more efficient use of this limited resource. Such markets must account for particular properties of the underlying wireless medium. In this paper we focus on one such aspect: the role of interference created among different agents who may purchase the right to use the same spectrum at nearby locations. Such interference can result in “complementarities” among the spectrum goods being traded, which complicates the design of an efficient market. We begin with a simple linear model for these complementarities that was shown to be computationally difficult in earlier work. We give several approximation algorithms for this model. We then consider several alternative models in which the spectrum goods are defined in different ways and explore the impact of these choices on the complexity of the resulting market.

We consider a network of K interfering transmitter-receiver pairs, where each node has N antennas and at most one beam is transmitted per user. We investigate the asymptotic performance of different beamforming strategies, as characterized by the slope and y-axis intercept (or offset) of the high signal-to-noise-ratio (SNR) sum rate asymptote. It is known that a slope (or multiplexing gain) of 2N-1 is achievable with interference alignment. On the other hand, a strategy achieving a slope of only N might allow for a significantly higher offset. Assuming that the number of fully aligned beamformer sets that achieve a slope of 2N-1 is finite for a given channel realization, we approximate the average offset when the best out of a large number L of these sets is selected. We also derive a simple large system approximation for the sum rate of a successive beam allocation scheme when K=N. We show that both approximations accurately predict simulated results for moderate system dimensions and characterize the large-system asymptotes for different relationships between L and N.

Multicell joint processing can mitigate inter-cell interference and thereby increase the spectral efficiency of cellular systems. Most previous work has assumed phase-aligned (coherent) transmissions from different base stations (BSTs), which is difficult to achieve in practice. In this work, a noncoherent cooperative transmission scheme for the downlink is studied, which does not require phase alignment. We consider two adjacent cells each with a single user, and assume that the BSTs share their messages through a dedicated link. Each BST transmits a superposition of two codewords, one for each receiver. Each receiver decodes its own message, and treats the signals for the other receiver as background noise. With narrowband transmissions the achievable rate region and maximum achievable weighted sum rate are characterized by optimizing the power allocation at each BST between its two codewords. For a wideband (multicarrier) system, a dual formulation of the optimal power allocation problem across subcarriers is presented, which admits efficient numerical solution. Results show that the proposed cooperation scheme can improve the sum rate substantially at low to moderate signal-to-noise ratios.

Analytical results for the average sum rate achievable in the Multiple-Input Multiple-Output (MIMO) broadcast channel with algorithms relying on full channel state information at the transmitter are hard to obtain in practice. In the large system limit, when the number of transmit and receive antennas goes to infinity at a finite fixed ratio, however, the eigenvalues of many random matrices become deterministic and analytical expressions for the sum rate can be derived in some cases. In this paper we will present large system expressions for the sum rate for three sub-optimum algorithms, namely the Successive Encoding Successive Allocation Method (SESAM), Block Diagonalization and Block Diagonalization with Dirty Paper Coding. In case the large system limit of the sum rate does not exist, we derive lower bounds. By simulation results it is shown that the asymptotic results serve as a good approximation of the system performance with finite system parameters of reasonable size.

The capacity of a fading channel can be substantially increased by feeding back channel state information from the receiver to the transmitter. If the feedback rate is limited, what state information to feed back and how to encode it are important questions. This paper studies power loading in a multicarrier system using no more than one bit of feedback per subchannel. The subchannels can be correlated and full channel state information is assumed at the receiver. First, a simple model withNparallel two-state (good/bad) memoryless subchannels is considered, where the channel state feedback is used to select a fixed number of subchannels to activate. The optimal feedback scheme is the solution to a vector quantization problem, and the associated performance for large N is characterized using a rate distortion function. As N increases, the loss in forward rate from the asymptotic (rate-distortion) value is shown to decrease as (logN)/N and √{(logN)/N} with optimal variable- and fixed-length feedback codes, respectively. These results are subsequently extended to parallel Rayleigh block fading subchannels, where the feedback designates a set of subchannels to be activated with equal power. Rate-distortion feedback codes are proposed for designating subsets of (good) subchannels with signal-to-noise ratios (SNRs) that exceed a threshold. The associated performance is compared with that of a simpler lossless source coding scheme, which designates groups of good subchannels, where both the group size and threshold are optimized. The rate-distortion codes can provide a significant increase in forward rate at low SNRs.

We consider the capacity of a wideband fading channel with partial feedback, subject to an average power constraint. The channel is modeled as a set of parallel independent block Rayleigh fading subchannels with finite coherence time (L channel uses). The transmitter probes a subset of subchannels during each coherence time by transmitting pilot sequences for channel estimation. For each subchannel probed, one bit of feedback indicates whether or not the channel gain exceeds a threshold allowing transmission. Our problem is to optimize jointly the training (both length and power), number of subchannels probed (probing bandwidth), and feedback threshold to maximize the achievable rate (lower bound on ergodic capacity) taking into account the subchannel estimation error. Optimizing the probing bandwidth balances diversity against the quality of the subchannel estimate. We show that the achievable rate increases as S log L, where S is the signal-to-noise ratio, and exceeds the capacity with impulsive signaling (given by S) when L exceeds a (positive) threshold value. Moreover, the optimal probing bandwidth scales as SL/log2L. In contrast, without feedback the optimal probing bandwidth for the probing scheme scales as SL1/3and the achievable rate converges to S, where the gap diminishes as SL-1/3.

We examine the capacity of beamforming over a single-user, multiantenna link taking into account the overhead due to channel estimation and limited feedback of channel state information. Multi-input-single-output (MISO) and multi-input-multi-output (MIMO) channels are considered subject to block Rayleigh fading. Each coherence block contains L symbols, and is spanned by T training symbols, B feedback bits, and the data symbols. The training symbols are used to obtain a minimum mean squared error estimate of the channel matrix. Given this estimate, the receiver selects a transmit beamforming vector from a codebook containing 2Bi.i.d. random vectors, and sends the corresponding B bits back to the transmitter. We derive bounds on the beamforming capacity for MISO and MIMO channels and characterize the optimal (rate-maximizing) training and feedback overhead (T and B) as L and the number of transmit antennas Ntboth become large. The optimal Ntis limited by the coherence time, and increases as L/logL. For the MISO channel the optimal T/L and B/L (fractional overhead due to training and feedback) are asymptotically the same, and tend to zero at the rate 1/log Nt. For the MIMO channel the optimal feedback overhead B/L tends to zero faster (as 1/log2Nt).

Transmitter preceding is a crucial technique for harnessing the potential of multiple-input multiple-output (MIMO) fading channels. In many practical wireless systems, a limited amount of feedback from the receiver is available at the transmitter, which can be used to direct the choice of the precoder from a codebook to match the channel state. Assuming noiseless, limited-rate feedback, this work studies the design of simple, efficient quantization and feedback schemes which achieve near-optimal ergodic channel capacity. In the case the precoder takes the form of a beamforming vector for modulating a single symbol stream, it is found that simple scalar quantization of the elements of the vector is nearly optimal over a wide range of feedback rates; it typically costs a fraction of a dB higher SNR to achieve the same capacity as that of far more sophisticated vector quantization schemes. In the case a precoding matrix consisting of multiple beams is used to modulate multiple symbol streams, separate encoding of the beams using scalar quantization also performs well. Roughly speaking, the rate loss due to separate encoding of the beams increases linearly with the number of beams but appears to be constant over a wide range of SNRs. The loss can be reduced substantially by more sophisticated encoding of each beam, e.g., two-state trellis coded quantization. The complexity of such quantization schemes is linear in the number of antennas and the number of feedback bits.

We study wireless multicasting from two sources to two destinations with the assistance of a single half-duplex relay. The objective is to evaluate the throughput and error performance of different analog and digital relay schemes with linear network coding at the relay. The analog relay node forwards either a scaled version of the received signal to the destinations, or alternatively, first filters the received signals to generate a linear Minimum Mean Squared Error (MMSE) estimate, which is subsequently forwarded. The digital relay scheme first detects the source transmissions, combines the packets with a network code, and forwards the resulting symbols to the destinations. For all schemes the destinations recover the source and relay signals by first applying linear MMSE filters, followed by decoding of the source bits. The performance of the schemes are compared in terms of normalized throughput (bits per channel use accounting for the delay due to the relay) and uncoded error probability, given a normalized power constraint. Both narrowband and wideband transmission schemes are considered. Our results show that the analog relay schemes outperform the digital network coding scheme with respect to both throughput and error probability because of error propagation through the relay. Numerical results are presented, which illustrate throughput-reliability trade-offs for all schemes considered.

We study distributed algorithms for updating transmit preceding matrices for a two-user Multi-Input/Multi-Output (MIMO) interference channel. Our objective is to maximize the sum rate with linear Minimum Mean Squared Error (MMSE) receivers, treating the interference as additive Gaussian noise. An iterative approach is considered in which given a set of preceding matrices and powers, each receiver announces an interference price (marginal decrease in rate due to an increase in interference) for each received beam, corresponding to a column of the precoding matrix. Given the interference prices from the neighboring receiver, and also knowledge of the appropriate cross-channel matrices, the transmitter can then update the beams and powers to maximize the rate minus the interference cost. Variations on this approach are presented in which beams are added sequentially (and then fixed), and in which all beams and associated powers are adjusted at each iteration. Numerical results are presented, which compare these algorithms with iterative water-filling (which requires no information exchange), and a centralized optimization algorithm, which finds locally optimal solutions. Our results show that the distributed algorithms perform close to the centralized algorithm, and by adapting the rank of the precoder matrices, achieve the optimal high-SNR slope.

Codebooks based on random vector quantization (RVQ) are popular in limited feedback beamforming applications over MIMO channels because of their low-complexity design properties. The goal of this work is on understanding the performance of an ensemble of RVQ codebooks as a function of the number of bits of feedback (B), antenna dimensions, and spatial correlation. We analyze the case of correlated MIMO channels and arbitrary choice of B. Towards this goal, we first study the distribution function of weighted norms of isotropically distributed beamforming vectors. From this, we compute the received SNR loss and mutual information loss of a B-bit RVQ scheme relative to a perfect channel information benchmark. Our computation reveals the following: (i) The loss terms are a product of two factors. The first factor, which is also common to analysis of i.i.d. channels, decays as B increases at the rate 2-B/(Nt-1)where Ntis the number of transmit antennas; (ii) The second factor reflects the condition number of the channel. A channel that minimizes/maximizes the condition number on average also minimizes/maximizes the performance loss, respectively. Such behavior is typical of channels that correspond to rich (i.i.d.) spatial scattering, and poor (rank-1 channels) spatial scattering, respectively.

We study distributed algorithms for allocating powers and/or adjusting beamforming vectors in a peer-to-peer wireless network which may have multiple-input-single-output (MISO) links. The objective is to maximize the total utility summed over all users, where each user's utility is a function of the received signal-to-interference-plus-noise ratio (SINR). Each user (receiver) announces an interference price, representing the marginal cost of interference from other users. A particular user (transmitter) then updates its power and beamforming vector to maximize its utility minus the interference cost to other users, which is determined from their announced interference prices. We show that if each transmitter update is based on a current set of interference prices and the utility functions satisfy certain concavity conditions, then the total utility is non-decreasing with each update. The proof is based on the convexity of the utility functions with respect to received interference, and applies to rate utility functions, and an arbitrary number of interfering MISO links. The extension to multi-carrier links is discussed as well as algorithmic variations in which the prices are not immediately updated after power or beam updates.

The achievable rate of a wideband multi-input single-output channel with multi-carrier transmission is studied with limited feedback of channel state information (CSI). The set of sub-channel vectors are assumed to be jointly quantized and relayed back to the transmitter. Given a fixed feedback rate, the performance of an optimal joint quantization scheme can be characterized by the rate-distortion bound. The distortion metric is the average loss in capacity (forward rate) relative to the capacity with perfect channel state information at the transmitter and receiver. The corresponding rate distortion function gives the forward capacity as a function of feedback rate, and is determined explicitly by casting the minimization of mutual information in the rate-distortion problem as an optimal control problem. Numerical results show that when the feedback rate is relatively small, the rate-distortion bound significantly outperforms separate quantization of the state information of each sub-channel.

This paper studies power loading in a multicarrier system with channel state feedback of no more than one bit per sub-channel. Full channel state information is assumed known at the receiver. A simple model with parallel two-state (good/bad) memoryless sub-channels is considered first, where feedback is used to select a given fraction of sub-channels to activate. The optimal feedback scheme is the solution to a vector quantization problem, the performance of which is characterized by a rate distortion function in the limit of infinite number of sub-channels. Bounds for performance loss with finite number of sub-channels are also developed. We then consider a second model of a bank of block Rayleigh fading sub-channels with total power constraint, where the feedback describes which sub-channels to activate with equal power. A scheme based on rate distortion code is proposed to describe which sub-channels exceed a threshold in signal-to-noise ratio and should be activated. With optimized threshold and moderate amount of feedback, the resulting capacity is known to be of the same order in the number of sub-channels as that achieved by water-filling with full channel state information at the transmitter. This scheme performs more favorably than alternative schemes based on channel state reduction (such as by grouping them) and subsequent entropy coding.

We consider multicast communications from a single source to multiple destinations through a wireless network with unreliable links. Random linear network coding achieves the min-cut flow capacity; however, additional overhead is needed for end-to-end error protection and to communicate the network coding matrix to each destination. We present a joint coding and training scheme in which training bits are appended to each source packet, and the channel code is applied across both the training and data. This scheme allows each destination to decode jointly the network coding matrix along with the data without knowledge of the network topology. It also balances the reliability of communicating the network coding matrices with the reliability of data detection. The throughput for this scheme, accounting for overhead, is characterized as a function of the packet size, channel properties (error and erasure statistics), number of independent messages, and field size. We also compare the performance with that obtained by individual channel coding of training and data. Numerical results are presented for a grid network that illustrate the reduction in throughput due to overhead.

This paper considers the problem of beamforming in multiple-input multiple-output (MIMO) wireless systems. Assuming perfect channel state information at the receiver, the choice of the beamforming vector is made possible through a noiseless limited-rate feedback of one or more bits per coefficient to the transmitter. This paper proposes the use of beamforming codebooks based on quadrature amplitude modulation (QAM) and phase-shift keying (PSK) constellations, which essentially eliminates the need for storage of the codebook. We show that such codebooks perform arbitrarily close to the perfect feedback case as the constellation size increases, and that full diversity order is achieved. We demonstrate an equivalence between the beamforming codebook search problem with that of noncoherent sequence detection. Based on this we propose fast beamforming vector search algorithms. Monte-Carlo simulations are presented to show that the performance is comparable to the best known codebooks, and that the search complexity can be reduced by several orders of magnitude.

Given a multiple-input multiple-output (MIMO) channel, feedback from the receiver can be used to specify a transmit precoding matrix, which selectively activates the strongest channel modes. Here we analyze the performance ofrandomvectorquantization(RVQ), in which the precoding matrix is selected from a random codebook containing independent, isotropically distributed entries. We assume that channel elements are independent and identically distributed (i.i.d.) and known to the receiver, which relays the optimal (rate-maximizing) precoder codebook index to the transmitter usingBbits. We first derive the large system capacity of beamforming (rank-one precoding matrix) as a function ofB, where large system refers to the limit asBand the number of transmit and receive antennas all go to infinity with fixed ratios. RVQ for beamforming is asymptotically optimal, i.e., no other quantization scheme can achieve a larger asymptotic rate. We subsequently consider a precoding matrix with arbitrary rank, and approximate the asymptotic RVQ performance with optimal and linear receivers (matched filter and minimum mean squared error (MMSE)). Numerical examples show that these approximations accurately predict the performance of finite-size systems of interest. Given a target spectral efficiency, numerical examples show that the amount of feedback required by the linear MMSE receiver is only slightly more than that required by the optimal receiver, whereas the matched filter can require significantly more feedback.

Channel uncertainty and co-channel interference are two major challenges in the design of wireless systems such as future generation cellular networks. This paper studies receiver design for a wireless channel model with both time-varying Rayleigh fading and strong co-channel interference of similar form as the desired signal. It is assumed that the channel coefficients of the desired signal can be estimated through the use of pilots, whereas no pilot for the interference signal is available, as is the case in many practical wireless systems. Because the interference process is non-Gaussian, treating it as Gaussian noise generally often leads to unacceptable performance. In order to exploit the statistics of the interference and correlated fading in time, an iterative message-passing architecture is proposed for joint channel estimation, interference mitigation and decoding. Each message takes the form of a mixture of Gaussian densities where the number of components is limited so that the overall complexity of the receiver is constant per symbol regardless of the frame and code lengths. Simulation of both coded and uncoded systems shows that the receiver performs significantly better than conventional receivers with linear channel estimation, and is robust with respect to mismatch in the assumed fading model.

Feedback of channel state information (CSI) enables a multi-carrier transmitter to optimize the power allocation across sub-channels. We consider a single user feedback scheme in which the entire set of sub-channels is evenly divided into smaller groups of sub-channels, and the receiver requests the use of a particular group if the gain of every sub-channel in the group is above a threshold. The transmit power is then uniformly spread across the requested sub-channel groups. The amount of feedback is therefore controlled by the group size and the threshold. For this scheme, given a total power constraint, we characterize how the channel capacity scales with the number of sub-channels N as a function of the feedback rate. We then consider transmission over a block fading channel, assuming that each coherence block contains both feedback and data transmission. We optimize the fraction of feedback overhead as a function of the number of feedback bits per channel use and coherence time. Numerical results show that the asymptotic (large-N) analysis accurately predicts the behavior of finite-size systems of interest.

This paper studies signal detection in wireless networks where the uncertainty is due to fading as well as a strong co-channel interference of the same form as that of the desired signal. In particular, unlike for the desired signal, no pilot for the interference signal is available for measuring its fading channel state. Still, the interference is a non-Gaussian process and treating it as Gaussian noise can lead to poor performance. We propose a joint channel estimation and interference mitigation scheme based on belief propagation, which is capable of fully exploiting the statistics of the interference. Simulation results show that the receiver performs significantly better compared to conventional receivers with linear channel estimation.

In a fading communication channel, it is often beneficial to feedback Channel State Information (CSI) and Receiver State Information (RSI) to the transmitter. The CSI generally refers to information about the channel condition available at the receiver, while the RSI in this work is defined as information about the receive’s estimate of the message. The RSI can be used to improve reliability, e.g., through retransmission. This paper considers multi-carrier transmission through a doubly-selective Rayleigh fading channel, and studies the trade-off between the feedback of CSI and RSI under total feedback constraint. In particular, the CSI feedback specifies which groups of sub-channels to activate with equal power, and the RSI feedback determines retransmissions of a codeword. The problem is how to allocate feedback bits between CSI and RSI in order to maximize the error probability exponent. It is found that the optimal trade-off exhibits phase transitions which depends critically on the coherence time and the total amount of feedback. Specifically, the first feedback bits should be CSI up to a critical amount. Additional feedback bits, if available, should be allocated to RSI first, and then to both CSI and RSI. For the model considered, as the amount of feedback exceeds a certain threshold, additional RSI feedback is not beneficial unless CSI feedback increases accordingly.

A multihop relay extension for IEEE 802.16e systems is the subject of ongoing standardization activities within the IEEE 802.16j Task Group. The emerging IEEE 802.16J standard enhances the 802.16e PHY and MAC to enable support of multihop routes between a mobile station and a base station through intermediate relay stations. Since it is believed that the capacity of a single-hop 802.16e system is uplink-limited, this paper evaluates potential capacity gains attained with the relay enhancement of the 802.16e uplink. The capacity here denotes either cumulative throughput for data traffic or total number of users for voice traffic supported, under certain system-specific constrains detailed below. We first develop a simplified one-dimensional model of a relay-enhanced 802.16e system and estimate the capacity gains via analysis and numerical optimization. Motivated by the capacity gains predicted by this first-order analysis, simulation results obtained from a full two-dimensional simulator modeling a realistic deployment of a relay-enhanced system are then presented. Based on the simulation results, a parametric analysis of relay deployment cost vs. the capacity gain is also presented.

We study a sequential auction for sharing a wireless resource (bandwidth or power) among competing transmitters. The resource is assumed to be managed by a spectrum broker (auctioneer), who collects bids and allocates discrete units of the resource via a sequential second-price auction. It is well known that a second price auction for a single indivisible good has an efficient dominant strategy equilibrium; this is no longer the case when multiple units of a homogeneous good are sold in repeated iterations. For two users with full information, we show that such an auction has a unique equilibrium allocation. The worst-case efficiency of this allocation is characterized under the following cases: (i) both bidders have a concave valuation for the spectrum resource, and (ii) one bidder has a concave valuation and the other bidder has a convex valuation (e.g., for the other useriquests power). Although the worst-case efficiency loss can be significant, numerical results are presented, which show that for randomly placed transmitter-receiver pairs with rate utility functions, the sequential second-price auction typically achieves the efficient allocation. For more than two users it is shown that this mechanism always has a pure strategy equilibrium, but in general there may be multiple equilibria. We give a constructive procedure for finding one equilibrium; numerical results show that when all users have concave valuations the efficiency loss decreases with an increase in the number of users.

In a downlink orthogonal frequency division multiple access (OFDMA) system, optimally allocating sub-channels across mobile users can require excessive feedback of channel state information (CSI). We consider an OFDMA model in which the feedback overhead is explicitly taken into account, given a fixed feedback rate and finite coherence time. The tradeoff between feedback rate and sum capacity is studied for two limited feedback schemes: a sequential scheme in which the users send compressed feedback bits over consecutive time slots, and a contention scheme in which users send their feedback via a random access protocol. For both schemes each feedback bit indicates a request for a group containing multiple subchannels. We show that the sum capacity for both schemes with optimized sub-channel groups grows linearly with the number of sub-channels N, and that the associated constant increases as the log of the normalized feedback rate measured in bits per coherence time per sub-channel. We also compare the asymptotic (large N) performance of the two limited feedback schemes as a function of the feedback rate and load (users per sub-channel). The sequential scheme performs best with moderate to large feedback rates, or small loads, whereas the contention scheme performs best with small feedback rates or large loads.

We consider the transmission of a Gaussian source through a block fading channel. Assuming each block is decoded independently, the received distortion depends on the tradeoff between quantization accuracy and probability of outage. Namely, higher quantization accuracy requires a higher channel code rate, which increases the probability of outage. We first treat an outage as an erasure, and evaluate the received mean distortion with erasure coding across blocks as a function of the code length. We then evaluate the performance of scalable, or multi-resolution coding in which coded layers are superimposed within a coherence block, and the layers are sequentially decoded. Both the rate and power allocated to each layer are optimized. In addition to analyzing the performance with a finite number of layers, we evaluate the mean distortion at high signal-to-noise ratios as the number of layers becomes infinite. As the block length of the erasure code increases to infinity, the received distortion converges to a deterministic limit, which is less than the mean distortion with an infinite-layer scalable coding scheme. However, for the same standard deviation in received distortion, infinite layer scalable coding performs slightly better than erasure coding, and with much less decoding delay.

This paper uses an incremental matrix expansion approach to derive asymptotic eigenvalue distributions (a.e.d.'s) of sums and products of large random matrices.We show that the result can be derived directly as a consequence of two common assumptions, and matches the results obtained from using R-and S-transforms in free probability theory.We also give a direct derivation of the a.e.d. of the sum of certain random matrices which are not free.This is used to determine the asymptotic signalto-interference-ratio of a multiuser CDMA system with a minimum mean-square error linear receiver.

We study the capacity of multicarrier transmission through a slow frequency-selective fading channel with limited feedback, which specifies channel state information. Our results are asymptotic in the number of subchannels$N$. We first assume independent and identically distributed (i.i.d.) subchannel gains, and show that, for a large class of fading distributions, a uniform power distribution over an optimized subset of subchannels, or on–off power allocation, gives the same asymptotic growth in capacity as optimal water filling, e.g.,$O(\log N)$with Rayleigh fading. Furthermore, the$O(\log N)$growth in data rate can be achieved with a feedback rate as$O(\log ^{3} N)$. If the number of active subchannels is bounded, the capacity grows only as$O(\log \log N)$with the feedback rate of$O(\log N)$. We then consider correlated subchannels modeled as a Markov process, and study the savings in feedback. Assuming a fixed ratio of coherence bandwidth to the total bandwidth, the ratio between minimum feedback rates with correlated and i.i.d. subchannels converges to zero with$N$, e.g., as$O\left (\sqrt {{ \log N}\over { N}}\right)$for Rayleigh-fading subchannels satisfying a first-order autoregressive process. We also show that adaptive modulation, or rate control schemes, in which the rate on each subchannel is selected from a quantized set, achieves the same asymptotic growth rates in capacity and required feedback. Finally, our results are extended to cellular uplink and downlink channel models.

This paper proposes a new QAM based codebook for beamforming in multiple-input multiple-output (MIMO) wireless systems with a limited-rate feedback channel. We show that such codebooks perform arbitrarily close to the perfect feedback case as the constellation size increases, and that full diversity order is achieved. We demonstrate an equivalence between the problems of beamforming codebook search and noncoherent sequence detection. Based on this we propose a fast beamforming vector search algorithm. Monte-Carlo simulations are presented to show that the performance is comparable to the best known codebooks, and that the search complexity can be reduced by several orders of magnitude.

Abstract — We consider an additive white Gaussian noise (AWGN) channel with partial sequential feedback. Namely, for every fixed-length block of forward transmissions a fraction of the received symbols are fed back sequentially to the transmitter through a noiseless feedback link. It is well known that complete noiseless feedback can provide a dramatic improvement in reliability (i.e., double-exponential error rate with block length). We show that partial feedback can also provide a substantial improvement in error rate. Specifically, we propose a capacityachieving coding scheme with partial feedback, in which the feedback is used to induce a prior distribution for the decoding of random forward error control (FEC) codewords. The errorexponent for this scheme is larger than the error-exponent with FEC coding only at all rates. For rates greater than those achieved by transmissions with feedback alone, we give an upper bound on the error exponent. Exponents close to this bound can be achieved with both the proposed scheme and a simple ratesplitting scheme. With finite block lengths, the proposed coding scheme achieves lower error rates than rate-splitting. I.

We consider the capacity of a downlink orthogonal frequency division multiple access (OFDMA) system with limited feedback rate RFper sub-channel and finite coherence time T. The feedback is used to relay channel state information (CSI) from K users to the base station. The order-optimal capacity growth with Rayleigh fading sub-channels is ominus(N log log K) as N and K increase with fixed ratio, where N is the number of sub-channels. However, to achieve this, previous work requires a feedback rate per subchannel that scales linearly with the system size. Here we explicitly include the feedback overhead when calculating the sum capacity, and study the tradeoff between feedback rate and sum capacity. We propose two limited feedback schemes, one based on sequential transmissions across users and the other based on random access, in which the each feedback bit requests the use of a sub-channel group containing multiple subchannels. With fixed RFT, the sum capacity for both schemes with optimized sub-channel groups increases as ominus(N). If RFT grows faster than log K, then both schemes can achieve the order- optimal capacity growth. We also show that when RFT is small, the random access scheme performs better than the sequential transmission scheme, whereas the reverse is true for large RFT.

We examine the capacity of beamforming over a block Rayleigh fading multi-input/multi-output (MIMO) channel with finite training for channel estimation and limited feedback. A fixed-length packet is assumed, which is spanned by T training symbols, B feedback bits, and the data symbols. The training symbols are used to obtain a minimum mean squared error (MMSE) estimate of the channel matrix. Given this estimate, the receiver selects a transmit beamforming vector from a codebook containing 2Bi.i.d. random vectors, and relays the corresponding B-bit index back to the transmitter. We derive bounds on the large system capacity, i.e., as the number of transmit antennas Ntrarr infin and receive antennas Nrrarr infin with fixed ratio Nt/Nr. The bounds are used to show that the optimal T, which maximizes the capacity, increases as Nt/ log Nt, whereas the optimal B increases as Nt/log2Nt.

This work studies the performance of multiuser detection and decoding in the downlink of cellular systems based on orthogonal frequency-division multiplexing (OFDM). Of particular interest is a worst case scenario where the desired user is at the cell boundary and subject to an equally strong interferer from a neighboring cell. A flexible iterative turbo decision-feedback equalizer (DFE) is proposed and studied numerically, which exhibits good error performance and resilience to fading, requires moderate training and low complexity, and accommodates multiple antennas easily. The scheme performs well without knowledge of the pilots of interfering signals from other cells, which is typically unavailable in practice, while such knowledge may improve the performance significantly. Furthermore, in the absence of knowledge of pilots for the out-of-cell interference, it is found that estimating the filter coefficients of the DFE directly is superior to deriving the coefficients from estimates of the instantaneous channel gains.

We consider the allocation of power across forward-link packets in a wireless data network. The packets arrive according to a random (Poisson) process, and have fixed length so that the data rate for a given packet is determined by the assigned power and the channel gain to the designated user. Each user's service preferences are specified by a utility function that depends on the received data rate. The objective is to determine a power assignment policy that maximizes the time-averaged utility rate, subject to a constraint on the probability that the total power exceeds a limit (corresponding to an outage). For a large, heavily loaded network, we introduce a Gaussian approximation for the total transmitted power, which is used to decompose the power constraint into three more tractable constraints. We present a solution to the modified optimization problem that is a combination of admission control and pricing. The optimal trade-off between these approaches is characterized. Numerical examples illustrate the achievable utility rate and power allocation as a function of the packet arrival rate.

We study the downlink coverage of a base station terminal (BST), which has access to a relay node. Continuing a previous study in which the BST is assumed to provide a variable-rate data service, here we assume that each active user requires a target data rate, corresponding to a voice type of service. The relay is assumed to serve a separate set of (non- cellular) users, corresponding to a WiFi Access Point (AP). A one-dimensional model is considered in which cellular and non- cellular users are uniformly distributed along a line. The BST and AP jointly allocate available power across users and the BST-AP link to maximize the total number of users served. We characterize the optimized set of active cellular users served by the BST directly and the AP relay, and the non-cellular users served by the AP. We also give a closed-form upper bound on the increase in the total number of users provided by the relay as a function of user densities and path loss exponents. Our results show that depending on the distance between the BST and the AP, the addition of a relay gives a modest increase in the total number of active users.

The coverage of a base station terminal (BST) in a cellular network can generally be increased through the use of a relay node within the cell boundary. We consider the downlink for a single, one-dimensional cell with a relay node, or access point (AP), which serves a separate set of (non-cellular) users (e.g., corresponding to a WiFi system). The BST and AP jointly allocate available power across users and the BST-AP link to maximize the sum data rate across all cellular and AP users. Two relay schemes are considered: (i) the information flows to the cellular users served by the relay are jointly encoded and transmitted from the BST to the AP; and (ii) the preceding information flows are transmitted in parallel from the BST to the AP. We give an upper bound on the increase in rate provided by the AP, which depends on the relative powers and bandwidths available to the BST and AP. Although the increase in total rate provided by sharing AP resources is typically modest, it can provide a more equitable rate distribution across cellular users, and extend the coverage of the BST.

Signature sequences and associated powers are optimized jointly with linear receivers for a multi-user forward-link CDMA system with multiple transmit and receive antennas. The performance criterion is sum capacity over all users. For the model considered, the optimal signatures are sinusoids so that multi-carrier signaling, in which each carrier is assigned to a single user, maximizes the achievable rate. An optimal assignment of carriers to users appears to be difficult to determine in general, but can be efficiently approximated numerically. The asymptotic sum capacity for large number of users and antennas is characterized at high SNRs. The accuracy of these results for moderate SNRs is illustrated through comparisons with numerically optimized power allocations.

We consider data transmission through a time-selective (correlated) flat Rayleigh fading channel under an average power constraint. The channel is estimated at the receiver with a pilot signal, and the estimate is fed back to the transmitter. The estimate is used for coherent demodulation, and to adapt the data and pilot powers. We start with a block fading channel in which the channel gain changes according to a Gauss-Markov process. The channel estimate is updated during each coherence block with a Kalman filter, and optimizing the data and pilot powers is formulated as a dynamic program. We then study a continuous limit in which the coherence time tends to zero, and the correlation between successive channel gains tends to one, so that the channel process becomes a diffusion process. In this limit it is shown that the optimal pilot power control policy is "bang-bang", i.e., depending on the current system state (channel estimate and associated error variance) the pilot power is either the maximum allowable, or zero. The associated regions of the state space are illustrated numerically for specific system values. This example shows that the achievable rate with the optimized training policy provides substantial gains relative to constant training power at low SNRs

We consider allocation of sub-channels to users in a downlink OFDMA system. Each user feeds back one bit per sub-channel, which indicates whether or not the gain exceeds a threshold. Users are assigned priority weights, and the thresholds are selected to maximize the weighted sum capacity. We analyze the behavior of the optimal thresholds and growth in capacity, assuming i.i.d. Rayleigh fading sub-channels, in the large system limit in which users K and sub-channels tend to infinity with fixed ratio. If all users have the same priority weight, then the optimized threshold increases as log K minus a second-order term, which is asymptotically bounded between log log K and log log log K. Furthermore, the sum capacity per sub-channel increases as log log K plus a second-order term, which decreases to a constant as log log K/ log K. We then consider two classes of users, each assigned a different weight, and show that the capacity of the low priority group tends to zero. Finally, we solve for the optimal thresholds given a fairness constraint on the ratio between the rates of different classes

We examine the capacity of beamforming over a multi-input/single-output block Rayleigh fading channel with finite training for channel estimation and limited feedback. A fixed-length packet is assumed, which is spanned by T training symbols, B feedback bits, and the data symbols. The training symbols are used to obtain a minimum mean squared error (MMSE) estimate of the channel vector. Given this estimate, the receiver selects a transmit beamforming vector from a codebook containing 2Bi.i.d. random vectors, and relays the corresponding B bits back to the transmitter. We derive bounds on the capacity and show that for a large number of transmit antennas Nt, the optimal T and B, which maximize the bounds, are approximately equal and both increase as Nt/logNt. We conclude that with limited training and feedback, the optimal number of antennas to activate also increases as Nt/logNt

We consider a distributed power control scheme for wireless ad hoc networks, in which each user announces a price that reflects compensation paid by other users for their interference. We present an asynchronous distributed algorithm for updating power levels and prices. By relating this algorithm to myopic best response updates in a fictitious game, we are able to characterize convergence using supermodular game theory. Extensions of this algorithm to a multichannel network are also presented, in which users can allocate their power across multiple frequency bands.

In this paper, we consider packet scheduling for the downlink in a wireless network, where each packet's service preferences are captured by a utility function that depends on the total delay incurred. The goal is to schedule packet transmissions to maximize the total utility. In this setting, we examine a simple gradient-based scheduling algorithm called the U/spl dot/R-rule, which is a type of generalized c/spl mu/-rule (Gc/spl mu/) that takes into account both a user's channel condition and derived utility when making scheduling decisions. We study the performance of this scheduling rule for a draining problem, where there is a given set of initial packets and no further arrivals. We formulate a "large system" fluid model for this draining problem where the number of packets becomes large while the packet-size decreases to zero, and give a complete characterization of the behavior of the U/spl dot/R scheduling rule in this limiting regime. Comparison with simulation results show that the fluid limit accurately predicts the corresponding behavior of finite systems of interest. We then give an optimal control formulation for finding the optimal scheduling policy for the fluid draining model. Using Pontryagin's minimum principle, we show that, when the user rates are chosen from a TDM-type of capacity region, the U/spl dot/R rule is in fact optimal in many cases. Sufficient conditions for optimality are also given. Finally, we consider a general capacity region and show that the U/spl dot/R rule is optimal only in special cases.

This paper presents an asymptotic analysis of multisignature code-division multiple access (CDMA) in the presence of frequency-selective channels. We characterize the sum spectral efficiency and spectral efficiency regions for both the optimal and linear minimum mean-squared error (MMSE) multiuser receivers. Both independent and identically distributed (i.i.d). signatures and isometric signatures, which are orthogonal at each transmitter, are considered. Our results are asymptotic as the number of signatures per user and processing gain both tend to infinity with fixed ratio. The spectral efficiency of the MMSE receiver is determined from the asymptotic output signal-to-interference-plus noise ratio (SINR). For isometric signatures, our results rely on approximating certain covariance matrices with unitarily invariant matrices that are asymptotically free. This approximation is shown to be very accurate through comparison with both simulation and an "incremental-signature" analysis, which can be used to compute asymptotic moments. Also, a novel proof of the convergence of the empirical spectral distribution of the signal correlation matrix is presented. From these results, we derive the optimal coding-spreading tradeoff, which maximizes the MMSE spectral efficiency, for the case of a single user with multiple i.i.d. signatures. Simulation studies demonstrate that the asymptotic results accurately predict the performance of finite-size systems of interest. The resulting expressions are used to highlight and infer properties of the multisignature CDMA system, including the benefit of orthogonal relative to i.i.d. signatures, and the tradeoff between spectral efficiency and the versatility of providing a variable data rate service through multiple signatures

We present a unified large-system analysis of linear receivers for a class of random matrix channels. The technique unifies the analysis of both the minimum-mean-squared-error (MMSE) receiver and the adaptive least-squares (ALS) receiver, and also uses a common approach for both random independent, identically distributed (i.i.d.) and random orthogonal precoding. We derive expressions for the asymptotic signal-to-interference-plus-noise ratio (SINR) of the MMSE receiver, and both the transient and steady-state SINR of the ALS receiver, trained using either i.i.d. data sequences or orthogonal training sequences. The results are in terms of key system parameters, and allow for arbitrary distributions of the power of each of the data streams and the eigenvalues of the channel correlation matrix. In the case of the ALS receiver, we allow a diagonal loading constant and an arbitrary data windowing function. For i.i.d. training sequences and no diagonal loading, we give a fundamental relationship between the transient/steady-state SINR of the ALS and the MMSE receivers. We demonstrate that for a particular ratio of receive to transmit dimensions and window shape, all channels which have the same MMSE SINR have an identical transient ALS SINR response. We demonstrate several applications of the results, including an optimization of information throughput with respect to training sequence length in coded block transmission

We evaluate the performance of reduced-rank equalizers for both single-input single-output (SISO) and multiple-input multiple-output (MIMO) frequency-selective channels. Each equalizer filter is constrained to lie in a Krylov subspace, and can be implemented as a reduced-rank multistage Wiener filter (MSWF). Both reduced–rank linear and decision-feedback equalizers (DFEs) are considered. Our results are asymptotic as the filter length goes to infinity. For SISO channels, the output mean-squared error (MSE) is expressed in terms of the moments of the channel spectrum. For MIMO channels, both successive and parallel interference cancellation are considered. The asymptotic performance in that case requires the computation of moments, which depend on shifted versions of the channel impulse response for different users. Those are also expressed in terms of the MIMO channel frequency response. Numerical results are presented, which show that near full-rank performance can be achieved with relatively low-rank equalizers.

Interference in code-division multiple access (CDMA) and multi-antenna systems can be avoided by choosing a signature (in space and/or time), which lies in the direction of least interference plus noise. If the interference statistics are unknown a priori, then the signature can be adaptively estimated with a training sequence. We present an iterative scheme for joint signature-receiver adaptation with an adaptive reduced-rank multi-stage Wiener filter (MSWF) at the receiver. We establish convergence of the iterative signature-receiver optimization scheme for a single user with fixed interference, and show that the limiting performance for any filter rank D ges 2 is the same as that obtained with a full-rank receiver. To reduce feedback requirements, we also consider joint signature-receiver adaptation with a reduced-rank signature, which is confined to a randomly chosen subspace. Numerical results are presented for both single- and multi-user (group) adaptation, which show that reduced-rank signature-receiver estimation can achieve near-optimal performance with relatively little training and low complexity

The performance of a wireless channel with multiple antennas benefits from channel knowledge at the receiver, which is typically unknown a priori. We study the capacity of a block fading multiple-input/multiple-output (MIMO) channel with a linear receiver, which is estimated from a training sequence via a least squares (LS) algorithm. Given a fixed block size, the amount of training overhead plays a key role in balancing the quality of the receiver estimate and the data transmission time. Here we study the optimal training length, which maximizes the large system MIMO capacity, i.e., the number of transmit and receive antennas go to infinity with fixed ratio. In order to obtain a meaningful limit, the training length and packet length also increase in fixed proportion to the number of antennas. We show that the optimal amount of training grows as the square root of the block size, as the block size becomes large. Furthermore, only a slight benefit is obtained from optimizing the allocation of power across training and data symbols. Numerical results show that for a fixed block length, the capacity can be increased somewhat by adding a properly chosen diagonal loading factor to the LS algorithm.

We consider the transmission of a Gaussian source through a block fading channel. Assuming each block is decoded independently, the received distortion depends on the tradeoff between quantization accuracy and probability of outage. Namely, higher quantization accuracy requires a higher channel code rate, which increases the probability of outage. Here we evaluate the received mean distortion with erasure coding across blocks as a function of the code length. We also evaluate the performance of scalable, or multi-resolution coding in which coded layers are superimposed, and the layers are sequentially decoded. In addition to analyzing a finite number of layers, we evaluate the mean distortion at high signal-to-noise ratios as the number of layers becomes infinite. As the block length of the erasure code increases to infinity, the received distortion converges to a deterministic limit, which is less than the mean distortion with an infinite-layer scalable coding scheme. However, for the same standard deviation in received distortion, infinite layer scalable coding performs slightly better than erasure coding.

Large system analysis has been used extensively in recent years to evaluate the performance of code division-multiple access (CDMA) and multi-input/multi-output (MIMO) communications systems. A key feature of this analysis is application of results on eigenvalue distributions and moments of large random matrices. These results enable the efficient computation of large system performance measures, such as spectral efficiency and probability of error, which are far more difficult to compute for finite-size systems. The large system results typically give an accurate prediction of the performance of finite-size systems, and offer important insights into system behavior. We give an overview of large system results for some different communications system models. Our emphasis is on techniques used previously by the authors to evaluate the performance of multi-carrier CDMA with the optimal linear receiver.

We consider a distributed power control scheme in a spread spectrum (SS) wireless ad hoc network, in which each user announces a price that reflects his current interference level. Given these prices, we present an asynchronous distributed algorithm for updating power levels, and provide conditions under which this algorithm converges to an optimal power allocation. We relate this algorithm to myopic best response updates of a fictitious game, and characterize the algorithm's convergence using supermodular game theory

We consider a large system analysis of the minimum-mean-squared-error (MMSE) receiver and the adaptive least-squares (ALS) receiver for a class of random matrix channels. We give a relationship between the transient/steady-state SINR of the ALS and the MMSE receivers. We demonstrate that for a particular ratio of receive to transmit dimensions and window shape, all channels which have the same MMSE SINR, would have an identical transient ALS SINR response

Incremental redundancy, or Hybrid type-II ARQ (HARQ), algorithms use a combination of forward error correction and retransmissions to guarantee reliable packet data communications. In this work, we propose a HARQ algorithm that exploits received packet reliability to improve system performance. Specifically, the receiver uses the average magnitude of the log-likelihood ratios of the information bits as the packet reliability metric, which is then used to determine the sizes of subsequent retransmissions. The proposed retransmission strategy attempts to maximize user throughput while satisfying a maximum packet delay constraint. The performance of our reliability-based HARQ algorithm is evaluated in static and time-varying channels through simulations. Furthermore, analytical results on the relationship between the reliability metric, the code rate and the block error rate are presented.

We study the performance of joint signature-receiver optimization for direct-sequence code-division multiple access (DS-CDMA) with limited feedback. The receiver for a particular user selects the signature from a signature codebook, and relays the corresponding B index bits to the transmitter over a noiseless channel. We study the performance of a random vector quantization (RVQ) scheme in which the codebook entries are independent and isotropically distributed. Assuming the interfering signatures are independent, and have independent and identically distributed (i.i.d.) elements, we evaluate the received signal-to-interference plus noise ratio (SINR) in the large system limit as the number of users, processing gain, and feedback bits B all tend to infinity with fixed ratios. This SINR is evaluated for both the matched filter and linear minimum mean-squared error (MMSE) receivers. Furthermore, we show that this large system SINR is the maximum that can be achieved over any sequence of codebooks. Numerical results show that with the MMSE receiver, one feedback bit per signature coefficient achieves close to single-user performance. We also consider a less complex and suboptimal reduced-rank signature optimization scheme in which the user's signature is constrained to lie in a lower dimensional subspace. The optimal subspace coefficients are scalar-quantized and relayed to the transmitter. The large system performance of the quantized reduced-rank scheme can be approximated, and numerical results show that it performs in the vicinity of the RVQ bound. Finally, we extend our analysis to the scenario in which a subset of users optimize their signatures in the presence of random interference.

The performance of adaptive least squares (LS) filtering is analyzed for the suppression of multiple-access interference. Both full-rank LS filters and reduced-rank LS filters, which reside in a lower dimensional Krylov space, are considered with training, and without training but with known signature for the desired user. We compute the large system limit of output signal-to-interference-plus-noise ratio (SINR) as a function of normalized observations, load, and noise level. Specifically, the number of users K, the degrees of freedom N, and the number of training symbols or observations i all tend to infinity with fixed ratios K/N and i/N. Our results account for an arbitrary power distribution over the users, data windowing (e.g., recursive LS (RLS) with exponential windowing), and initial diagonal loading of the covariance matrix to prevent ill-conditioning. Numerical results show that the large system analysis accurately predicts the simulated convergence performance of the algorithms considered with moderate degrees of freedom (typically N=32). Given a fixed, short training length, the relative performance of full- and reduced-rank filters depends on the selected rank and diagonal loading. With an optimized diagonal loading factor, the performance of full- and reduced-rank filters are similar. However, full-rank performance is generally much more sensitive to the choice of diagonal loading factor than reduced-rank performance.

A model for downlink wireless scheduling is studied, which takes into account both user-channel conditions and retransmissions with packet combining hybrid [automatic repeat request (ARQ)]. Quality-of-service (QoS) requirements for each user are represented by a cost function, which is an increasing function of queue length. The objective is to find a scheduling rule that minimizes the average cost over time. We consider two scenarios: 1) the cost functions are linear, and packets arrive to the queues according to a Poisson process and 2) the cost functions are increasing, convex, and there are no new arrivals (draining problem). In each case, we transform the system model into a different model that fits into a framework for stochastic scheduling developed by Klimov. Applying Klimov's results, we show that the optimal schedulers for the transformed models in both scenarios are specified by fixed priority rules. Applying the inverse transformation in each case gives the optimal scheduling policy for the original problem. The priorities can be explicitly computed, and in the first scenario, are given by simple closed-form expressions. For the draining problem, we show that the optimal policy never interrupts the retransmissions of a packet. We also show that a simple myopic scheduling policy, called the U'R rule, performs very close to the optimal scheduling policy in specific cases. We present numerical examples, which compare the performance of the optimal scheduling rule with several heuristic rules.

An adaptive iterative (turbo) decision-feedback equalizer (DFE) for channels with intersymbol interference (ISI) is presented. The filters are computed directly from the soft decisions and received data to minimize a least-squares (LS) cost function. Numerical results show that this method gives a substantial improvement in performance relative to a turbo DFE computed from an exact channel estimate, assuming perfect feedback. Adaptive reduced-rank estimation methods are also presented, based on the multistage Wiener filter (MSWF). The adaptive reduced-rank turbo DFE for single-input/single-output channels is extended to multiple-input/multiple-output (MIMO) channels with ISI and multiple receive antennas. Numerical results show that for MIMO channels with limited training, the reduced-rank turbo DFE can perform significantly better than the full-rank turbo DFE.

Power allocation across users in two adjacent cells is studied for a code-division multiple access (CDMA) data service. The forward link is considered and cells are modeled as one-dimensional with uniformly distributed users and orthogonal signatures within each cell. Each user is assumed to have a utility function that describes the user's received utility, or willingness to pay, for a received signal-to-interference-plus-noise ratio (SINR). The objective is to allocate the transmitted power to maximize the total utility summed over all users subject to power constraints in each cell. It is first shown that this optimization can be achieved by a pricing scheme in which each base station announces a price per unit transmitted power to the users, and each user requests power to maximize individual surplus (utility minus cost). Setting prices to maximize total revenue over both cells is also considered, and it is shown that, in general, the solution is different from the one obtained by maximizing total utility. Conditions are given for which independent optimization in each cell, which leads to a Nash equilibrium (NE), is globally optimal. It is shown that, in general, coordination between the two cells is needed to achieve the maximum utility or revenue.

In this paper we derive asymptotic performance measures for multiuser receivers in the uplink of multi-carrier (MC) CDMA communication systems with multiple signatures per user. We examine spectral efficiency regions of multi-signature CDMA, for both the optimal and optimal-linear receivers. We also derive an approximate expression for the asymptotic average signal to interference and noise ratio at the output of the optimal-linear multiuser receiver in the case of two users. Simulation studies demonstrate that the asymptotic results closely predict performance of practical finite systems.

We derive asymptotic performance measures for peer-to-peer multi-carrier CDMA networks with low data rate feedback channels between transmitter-receiver pairs. We derive expressions for the asymptotic average signal to interference and noise ratio at the output of the optimal linear multi-signature receiver using a simple feedback scheme in the single-user case, and an approximate ,expression in the two-user case. The asymptotic results closely predict performance of practical finite systems. We demonstrate that the simple feedback scheme yields most gain for either low system loads or low SNR. The power saving is in the order of 1-2 dB per signature for a wide range of system loads and SNRs.

We characterize the asymptotic spectral efficiency of the linear minimum mean squared error (LMMSE) receiver for multiuser multisignature multicarrier (MC) code-division multiple access (CDMA) communication systems. We consider signatures which are orthogonal at each transmitter. Our results are asymptotic as the number of signatures per user and processing gain both tend to infinity with fixed ratio. Our results rely on approximating covariance matrices with unitarily invariant matrices that are asymptotically free.

We study the capacity of a single-user channel with multiple antennas and limited feedback. The receiver has perfect channel knowledge, and can relay B bits, which specify a beamforming vector, to the transmitter. We show that a random vector quantization scheme is asymptotically optimal, and give a simple expression for the associated capacity.

Incremental redundancy, or hybrid type-II ARQ (HARQ), algorithms use a combination of forward error correction and retransmissions to guarantee reliable packet data communication. In our previous work (V. Tripathi et al. 2003), we have proposed an adaptive HARQ algorithm that exploits received codeword reliability for optimizing the size of the subsequent retransmissions. The optimization is based on two mappings: the codeword reliability to block error rate (BLER) mapping and the coding rate to codeword reliability mapping. We provide analytical approximations for these mappings for any convolutional code. Through simulations, the approximations are shown to be accurate in the range of interest.

This paper considers a multicarrier (MC) code-division multiple-access system where each user employs multiple signatures. The receiver is linear and minimizes the mean square error of the data estimate. Both multiple-user and single-user systems are considered, as well as single and multiple signatures per user. In each case, an asymptotic analysis is used to derive the output signal-to-interference-plus-noise ratio (SINR) as a function of the system loading, the noise power, and the fading properties of the channel. Asymptotic in this case means that the number of independent subcarriers and number of signatures per user each tends to infinity with fixed ratio. The associated bit-error rate (BER) is evaluated for binary phase-shift keying symbols. Simulations show that the asymptotic SINRs and BERs derived in each case are accurate for realistic finite systems.

Adaptive iterative receivers which combine multiuser decision-feedback detection with maximum a posteriori (MAP) decoding and soft feedback are presented for synchronous coded direct sequence-code-division multiple access. Both successive and parallel demodulation of users are considered. Optimal filters are derived using both minimum mean squared error and least squares (LS) criteria. The latter assumes short (repeated) spreading codes and that the users to be demodulated simultaneously transmit training sequences. The LS criterion does not require prior knowledge or estimates of spreading codes and channels. Simulation results show that the adaptive receiver can perform significantly better than the standard (soft) interference canceller, since the adaptive algorithm attempts to measure and exploit the second-order statistics between the input and output of the MAP decoder. With limited training, successive feedback and decoding performs significantly better than parallel feedback. The effect of code rate on performance is examined, and reduced-rank versions of the adaptive LS algorithms, which can reduce training overhead, are also presented.

We consider forward link power allocation for voice users in a code-division multiple-access wireless network. Admission control policies are investigated, which base a new call admission decision not only upon available capacity, but also upon the required forward link transmit power and upon the user's willingness to pay. We assume that each voice user has a utility function that describes the user's willingness to pay as a function of forward link signal-to-interference plus noise ratio. The network objective is to maximize either total utility summed over all users or total revenue generated from all users. Properties of the optimal power and code allocations are presented. Our key results show how these optimal allocations can be achieved using pricing. The analysis is complemented with a numerical study, which shows how the optimal prices and corresponding utility or revenue vary with load.

Power and code allocation across two adjacent cells is studied for the downlink of a code-division multiple-access voice network. Each user has a utility function that measures the user's willingness to pay, or utility, as a function of the received signal-to-interference-plus-noise-ratio. The objective is to maximize the total utility over the two cells subject to code and power constraints. When all active users receive the same utility, the optimal allocation is characterized by a pair of threshold radii for the two cells, where each radius specifies the set of active users in that cell. The behavior of the optimal radii are characterized as a function of load and available resources (power and codes). The corresponding optimal power allocation can be achieved through a pricing scheme, in which each base station announces a price for each resource, and each user responds by requesting the amount of resources that maximizes the user's surplus (utility minus cost). We show that, depending on the load and resource constraints, the two cells may have to coordinate, or exchange information, in order to maximize the total utility.

The asymptotic growth in forward-link sum capacity is characterized as a function of the number of users and transmit antennas with linear receivers. We assume a single cell with frequency-selective fading channels, which are known at the cellular base station transmitter, and a single receive antenna at each mobile. We first show that when the channel matrices are circulant, multicarrier transmission maximizes the sum mutual information. A particular subchannel is allocated to the user with the largest channel gain with maximum-ratio combining at the transmitter, and the optimal power allocation across subchannels is determined by water pouring over those gains. By applying results from extreme value theory, we then show that when the channel consists of a large number of i.d.d. Rayleigh fading subchannels, the sum capacity grows as O(log(/spl radic/(N log U )+N)) where N is the number of transmit antennas, and U is the number of users. Numerical results are presented, which show that the asymptotic results are valid for moderately sized systems.

We present an asymptotic analysis of a multi-signature multi-carrier CDMA communications system. Such a system is suited to scalable data rate services with decentralized control. Specifically, we derive the asymptotic SINR at the output of a multi-user linear minimum mean squared error (LMMSE) receiver and the asymptotic sum spectral efficiency of both the LMMSE and optimal receivers. Simulation studies demonstrate that the asymptotic results closely predict the performance of practical finite systems.

In this paper, we consider multicarrier transmission through a frequency-selective fading channel with limited feedback. An on-off power allocation activates the set of subchannels with gains above a threshold. We model the sequence of subchannel gains as a Markov process, and give a lower bound on the feedback rate in bits per subchannel needed to specify the sequence of activated subchannels as a function of the activation threshold. Optimizing the threshold gives the same asymptotic growth in capacity as optimal water-filling as the number of subchannels N goes to infinity. If the ratio of coherence bandwidth to the total available bandwidth is fixed, then the ratio between minimum feedback rates with correlated and i.i.d. subchannels, respectively, converges to zero with N. For a sequence of Rayleigh fading subchannels, which are modeled as a first-order autoregressive process, the ratio goes to zero as O (/spl radic/logN/N) with the optimized threshold. We also consider finite-precision rate control on each subchannel, and show that the feedback rate required to specify the sequence of assigned rate levels across subchannels gives the same asymptotic increase in achievable rate with N as the (infinite-precision) on-off power allocation.

In this paper we derive asymptotic performance measures for multiuser receivers in multi-carrier CDMA communication systems. We consider both single-code-per-user and multi-code cases. Specifically, we derive the asymptotic average SINR and BER at the output of a multiuser LMMSE receiver. Simulation studies demonstrate that the asymptotic results closely predict performance of practical finite systems.

Hybrid ARQ (HARQ) schemes use a combination of forward error correction and retransmissions to guarantee reliable packet data communications. In this work, we propose a HARQ scheme that exploits channel state information and received packet quality to improve system performance. Specifically, the receiver uses the average magnitude of the log-likelihood ratios corresponding to the received information bits, in order to determine the sizes of subsequent retransmissions. The proposed retransmission strategy attempts to maximize user throughput while satisfying a maximum packet delay constraint. The performance of our reliability-based type II HARQ (RBHARQ) scheme is evaluated in static and time-varying channels through simulations.

We consider "opportunistic" downlink scheduling of data traffic in a wireless network. In particular, we focus on the delay performance of such schedulers. First a channel-dependent scheduling algorithm is considered that maximizes throughput by always transmitting to the user with the best channel conditions. The delay distribution of this scheduling rule is analyzed and asymptotic results are given when the number of competing users becomes large. Simulations show these asymptotic results are a good approximation for even a small number of users. This scheduling rule may result in unfair treatment of users that have relative bad channels for a long period of time; to remedy this we propose a simple utility-based scheduling algorithm. The motivation is to maximize the time-averaged utility, where utility is a decreasing function of the delay incurred when serving a request. The scheduling algorithm takes into account both the utility function and the channel state. We give simulation results that characterize the performance of the scheduling algorithm. The effect of the temporal correlation of the channel of the performance is also studied.

Resource allocation is studied for a forward-link two-cell code division multiple access (CDMA) voice network with multiple service classes. System resources are transmitted power and codes. The service classes are specified by different user utility functions that relate utility to received signal-to-interference-plus-noise-ratio (SINR). The objective of the resource allocation is to maximize total utility over the two cells. The optimal power allocation is characterized by a set of distances, or radii, from the desired base station. Each radius corresponds to the set of active users in a particular service class, and can be enforced through a pricing scheme. We also consider setting prices to maximize revenue. In general, the prizes and power allocation that maximize revenue differ from those that maximize utility.

The large-system performance of iterative multiuser decision-feedback detectors (DFDs) is studied for synchronous coded direct-sequence code-division multiple access. Both successive and parallel demodulation of users are considered. The filters are optimized according to the minimum mean-squared error criteria, assuming perfect feedback. We first consider Viterbi decoding with hard decision feedback, and compute union bounds on the large-system error rate. We then consider maximum a posteriori (MAP) decoding with soft decision feedback, and evaluate the error rate semianalytically by assuming the log-likelihood ratios computed by the MAP decoder are Gaussian random variables. Performance is studied numerically as a function of noise level, spectral efficiency, and code rate. Results show that soft decision feedback gives substantial gains relative to hard decision feedback. At moderate spectral efficiencies (users divided by bandwidth expansion less than 0.9), the iterative DFDs with soft decision feedback based on a posteriori probabilities can achieve near-single-user performance at an E/sub b//N/sub 0/ close to the large-system capacity bound.

We consider forward-link power allocation in a wireless network with stochastically varying data requests. We assume a user's service preferences are specified via a utility function that depends on the received data rate. The allocation of power across users is studied, where this allocation may depend on both a user's channel and utility. The objective is to maximize the time-averaged utility rate subject to a stochastic total power constraint at the transmitter. For a large, heavily loaded network, we introduce a Gaussian approximation for the total transmitted power, which is used to decompose the power constraint into three more tractable constraints. We present a solution to this problem that is a combination of admission control and pricing of power. The optimal trade-off between these approaches is characterized. Numerical examples are given to illustrate these ideas.

User signature sequences and powers are jointly optimized with linear receivers for forward link code-division multiple access (CDMA). The channels are assumed to be stationary and known to the transmitter. Both voice and data services are considered, which have different requirements. For the voice service, the signatures are selected to minimize the total transmitted power, subject to a constraint on received mean squared error (MSE). For the data service, the signatures are selected to maximize the total mutual information summed over the users, subject to a transmitted power constraint. In the latter case, we show that the optimized user signatures are orthogonal.

Power allocation across users in two adjacent cells is studied for a wireless code division multiple access (CDMA) network with mixed voice and data services. We assume that each user has a utility function that measures the user's satisfaction, or utility, as a function of the received signal-to-interference-plus-noise ratio (SINR). Each particular service (voice or data) is associated with a different utility function. We consider the forward link. Our objective is to allocate transmitted power to maximize the total utility summed over all active users subject to rate and power constraints. We show that the maximum utility can be achieved with a pricing scheme. We characterize the solution to a one-cell utility maximization problem with fixed interference from the other cell. For two-cell utility maximization, the two cells must cooperate to achieve the maximum utility.

Joint transmitter-receiver adaptation is studied for the reverse link of a direct sequence-code division multiple access system with short signature sequences. The signature for a particular user is computed at the receiver and transmitted back to the transmitter via a feedback channel. A reduced-rank transmitter adaptation scheme is presented in which the signature is constrained to lie in a lower dimensional subspace. This allows a tradeoff between system performance and the number of estimated parameters. Analytical and simulation results show that adaptation of relatively few transmitter coefficients can lead to significant performance improvements. Adaptive algorithms are derived for estimating the transmitter coefficients in the presence of multipath. We consider both collective optimization, in which the users adapt together to improve a global system performance criterion, and individual optimization, in which the signature for a particular user is adapted to optimize individual performance. Numerical results are presented, which show that both individual and collective joint transmitter-receiver adaptation can effectively preequalize the channel and avoid interference at high loads.

A class of adaptive reduced-rank interference suppression algorithms is presented based on the multistage Wiener filter (MSWF). The performance is examined in the context of direct-sequence (DS) code division multiple access (CDMA). Unlike the principal components method for reduced-rank filtering, the algorithms presented can achieve near full-rank performance with a filter rank much less than the dimension of the signal subspace. We present batch and recursive algorithms for estimating the filter parameters, which do not require an eigen-decomposition. The algorithm performance in a heavily loaded DS-CDMA system is characterized via computer simulation. The results show that the reduced-rank algorithms require significantly fewer training samples than other reduced- and full-rank algorithms.

We consider a direct sequence (DS-) code division multiple access (CDMA) system with orthogonally multiplexed pilot signals and minimum mean squared error (MMSE) data and channel estimation. Both flat and frequency-selective fading channels are considered. Large system analysis is used to optimize the pilot-to-data power ratio (PDR) and the code rate for a fixed bandwidth expansion. Specifically, the PDR is selected to minimize the probability of error subject to a constraint on transmitted power. When the MMSE filter estimates the channel of the desired user, but averages over the channels of the interferers (corresponding to an adaptive filter in moderate to fast fading), the optimal PDR is less than that for the matched filter (MF). That is, the MMSE filter benefits from allocating more power to the data. When the MMSE filter directly incorporates estimates of all users' channel coefficients, the optimal PDR is greater than that for the MF. System performance as a function of code rate is characterized through both probability of error and cutoff rate. The optimal code rate for the MMSE receiver is generally higher than that for the MF, and increases with load and E/sub b//N/sub 0/. In the presence of fading, and with channel estimation, the optimal code rate approaches zero for both MMSE and MF receivers, but the MMSE filter is more robust with respect to a suboptimal choice of code rate.

Multiuser decision-feedback detectors (DFDs) for direct-sequence code-division multiple access, based on the minimum mean-squared error (MMSE) performance criterion, are described. Both successive and parallel feedback (interference cancellation) with hard decisions are considered. An iterative DFD is presented, which consists of cascaded DFDs, each performing successive cancellation. The two-stage DFD achieves the single-user bound in the absence of error propagation, and performs significantly better than an MMSE DFD with parallel feedback. The filter structures are generalized to include finite impulse response feedforward and feedback matrix filters, which account for asynchronous users and intersymbol interference. The effect of error propagation is illustrated through simulation. Both uncoded and coded performance results are presented. Although error propagation can significantly degrade performance, the DFDs still offer a significant performance gain relative to linear MMSE detection.

Wideband direct-sequence (DS)-code-division multiple-access (CDMA) is a strong candidate for both terrestrial and satellite components of UMTS. The forward-link capacity of a satellite DS-CDMA system with a conventional matched filter (MF) receiver is limited by interference from adjacent beams and possibly overlapping beams from multiple satellites. In this paper, we study the performance of the linear minimum mean squared error (MMSE) receiver for the satellite forward link. System constraints are long propagation delay, which prevents accurate closed-loop power control, and low on-board power consumption, which implies a low received bit energy to noise density ratio at the mobile receiver. We consider a "one-step" power adjustment algorithm which attempts to compensate for random shadowing and path loss, and compare the associated performance of the MMSE and MF receivers. Dual-satellite diversity is also considered. The effect of code rate on performance is studied through the use of punctured convolutional codes and the evaluation of random coding bounds. Our results indicate that linear MMSE interference suppression can improve the quality of service and increase system capacity significantly.

An adaptive receiver which combines multiuser parallel decision feedback with MAP decoding in an iterative manner is presented for synchronous coded DS-CDMA. Performance with various convolutional code rates is considered. optimal filters are derived using both minimum mean squared error (MMSE) and least squares (LS) criteria. When used with short (repeated) spreading codes, the adaptive LS receiver requires only a training sequence and timing for estimation of all filter coefficients. The adaptive receiver performs significantly better than the standard (soft) interference canceller, since the adaptive algorithm attempts to measure and exploit the joint statistics of the output of the MAP decoder with the input symbols. Numerical results are presented which illustrate how performance depends on the rate of the convolutional code, assuming similar decoding complexity. These results show that low code rates perform best at moderate loads and low received power. Higher code rates can achieve very low packet error rates for an overloaded system (number of users greater than the bandwidth expansion).

We compare the performance of iterative multi-user successive and parallel decision feedback detectors (DFDs) for code-division multiple access (CDMA). An adaptive successive-DFD (S-DFD) is first presented, which requires only a training sequence and associated timing to estimate all filter coefficients. Simulation results show that with limited training, the adaptive S-DFD performs significantly better than the adaptive parallel-DFD (P-DFD). A large system analysis of error rate for non-adaptive iterative DFDs is also presented, and shows that the S-DFD converges with fewer iterations than the P-DFD.

We consider dynamic resource allocation (DRA) for the reverse-link of a multiuser packet DS-CDMA system with voice and data traffic. Our objective is to minimize the total received power for voice users, and allocate all remaining power to data users so as to maximize throughput. The performance of a DRA scheme depends on how frequently resources are reassigned. We compare the performance of an "aggressive" scheme, in which the processing gain (PG) is reassigned to all users each time a packet arrives or departs, with "timid" schemes, in which the PG cannot be changed in the middle of a packet ("packet-timid") or a session ("flow-timid"). For the parameters considered, our results show that aggressive and packet-timid DRA perform similarly. Flow-timid DRA performs significantly worse than the other two schemes, and the difference in performance increases with traffic intensity.

Resource allocation is studied for the forward link of a two-cell wireless direct sequence (DS)-code division multiple access (CDMA) network. A voice service is assumed, for which system resources are transmitted power and codes. Each user has a utility function that measures the user's willingness to pay as a function of the received quality of service (QoS). Our objective is to maximize the total utility over all active users. We characterize the optimal power distribution across the two cells, and show that in general, the cells must coordinate, or exchange information, to achieve the maximum utility. The optimal allocation can be achieved by a pricing scheme, in which each base station announces a price for each resource, and each user responds by buying an amount of resources that maximizes the user's surplus (utility minus cost).

Adaptive linear interference suppression for direct-sequence (DS) code-division multiple access (CDMA) is studied in the presence of time- and frequency-selective fading. Interference suppression is achieved with an adaptive digital filter which spans a single symbol interval. Both decision-directed and blind adaptive algorithms, which do not require a training sequence, are considered. Modifications to least squares adaptive algorithms are presented which are compatible with differential coding and detection. For frequency-selective fading, adaptive algorithms are presented based upon different assumptions concerning knowledge of the desired user's channel. Specifically, the cases considered are as follows: (1) perfect knowledge of the desired channel; (2) knowledge of only the relative path delays; and (3) knowledge of only one delay corresponding to the strongest path. Computer simulation results are presented which compare the performance of these algorithms with the analogous RAKE receivers. These results show that for case (3), even slow fading can cause a significant degradation in performance. Effective use of channel parameters in the adaptive algorithm reduces the sensitivity to fade rate, although moderate to fast fading can significantly compromise the associated performance gain relative to the RAKE receiver.

The performance of reduced-rank linear filtering is studied for the suppression of multiple-access interference. A reduced-rank filter resides in a lower dimensional space, relative to the full-rank filter, which enables faster convergence and tracking. We evaluate the large system output signal-to-interference plus noise ratio (SINR) as a function of filter rank D for the multistage Wiener filter (MSWF) presented by Goldstein and Reed. The large system limit is defined by letting the number of users K and the number of dimensions N tend to infinity with K/N fixed. For the case where all users are received with the same power, the reduced-rank SINR converges to the full-rank SINR as a continued fraction. An important conclusion from this analysis is that the rank D needed to achieve a desired output SINR does not scale with system size. Numerical results show that D=8 is sufficient to achieve near-full-rank performance even under heavy loads (K/N=1). We also evaluate the large system output SINR for other reduced-rank methods, namely, principal components and cross-spectral, which are based on an eigendecomposition of the input covariance matrix, and partial despreading. For those methods, the large system limit lets D/spl rarr//spl infin/ with D/N fixed. Our results show that for large systems, the MSWF allows a dramatic reduction in rank relative to the other techniques considered.

We study the forward link of a DS-CDMA system with transmitter diversity, assuming the channel is known at the receiver but not at the transmitter. Space-time coding is compared to orthogonal designs for a block fading channel, including frequency-selective fading. A minimum mean squared error (MMSE) decision-feedback detector (DFD) suppresses multiple-access interference and cancels self-interference from the multiple transmitter antennas. This receiver can be implemented adaptively in the absence of channel estimates. We consider both hard decision-feedback and iterative soft decision-feedback in combination with MAP decoding. Our results show that for the cases considered, the hard and soft DFDs perform close to the receiver with perfect cancellation, which offers significant gain with respect to the orthogonal designs.

This paper studies pricing as a means for resource allocation in a wireless direct-sequence (DS) code division multiple access (CDMA) system. We consider the forward link of a single cell with orthogonal codes and voice traffic. The base station announces a price per unit transmitted power and a price per code, and the users respond according to their individual utilities. The objective is to set prices to maximize either total user utility or total revenue. The solution to the former problem (maximize utility) is presented. To study the latter problem we derive the large system revenue as the number of users and codes tend to infinity with fixed ratio. The large system revenue depends on the distribution of utilities and path loss across the user population, and may not be a unimodal function of the prices. Numerical results based on a simple model for user utility show how the optimal prices and revenue vary with the offered load.

We consider a direct sequence (DS-) CDMA system with orthogonally multiplexed pilot signals and minimum mean square error (MMSE) data and channel estimation. Large system analysis is used to optimize the pilot-to-data power ratio (PDR). Specifically, the PDR is selected to minimize the probability of error subject to a transmitted power constraint. Both flat and frequency-selective fading channels are considered. When the MMSE filter averages over the channels of the interferers, the optimal PDR is less than that for the matched filter. That is, the MMSE filter benefits from allocating more power to the data. For the case considered, when the MMSE filter directly incorporates channel estimates, the optimal PDR is greater than that for the matched filter.

The performance of the minimum mean-squared error (MMSE) receiver for the detection of direct sequence code division multiple access is considered in various fading channel models. Several modifications to the basic MMSE receiver structure which have been previously proposed for use on nonselective fading channels are reviewed and shown to represent different approximations to a single common form. The performance of this general structure is analyzed as well as various extensions suitable for frequency-selective fading channels. Particular attention is given to the performance advantage gained through knowledge of the fading parameters of the various transmission paths of each user's signal. It is shown that having this knowledge is not particularly useful on a flat fading channel unless the loading is very heavy and even then the difference in performance is only minimal. On the other hand, having this knowledge is crucial in a multipath fading channel and the inability to learn the fading channel parameters will lead to substantial degradation in capacity. A heuristic explanation to support this result based on a dimensionality argument is also presented.

Multiuser decision-feedback detectors (DFDs) for DS-CDMA are presented using the minimum mean squared error (MMSE) criterion. Both successive and parallel feedback (interference cancellation) are considered. Short spreading codes are assumed, eliminating the need for remodulation. A multi-stage DFD is presented which consists of cascaded DFDs each performing successive cancellation. In the absence of error propagation, a two-stage structure achieves the single-user bound for all users, and is shown to be equivalent to an MMSE DFD with parallel feedback. The effect of error propagation is illustrated through simulation. Both uncoded and coded performance results are presented. These results show that the DFDs can offer a significant performance gain relative to linear MMSE detection.

The performance of a near-far-resistant, finite-complexity, minimum mean squared error (MMSE) linear detector for demodulating direct sequence (DS) code-division multiple access (CDMA) signals is studied, assuming that the users are assigned random signature sequences. We obtain tight upper and lower bounds on the expected near-far resistance of the MMSE detector, averaged over signature sequences and delays, as a function of the processing gain and the number of users. Since the MMSE detector is optimally near-far-resistant, these bounds apply to any multiuser detector that uses the same observation interval and sampling rate. The lower bound on near-far resistance implies that, even without power control, linear multiuser detection provides near-far-resistant performance for a number of users that grows linearly with the processing gain.

Minimum mean squared error (MMSE) detection has been proposed for direct sequence-code division multiple access (DS-CDMA) systems. The MMSE detectors are near-far resistant, and can be adapted with standard adaptive algorithms without knowledge of user parameters (i.e., spreading codes). These algorithms rely on a known training sequence for initial adaptation, and subsequently switch to a decision-directed mode. After the switch, the performance of the adaptive algorithm may degrade substantially if a strong interferer suddenly appears (i.e., if power control is relaxed). We present a "rescue" algorithm that monitors for sudden changes in the signal space, which may be caused by the appearance of a strong interferer. If a new interferer is detected, decision-directed adaptation is suspended, and an estimate of the optimal filter coefficients is obtained without a training sequence. It is shown that in the presence of low-level background noise, a good estimate can be obtained within a few symbol intervals. A numerical example is given which illustrates the performance of the rescue algorithm in a synchronous DS-CDMA system.

The growing demand to transmit high-speed digital data in many local area networks (LANs) and digital subscriber lines (DSLs) has resulted in a wide variety of transmission systems that have to co-exist on twisted wire copper pairs. In this paper, we address the problem of maintaining spectrum compatibility between various services that may use different transmission technologies, by shaping in an optimal manner, the power spectral density (PSD) of the transmit signal. A multitone modulation scheme such as discrete multitone (DMT) has the flexibility of optimizing the power spectrum over more than one (disjoint) frequency band, and is suitable for twisted pair subscriber loops, and other transmission media, where the optimized transmit spectrum is likely to occupy more than one frequency band. DMT has been selected by the American National Standards Institute (ANSI) T1E1.4 Standards Committee as the standard modulation scheme for asymmetric DSL (ADSL). The results presented in this paper are for the specific application of DMT to transport ADSL payloads of over 6 Mb/s from the network to the customer. We consider spectral compatibility between ADSL, the T1 repeater system, high bit-rate DSL (HDSL), and integrated services digital networks (ISDN) basic rate access (BRA) systems. The simulation results show that: 1) one can customize the transmit PSD to achieve optimum ADSL performance in a specified noise environment; 2) this optimum performance can result in as much as approximately 6 dB improvement in signal-to-noise ratio (SNR) when compared to the nonoptimized PSD chosen by the T1E1.4 committee; 3) in achieving the above improvements, the total maximum transmit power is still consistent with the limit set by the T1E1.4 committee. Further work is required to support the simulation results with measured data. The mathematical analysis is based on the use of Lagrange multipliers to solve the constrained optimization problem, and is easily extended to other asymmetric and full-duplex wireline transmission systems operating at much higher data rates. The practicality of implementing the proposed optimization routine requires further investigation

An alternative code-division multiple-access (CDMA) scheme to spread spectrum (SS), called spread time (ST) is proposed for bandlimited multiple-access channels. ST-CDMA can be considered the time-frequency dual of SS-CDMA. In ST-CDMA pseudorandom (PN) sequences are assigned to each user, and the Fourier transform of the transmitted pulse for a given user is determined by modulating the phase of the desired transmitted spectrum by the user's PN-sequence. The transmitted data for a particular user can be recovered by sampling the output of a filter matched to the user's pulse. Implementations are described in which surface acoustic wave devices are used to perform the matched filtering or Fourier transformation. Averaged signal-to-interference plus noise ratio (SIR) and spectral efficiency are computed for both asynchronous ST and direct-sequence SS-CDMA systems, assuming an arbitrary channel transfer function H(f), which is the same between all pairs of users. The results are the same for SS and ST provided that the magnitude of the Fourier transform of the chip shape in the SS system is the same as the magnitude of the Fourier transform of the ST pulse shape. The main advantage of the ST technique Is the flexibility with which the transmitted spectrum can be selected. We derive the transmitted spectrum that maximizes the SIR subject to an average power constraint.>

The decorrelating detector and the linear minimum mean-square error (MMSE) detector are known to be effective strategies to counter the presence of multiuser interference in code-division multiple-access channels; in particular, those multiuser detectors provide optimum near-far resistance. When training data sequences are available, the MMSE multiuser detector can be implemented adaptively without knowledge of signature waveforms or received amplitudes. This paper introduces an adaptive multiuser detector which converges (for any initialization) to the MMSE detector without requiring training sequences. This blind multiuser detector requires no more knowledge than does the conventional single-user receiver: the desired user's signature waveform and its timing. The proposed blind multiuser detector is made robust with respect to imprecise knowledge of the received signature waveform of the user of interest.>

Given a discrete-time, linear, shift-invariant channel with finite impulse response, the problem of designing finite-length input signals with bounded amplitude (l/sub /spl infin// norm) such that the corresponding output signals are maximally separated in amplitude (l/sub /spl infin// sense) is considered. In general, this is a nonconvex optimization problem, and appears to be computationally difficult. An optimization algorithm that seems to perform well is described. Optimized signal sets and associated minimum distances (minimum l/sub /spl infin// separation between two distinct channel outputs) are presented for some example impulse responses. A conjectured upper bound on the minimum distance is given that is easily computed given the impulse response of the channel, the number of inputs, and the input length. This upper bound is shown to be valid for a limited class of impulse response functions.>

In personal communications applications, users communicate via wireless with a wireline network. The wireline network tracks the current location of the user, and can therefore route messages to a user regardless of the user's location. In addition to its impact on signaling within the wireline network, mobility tracking requires the expenditure of wireless resources as well, including the power consumption of the portable units carried by the users and the radio bandwidth used for registration and paging. Ideally, the mobility tracking scheme used for each user should depend on the user's call and mobility pattern, so the standard approach, in which all cells in a registration area are paged when a call arrives, may be wasteful of wireless resources. In order to conserve these resources, the network must have the capability to page selectively within a registration area, and the user must announce his or her location more frequently. We propose and analyze a simple model that captures this additional flexibility. Dynamic programming is used to determine an optimal announcing strategy for each user. Numerical results for a simple one-dimensional mobility model show that the optimal scheme may provide significant savings when compared to the standard approach even when the latter is optimized by suitably choosing the registration area size on a per-user basis. Ongoing research includes computing numerical results for more complicated mobility models and determining how existing system designs might be modified to incorporate our approach.

In personal communications applications, users communicate via wireless with a wireline network. The wireline network tracks the current location of the user, and can therefore route messages to a user regardless of the user's location. In addition to its impact on signaling within the wireline network, mobility tracking requires the expenditure of wireless resources as well, including the power consumption of the portable units carried by the users and the radio bandwidth used for registration and paging. Ideally, the mobility tracking scheme used for each user should depend on the user's call and mobility pattern, so that the current registration area approach (which ignores such information) may be wasteful of wireless resources under certain circumstances. In the paper, the authors provide a model and an optimization algorithm based on dynamic programming for choosing the mobility tracking scheme on a per-user basis. While illustrative results are provided for a simple one-dimensional mobility model, the approach is shown to be applicable to a very general class of problems.>

We consider interference suppression for direct-sequence spread-spectrum code-division multiple-access (CDMA) systems using the minimum mean squared error (MMSE) performance criterion. The conventional matched filter receiver suffers from the near-far problem, and requires strict power control (typically involving feedback from receiver to transmitter) for acceptable performance. Multiuser detection schemes previously proposed mitigate the near-far problem, but are complex and require explicit knowledge or estimates of the interference parameters. In this paper, we present and analyze several new MMSE interference suppression schemes, which have the advantage of being near-far resistant (to varying degrees, depending on their complexity), and can be implemented adaptively when interference parameters are unknown and/or time-varying, Numerical results are provided that show that these schemes offer significant performance gains relative to the matched filter receiver. We conclude that MMSE detectors can alleviate the need for stringent power control. In CDMA systems, and may be a practical alternative to the matched filter receiver.>

The problem of jointly selecting optimal transmitted signals and the channel frequency response, assuming the channel is linear and time-invariant, is considered where the minimum L/sub 2/ distance between channel outputs is the optimization criterion. Results indicate that, for a fixed information rate, as the length of the inputs goes to infinity the optimal channel frequency response is a constant wherever it is positive. A crude but simple volume estimate suggests that the optimal channel bandwidth is equal to twice the information rate. A second problem considered is the joint optimization of channel inputs and a transmitter filter, given a fixed channel response. This problem remains unsolved in general, although the present discussion indicates that the optimal filter transfer function should simply be constant over the bandwidth where the asymptotic transmitted spectrum is nonzero.>

Full-duplex data communication over a multi-input/multi-output linear time-invariant channel is considered. The minimum mean square error (MMSE) linear equalizer is derived in the presence of both near- and far-end crosstalk and independent additive noise. The MMSE equalizer is completely specified in terms of the channel and crosstalk transfer functions by using a generalization of previous work due to Salz (1985). Conditions are given under which the equalizer can completely eliminate both near- and far-end crosstalk and intersymbol interference. The MMSE transmitter filter, subject to a transmitted power constraint, is specified when the channel and crosstalk transfer functions are bandlimited to the Nyquist frequency. Also considered is the design of MMSE transmitter and receiver filters when the data signals are arbitrary wide-sense stationary continuous or discrete-time signals, corresponding to the situation where the crosstalk is not phase-synchronous with the desired signal.>

The problem of maximizing the output energy of a linear time-invariant channel, given that the input signal is time and amplitude limited, is considered. It is shown that a necessary condition for an input mu to be optimal, assuming a unity amplitude constraint is that it satisfy the fixed-point equation=sgn (F( mu )), where the functional F is the convolution of mu with the autocorrelation function of the channel impulse response. It is also shown that all solutions to this equation for which mod mu mod =1 almost everywhere correspond to local maxima of the output energy. Iteratively recomputing mu from the fixed-point equation leads to an algorithm for finding local optima. Numerical results are given for the cases where the transfer function is ideal low-pass and has two poles. These results support the conjecture that in the ideal low-pass case the optimal input signal is a single square pulse. A generalization of the preceding fixed-point condition is also derived for the problem of maximally separating N outputs of a discrete-time, linear, time-invariant channel.>

A decision feedback equalizer (DFE) containing a feedback filter with both poles and zeros is proposed for high-speed digital communications over the subscriber loop. The feedback filter is composed of a relatively short FIR filter that cancels the initial part of the channel impulse response, which may contain rapid variations due to bridge taps, and a pole-zero, or IIR, filter that cancels the smoothly decaying tail of the impulse response. Modifications of an adaptive IIR algorithm, based on the Steiglitz-McBride (1965) identification scheme, are proposed to adapt the feedback filter. A measured subscriber loop impulse response is used to compare the performance of the adaptive pole-zero DFE, assuming a two-pole feedback filter, with a conventional DFE having the same number of coefficients. Results show that the pole-zero DFE offers a significant improvement in mean squared error relative to the conventional DFE. The speed convergence of the adaptive pole-zero DFE is comparable to that of the conventional DFE using the standard least mean square (LMS) adaptive algorithm.>

The maximum data rate that can be reliably communicated given a linear, time-invariant, dispersive channel, a receiver that samples the channel output to within an accuracy of +or-d where d>0, and a transmitter with an output amplitude constraint is evaluated. For any dispersive channel the maximum rate depends on d and is finite. The transmitted waveforms must be designed so that two channel outputs associated with two distinct transmitted signals are separated in amplitude at a particular time by d. It is shown that given any channel impulse response with rational Laplace transform, there exists an optimal sets of inputs that are +or-A everywhere where A is the maximum allowable amplitude. Furthermore, in any finite time interval, each input changes sign a finite number of times. If the channel impulse response is a single decaying exponential, it is shown that simple binary signaling, in which A or -A, depending on the current message bit, is transmitted during each symbol interval, maximizes the data rate.>

For Pt. I see ibid., vol.37, no.5, p.1327-141 (1991). For a linear, time-invariant, discrete-time channel with a given transfer function H(f), and information rate R bits/T, where T is the symbol interval, an optimal signal set of length K is defined to be a set of 2/sup RK/ inputs of length K that maximizes the minimum l/sub 2/ distance between pairs of outputs. The author studies the minimum distance between outputs, or equivalently, the coding gain of optimal signal sets as K to infinity . He shows how to estimate the coding gain, relative to single-step detection, of an optimal signal set length K when K is large.>

Given a linear, time-invariant, discrete-time channel, the problem of constructing N input signals of finite length K that maximize minimum l/sub 2/ distance between pairs of outputs is considered. Two constraints on the input signals are considered: a power constraint on each of the N inputs (hard constraint) and an average power constraint over the entire set of inputs (soft constraint). The hard constraint, problem is equivalent to packing N points in an ellipsoid in min(K,N-1) dimensions to maximize the minimum Euclidean distance between pairs of points. Gradient-based numerical algorithms and a constructive technique based on dense lattices are used to find locally optimal solutions to the preceding signal design problems. Two numerical examples are shown for which the average spectrum of an optimized signal set resembles the water pouring spectrum that achieves Shannon capacity, assuming additive white Gaussian noise.>

Transceiver designs for multiple coupled channels typically treat the crosstalk between adjacent twisted pairs as random noise uncorrelated with the transmitted signal. The authors propose a transmitter/receiver pair that compensates for crosstalk by treating an entire bundle of twisted pairs as a single multi-input/multi-output channel with a (slowly varying) matrix transfer function. The proposed transceiver uses multichannel adaptive FIR filters to cancel near- and far-end crosstalk, and to pre- and postprocess the input/output of the channel. Linear pre- and postprocessors that minimize mean squared error between the received and transmitted signal in the presence of both near- and far-end crosstalk are derived. The performance of an adaptive near-end crosstalk canceller using the stochastic gradient (least-mean-square) transversal algorithm is illustrated by numerical simulation. Plots of mean squared error versus time and eye diagrams are presented, assuming a standard transmission line model for the channel. A signal design algorithm that maps a vector input bit stream to a stream of channel symbol vectors is also presented and illustrated explicitly for s simple model of two coupled channels.>

Upper and lower bounds on the epsilon -rate of a linear, time-invariant multiple input multiple output channel are derived by using the same volume argument previously used by W.L. Root (1968) for single input single output channels. Because these bounds are not very tight, an approximation to the epsilon -rate is presented which lies between the upper and lower bounds, and can be used to compare epsilon -rates for different channels. The extension considered uses a result due to Lerer (1978) on the eigenvalue distribution of a convolution operator with a matrix kernel (impulse response). The present results are used to assess the increase in data rate attainable by designing input signals which exploit the multidimensional nature of the channel, relative to treating each constituent channel in isolation. Numerical results based upon a simple model for two coupled twisted-pair wires are presented.>

The problem of finding the maximum achievable data rate over a linear time-invariant channel is considered under constraints different from those typically assumed. The limiting factor is taken to be the accuracy with which the receiver can measure the channel output. More precisely, the following problem is considered. Given a channel with known impulse response h(t), a transmitter with an output amplitude constraint, and a receiver that can distinguish between two signals only if they are separated in amplitude at some time t/sub 0/ by at least some small positive constant d, what is the maximum number of messages, N/sub max/, that can be transmitted in a given time interval (0,T)? Lower bounds on N/sub max/ can be easily computed by constructing a particular set of inputs to the channel. The main result is an upper bound on N/sub max/ for arbitrary h(t). The upper bound depends on the spread of h(t), which is the maximum range of values the channel output may take at some time t/sub 0/>0 given that the output takes on a particular value alpha at time t=0. Numerical results are shown for different impulse responses, including two simulated telephone subscriber loop impulse responses.>

The following problem is discussed: given a channel with known impulse response h(t), a transmitter with an output amplitude constraint, and a receiver that can distinguish between two signals only if they are separated in amplitude at some time t/sub 0/ by at least some small positive constant d, then what is the maximum number of messages, N, that can be transmitted in a given time interval (0, T)? Upper bounds for arbitrary h(t) are computed by solving linear programs with bounded variables and one equality constraint. Solutions to linear programs in this class can be obtained very fast using, for example, a linear-time algorithm due to C. Witzgall (1980). Numerical results are shown for different impulse responses, including a simulated telephone subscriber loop impulse response. Assuming that the receiver resolution d is small, the upper bound is typically two to three times the lower bound for the cases examined.>

The authors consider transmission of data over multiple coupled channels, such as bundles of twisted-pair cables in the local subscriber loop, and between central offices in the public switched telephone network. Transceiver designs for such channels typically treat the crosstalk between adjacent cables as random noise uncorrelated with the transmitted signal. A transmitter/receiver pair is proposed which compensated for crosstalk by treating an entire bundle of cables as a single multi-input/multioutput channel with a (slowly varying) matrix transfer function. One attribute of the proposed transceiver is the use of a multichannel adaptive FIR (finite-impulse response) filter to cancel near-end crosstalk. Results of numerical simulations, including plots of mean squared error vs. time, and eye diagrams, are presented assuming a standard transmission line mode for the channel. These results indicate that data rates over coupled channels can be significantly increased by exploiting the multidimensional character of the channel.>

A design technique to reduce the search time for trellis codes with multilevel phase modulation is presented. Codes are constructed by connecting trellis diagrams for codes with fewer states in parallel. For example, an N-state code can be constructed by connecting two N/2-state codes. The way in which the embedded codes are connected increases the upper limit on minimum free distance otherwise imposed by parallel transitions between states. In some cases, this technique can reduce the number of codes in a code search by a factor of approximately 2/sup nu /, the number of coder states. A computer search incorporating this technique for eight-level amplitude modulation (8-AM) codes having 2/sup 11/ and 2/sup 12/ states produced codes with greater minimum free distance than reported previously (i.e. greater than 6 dB coding gain). New eight-level phase-shift-keying (8-PSK) codes, which have a different structure from previously reported codes, are also presented.>

An easily computed upper bound on the error probability of a data communications system with combined trellis coding and multilevel/phase modulation is derived, assuming an additive white Gaussian noise channel and maximum-likelihood decoding. This bound is used to search for codes obtained by set-partitioning that minimize the bound for a fixed number of trellis states. Only amplitude modulated signals typically used in voiceband modem applications are considered. The signal levels that minimize the error probability bound subject to an average power constraint are presented for some specific codes.

The convergence properties of adaptive least squares (LS) and stochastic gradient (SG) algorithms are studied in the context of echo cancellation of voiceband data signals. The algorithms considered are the SG transversal, SG lattice, LS transversal (fast Kalman), and LS lattice. It is shown that for the channel estimation problem considered here, LS algorithms converge in approximately2Niterations whereNis the order of the filter. In contrast, both SG algorithms display inferior convergence properties due to their reliance upon statistical averages. Simulations are presented to verify this result, and indicate that the fast Kalman algorithm frequently displays numerical instability which can be circumvented by using the lattice structure. Finally, the equivalence between an LS algorithm and a fast converging modified SG algorithm which uses a maximum length input data sequence is shown.

A comparison of adaptive differential pulse code modulation (ADPCM) speech compression systems is made using different recursive adaptive linear prediction algorithms. The particular algorithms considered are 1) a fixed predictor, 2) the adaptive least mean square (LMS) transversal predictor, 3) the LMS (gradient) lattice predictor, 4) the leas squares (LS) lattice predictor, and 5) an LS lattice predictor combined with a third-order pitch inverse filter. The results indicate that for the conditions simulated, the difference in system performance using the different adaptive algorithms is negligible, suggesting that the predictor having the simplest implementation is the best.

A simple model characterizing the convergence properties of an adaptive digital lattice filter using gradient algorithms has been reported [1]. This model is extended to the least mean square (LMS) lattice joint process estimator, to the recursive least squares (LS) algorithms, and is compared with computer simulations. Interestingly, the LS models are more accurate than the previous LMS models. In addition, although the LS lattice consistently converges somewhat faster than the LMS lattice, they both exhibit similar behavior.

Convergence properties of a continuously adaptive digital lattice filter used as a linear predictor are investigated for both an unnormalized and a normalized gradient adaptation algorithm. The PARCOR coefficient mean value and the output mean square error are approximated and a simple model is described which approximates these quantities as functions of time. Calculated curves using this model are compared with simulation results. Results obtained for a two stage lattice are then compared with the two-stage 1ms transversal filter algorithm, demonstrating that it is possible but unlikely for the transversal filter to converge faster than the analogous lattice filter.