We consider the problem of localizing multiple targets by millimeter wave (mmWave) radars with irregular antenna placement, i.e., trapezoid virtual antenna array. The goal is to estimate both the number of targets and their 3-D locations. While many well-known algorithms have been developed for either problems, they still suffer from several limitations, such as the need for a large amount of sampled radar data and high computation complexity. In this work, we develop an efficient solution by exploring the received signal structure in two steps: 1) estimating the number of targets and their ranges by extending Barone’s method to handle data from multiple antennas and 2) estimating the angle of arrival of each target by a Least-Square algorithm optimization. The proposed algorithm has been evaluated through Monte-Carlo simulations and an indoor testbed. By comparing with baseline algorithms, including 2D-FFT and multiple signal classification (MUSIC), we find that the proposed algorithm has the best performance in high signal-to-noise ratio regimes.

In this paper, we propose a new sparse coprime array design that achieves a higher number of degrees-of-freedom for direction-of-arrival (DOA) estimation. The proposed array design completely avoids lag redundancies between the two constituting subarrays of the coprime array, thus achieving the maximum number of unique correlation lags under the coprime array framework. As a result, given the same number of physical sensors, the proposed design resolves more sources than other coprime array designs with enhanced DOA estimation performance. Simulation results demonstrate the superior performance of the proposed coprime array design.

To enable ultrareliable low-latency wireless communications required in the Industrial Internet of Things, in this paper we develop an energy-based modulation [i.e., non-negative pulse amplitude modulation (PAM)] constellation design framework for noncoherent detection in massive single-input multiple-output (SIMO) systems. We consider that one single-antenna transmitter communicates to a receiver with a large number of antennas over a Rayleigh fading channel, and the receiver decodes the transmitted information at the end of every symbol. For such an SIMO system with non-negative PAM modulation, we first propose a fast noncoherent maximum-likelihood decoding algorithm and derive a closed-form expression of its symbol error probability (SEP). We then enhance the system energy efficiency by finding the optimal PAM constellation that minimizes the exact SEP subject to a total signal power constraint for such a system with an arbitrary number of receiver antennas, signal-to-noise ratio (SNR), and constellation size. Furthermore, the closed-form upper and lower bounds on the optimal SEP are derived. Based on these bounds, the exact expression for coding gain of the dominant term of the SEP is presented for such an optimal massive SIMO system. We also present an asymptotic SEP expression at a high SNR regime and the approximate diversity gain of the system. Simulation results for the proposed optimal PAM constellation validate the theoretical analysis, and show that our presented optimal constellation attains significant performance gains over the currently available minimum-distance-based constellation systems.

Spatial modulation (SM) is viewed as a promising multi-antenna technology for future communications. Numerous works on SM have been done on the specific optimized designs and performance analysis mainly based on high signal-to-noise ratio (SNR) union bound approximation. However, the existing information-theoretical investigation indicates that SM is more efficient in low SNR regimes. Therefore, the most prominent potential of SM with respect to the error performance is still not well understood. As a first step to filling this void, we consider the fundamental applicability of SM in multi-antenna channels. On the one hand, for high SNR regimes, by developing the optimal structure of multi-input single-output (MISO) and proposing efficient multiple-input multiple-output (MIMO) transmission schemes, we prove that the performance limits of SM-MISO and SM-MIMO with respect to the received minimum Euclidean distance (MED) can be outperformed even by single radio-frequency chain transmission. On the other hand, for the low-SNR regimes, we show the respective optimality of: 1) SM for single-user energy-based noncoherent massive MIMO (ED-MaMIMO) channels; and 2) dual SM of multi-user ED-MaMIMO which collaboratively modulates data onto both the indexes of transmitter antennas and those of the users. In addition, the dual SM for multiuser ED-MaMIMO has a practically important property that partial coordination via user index modulation can be as useful as full one. Our analytical findings and numerical results strongly suggest that more attention should be paid to the low-SNR behavior and designs of SM rather than the currently popular MED optimization in high-SNR regimes. This paper points out a direction, towards which SM should evolve, and also shows that combination of SM with the users' index modulation can be very useful for designing the optimal finite-alphabet nonorthogonal multiple-access.

This paper investigates the symbol error probability (SEP) of point-to-point massive multiple-input multiple-output (MIMO) systems using equally likely PAM, PSK, and square QAM signallings in the presence of transmitter correlation. The receiver has perfect knowledge of the channel coefficients, while the transmitter only knows first- and second-order channel statistics. With a zero-forcing (ZF) detector implemented at the receiver side, we design and derive closed-form expressions of the optimal precoders at the transmitter that minimizes the average SEP over channel statistics for various modulation schemes. We then unveil some nice structures on the resulting minimum average SEP expressions, which naturally motivate us to explore the use of two useful mathematical tools to systematically study their asymptotic behaviors. The first tool is the Szegö's theorem on large Hermitian Toeplitz matrices and the second tool is the well-known limit: limx→∞(1 + 1/x)x= e. The application of these two tools enables us to attain very simple expressions of the SEP limits as the number of the transmitter antennas goes to infinity. A major advantage of our asymptotic analysis is that the asymptotic SEP converges to the true SEP when the number of antennas is moderately large. As such, the obtained expressions can serve as an effective SEP approximations for massive MIMO systems even when the number of antennas is not very large. For the widely used exponential correlation model, we derive closed-form expressions for the SEP limits of both optimally precoded and uniformly precoded systems. Extensive simulations are provided to demonstrate the effectiveness of our asymptotic analysis and compare the performance limit of optimally precoded and uniformly precoded systems.

In this paper, we consider a single-input multiple-output (SIMO) system, in which a single-antenna transmitter communicates with a receiver having multiple antennas. It is assumed that the channel coefficients keep constant during two consecutive time slots, after which they become new independent values. For such a system, we focus on the concept of uniquely factorable constellations (UFCs) in the design of noncoherent coding schemes under two communication scenarios. The first scenario is the massive SIMO system, in which only the first and second order channel statistical information is available. The second is the traditional Rayleigh fading SIMO system. First, parameterized massive UFC (MUFC) and unitary UFC (UUFC) are designed for each scenario. It is proved that these designs ensure the unique identification of the transmitted signals when there is no additive Gaussian white noise. Second, using the Riemannian distance (RD) metric for the RD-based detector and coding gain criterion for generalized likelihood ratio test receiver, the optimal MUFCs and UUFCs of various sizes are constructed, respectively. Finally, we exploit the structures of our proposed designs to reduce the decoding complexities compared to the exhaustive search methods. Comprehensive computer simulations show that our proposed schemes outperform the current designs in literature.

It is a difficult task for high-resolution maritime radars operating at a fast scan mode to find sea-surface floating and low-velocity small targets due to ubiquitous sea clutter, sporadic sea spikes like target returns, and shortage of shared database. In this paper, a simulation method is presented to generate high-resolution radar returns of a local sea surface with a structural trend in texture and sea spikes by integrating the existing results on large-scale sea surface generation, sea surface reflectivity, Doppler characteristics of sea clutter, and properties of sea spikes. Generally, sea-surface small target detection at a fast scan mode is composed of intrascan integration to suppress sea clutter and interscan integration to exclude false alarms and sea spikes. Based on the Doppler difference between targets and sea clutter at the two time scales of a coherent processing interval (CPI) of tens of milliseconds and a scan period of several seconds, a Doppler-guided retrospective filter (DGRF) detector is proposed, which uses the optimum coherent detection in intrascan integration and a DGRF in interscan binary and test statistic integrations. The two integrations and Doppler consistency of integrated plots are fused for the final decision. Owing to the Doppler guidance, the proposed detector effectively impedes the integration of false alarms of the intrascan processing and provides significant detection performance improvement, which is verified by the simulated data and real radar data with test small targets.

Every channel can be expressed as a convex combination of deterministic channels with each deterministic channel corresponding to one particular intrinsic state. Such convex combinations are, in general, not unique, each giving rise to a specific intrinsic-state distribution. In this paper, we study the maximum and minimum capacities of a channel when the realization of its intrinsic state is causally available at the encoder and/or the decoder. Several conclusive results are obtained for binary-input channels and binary-output channels. By-products of our investigation include a generalization of the Birkhoff-von Neumann theorem and a condition on the uselessness of causal state information at the encoder.

In this paper, we design energy-efficient space constellations for multiuser multi-input single-output visible light communication broadcast systems with channel state information (CSI) at the receiver in the three scenarios: 1) with CSI at the transmitter (CSIT); 2) with statistical CSIT; and 3) without CSIT. By utilizing the cooperation of multiuser interference, optimal multidimensional additively uniquely decomposable constellation groups are designed to optimize the received worst case performance metrics of all users subject to two commonly used power constraints, i.e., average and peak optical power constraints. The resulting optimal designs are proved to be pulse amplitude modulated with an optimal beamformer, which can be efficiently attained by numerical search for Scenarios 1 and 2 and be given in a closed form for Scenario 3. One of the common significant advantages of these designs is the fast demodulation of the sum signal from a noisy received signal, since these optimal designs result in an equivalent ideal scalar AWGN channel. Comprehensive computer simulations demonstrate that our designs significantly outperform traditional zero-forcing, minimum mean square error, and time-division methods.

We consider the non-orthogonal multiple access (NOMA) design for a classical two-user multiple access channel (MAC) with finite-alphabet inputs. In contrast to the majority of existing NOMA schemes using continuous Gaussian distributed inputs, we consider practical quadrature amplitude modulation (QAM) constellations at both transmitters, whose sizes are not necessarily the same. By adjusting the scaling factors (i.e., instantaneous transmitting powers) of both users, we aim to maximize the minimum Euclidean distance of the received sum-constellation for a maximum likelihood (ML) receiver. The formulated problem is a mixed continuous-discrete optimization problem and in general it is nontrivial to resolve. By carefully examining the structure of the objective function, we discover that Farey sequence can be employed to tackle the formulated problem. However, the existing Farey sequence is not applicable when the constellation sizes of the two users are different. To address this challenge, we define a new type of Farey sequence, termed punched Farey sequence. Based on this new definition and its properties, we manage to attain a closed-form optimal solution to the original problem by first dividing the entire feasible region into a finite number of Farey intervals and then taking the maximum over all the subintervals. Finally, computer simulations are carried out to verify our theoretical analysis, and to demonstrate the advantages of the proposed NOMA over known orthogonal and non-orthogonal designs.

In this paper, we investigate the design of energy-efficient space-time modulation for peak-limited MISO broadcast visible light communication (VLC) systems by cooperatively managing the non-negative multiuser interference. We first characterize a constellation-optimal structure that maximizes the worst-case minimum Euclidean distance of all users for a general space-time modulation design. It turns out that the optimal space-time constellation can be constructed via the spatial repetition of the optimal multidimensional constellation in time dimension over ideal additive white Gaussian noise channels. Then, based on this structure, we specifically design two classes of energy-efficient time-dimensional constellations: 1) for the integer overall bit rate, we design the optimal linear precoded block design, which admits fast maximum likelihood demodulation algorithms. 2) for the non-integer case, we propose a nonlinear precoding scheme called block coded modulation, which sums the code word sets of the optimal linear design and a block channel code. In addition, we show that these two classes of designs are addition-unique, thus, generating an energy-efficient mapping from users' data to the transmitted constellations. This property enables the efficient demodulation of the sum signal from a noisy received signal as well as the decoding of individual signal from the estimated sum signal. Extensive computer simulations indicate that our addition-unique designs have remarkable performance gains over the currently available zero-forcing, minimum mean square error and time-division multiple access methods for the multiuser multi-input-single-output VLC broadcast systems.

This paper investigates the artificial noise (AN) aided physical layer security (PLS) for energy-based massive multi-input multi-output multi-access channels with finite-alphabet data inputs, where both the legitimate base station (Bob) and the passive eavesdropper (Eve) are equipped with large antenna arrays and each user has multiple antennas. For such system, the main challenge is how to allocate power between the transmitted constellation of finite size and AN for both interference management and PLS enhancement. To this end, we first characterize a distance-optimal (DO) constellation structure that maximizes the minimum Euclidean distance of the received signals with energy detection. It turns out that the DO multiuser constellations constitute a commonly-used pulse amplitude modulation (PAM) constellation at the receiver side. Then, we specifically design an energy-efficient PAM-constellation alignment to form a received sizeable PAM constellation by adaptively aligning the power of multi-users' PAM sub-constellations. This design provides us with a new finite-alphabet non-orthogonal multi-access scheme as well as with a stepped water filling (SWF) power allocation between the constellation and AN for each user, which can provide the power-domain freedom for PLS. To spatially exploit this freedom, a SWF-based product-constant AN generation algorithm is developed such that the product of Bob's channel and the AN is a constant which can be inferred by Bob, and the channel-noise product for Eve cannot be uniquely determined, even for noise-free channels. Simulations indicate that for SWF, Bob's error rate will vanish when the number of the receiver antennas goes to large, but Eve's error rate has a non-vanishing lower-bound, even with an unlimited number of antennas. In addition, PAMA, as a new finite-alphabet NOMA scheme, has significant advantages in both security and communication error performance over the time division multi-access.

In this letter, we consider a two-way relay system in which there are two source nodes with each having a single antenna and one relay node equipped with a large number of antennas. It is assumed that each node has no channel information. For such a relay system, we systematically design a pair of absolutely additively uniquely decomposable phase-shift keying (PSK) constellations such that when any linear combination of two PSK signals with positive weight coefficients is received, each individual PSK signal can be uniquely decoded. With this, a novel distributed space-time modulation scheme is proposed for the system. We prove that when the number of antennas at the relay node grows to infinite, two user PSK symbols and large scale coefficients can be uniquely determined in a noise-free case. In a noisy case, a minimum Riemannian distance detector is developed for efficiently and effectively estimating both the channel coefficients and the transmitted signals.

This paper focuses on the non-orthogonal multiple access (NOMA) design for a classical two-user multiple access channel (MAC) with finite-alphabet inputs. In contrast to most of the existing NOMA designs using continuous Gaussian input distributions, we consider practical quadrature amplitude modulation (QAM) constellations at both transmitters, the sizes of which are assumed to be not necessarily identical. We propose maximizing the minimum Euclidean distance of the received sum constellation with a maximum likelihood (ML) detector by adjusting the scaling factors (i.e., instantaneous transmitted powers and phases) of both users. The formulated problem is a mixed continuous-discrete optimization problem, which is nontrivial to resolve in general. By carefully observing the structure of the objective function, we define a new type of Farey sequence, termed punched Farey sequence to tackle the formulated problem. Based on this, we manage to achieve a closed-form optimal solution to the original problem by first dividing the entire feasible region into a finite number of Farey intervals and then taking the maximum over all possible intervals. The resulting sum constellation is proved to be a regular QAM constellation of a larger size, and hence, a simple quantization receiver can be implemented as the ML detector for the demodulation. Moreover, the superiority of NOMA over time-division multiple access in terms of minimum Euclidean distance is rigorously proved. We subsequently address how to extend our design framework intended for the two-user MAC to systems with multiple users and multiple antennas. Finally, simulation results are provided to verify our theoretical analysis and demonstrate the merits of the proposed NOMA over existing orthogonal and non-orthogonal designs.

This paper considers a flat fading noncoherent wireless communication system with a single transmitter antenna and massive multiple receiver antennas, in which the channel coefficients change every two time slots. For such a system, we first parameterize all the high rate constellations which enable each transmitted symbol and the channel coefficients to be uniquely identified in a noise-free case when the number of the receiver antennas goes to infinity. Then, for a noisy channel with the limited number of the receiver antennas, we propose the design of an optimal constellation that maximizes the minimum distance between any two distinct constellation points using the first kind of a Riemannian distance (RD) measure subject to constraints on an average power and total transmission bits. A closed-form optimal solution is attained by first characterizing the optimal structure for any fixed bits on each parameter space and then, finding an optimal bit assignment that further maximizes the achieved minimum distance. One of the significant advantages of such optimal design is that it enables us to develop a fast closedform RD detector. Finally, computer simulations demonstrate that our proposed scheme outperforms the methods in literature for the same system.

In this paper, we consider the design of multi-users space-time modulation (MUSTM) for an uplink MIMO system with one base station equipped with the massive number of antennas and N single-antenna users, where it is assumed that only large scale channel coefficients are available at both the transmitter and the receiver. For such a system, a novel concept called uniquely factorable (UF) MUSTM is introduced. Then, using our recently developed framework on uniquely decomposable constellation group with energy-efficient quadrature amplitude modulation (QAM), and properly and timely assigning each sub-constellation to each user at each time slot, we develop a machinery method for systematically designing a family of invertible UF-MUSTM with flexible data rates in order to assure the reliable estimation of the transmitted signal as well as of the channel for the massive MIMO system. In addition, a simple cross-correlation receiver is proposed to efficiently and effectively detect such UF-MUSTM. Its pair-wise error probability (PEP) is derived, showing that our proposed invertible UF-MUSRM enables full receiver diversity. Furthermore, the optimal closed-form power allocation and the optimal user constellation assignment are found to maximize the worst-case coding gain under a peak power constraint on each user and each time slot.

We consider a multi-user massive MIMO uplink system in which there are multiple users with each having a single antenna and one base station (BS) with a large number of antennas. It is assumed that each user and BS have neither small scale nor large scale channel state information. For such a noncoherent system, we systematically design a series of absolutely additively uniquely decomposable constellation pairs (AAUDCPs) using the phase-shift keying (PSK) constellations such that when any linear combination of two PSK constellation points with positive weighting coefficients is received, each individual PSK signal can be uniquely decoded. With this, a novel noncoherent massive space-time block code with PSK modulation is developed for the system. In a noise-free case, we prove that when the number of antenna at BS grows to infinite, the transmitted symbols and uplink channel can be uniquely determined if the channel coherence time is at least equal to the number of users. In a noisy case, a robust Euclidean distance receiver is developed for efficiently and effectively estimating both the channel coefficients and the transmitted signals.

Every channel can be expressed as a convex combination of deterministic channels with each deterministic channel corresponding to one particular intrinsic state. Such convex combinations are in general not unique, each giving rise to a specific intrinsic-state distribution. In this paper we study the maximum and the minimum capacities of a channel when the realization of its intrinsic state is causally available at the encoder and/or the decoder. Several conclusive results are obtained for binary-input channels and binary-output channels. Byproducts of our investigation include a generalization of the Birkhoff-von Neumann theorem and a condition on the uselessness of causal state information at the encoder.

This paper focuses on the design of non-orthogonal multiple access in a classical two-transmitter two-receiver Z-channel, wherein one transmitter sends information to its intended receiver from the direct link while the other transmitter sends information to both receivers from the direct and cross links. Unlike most existing designs using (continuous) Gaussian input distribution, we consider the practical finite-alphabet (i.e., discrete) inputs by assuming that the widely used quadrature amplitude modulation constellations are adopted by both transmitters. To balance the error performance of two receivers, we apply the max-min fairness design criterion in this paper. More specifically, we propose to jointly optimize the scaling factors at both transmitters, which control the minimum Euclidean distance of transmitting constellations, to maximize the smaller minimum Euclidean distance of two resulting constellations at the receivers, subject to an individual average power constraint at each transmitter. The formulated problem is a mixed continuous-discrete optimization problem and is thus intractable in general. By resorting to the Farey sequence, we manage to attain the closed-form expression for the optimal solution to the formulated problem. This is achieved by dividing the overall feasible region of the original optimization problem into a finite number of sub-intervals and deriving the optimal solution in each sub-interval. Through carefully observing the structure of the optimal solutions in all sub-intervals, we obtain compact and closed-form expressions for the optimal solutions to the original problem in three possible scenarios defined by the relative strength of the cross link. Simulation studies are provided to validate our analysis and demonstrate the merits of the proposed design over existing orthogonal or non-orthogonal schemes.

For any binary-input channel with perfect state information at the decoder, if the mutual information between the noisy state observation at the encoder and the true channel state is below a positive threshold determined solely by the state distribution, then the capacity is the same as that with no encoder side information. A complementary phenomenon is revealed for the generalized probing capacity. Extensions beyond binary-input channels are developed.

In this paper, we consider a multiple-input-multiple-output optical wireless communication (MIMO-OWC) system in the presence of log-normal fading. In this scenario, a general criterion for the design of full-diversity space code (FDSC) with the maximum likelihood detector is developed. This criterion reveals that in a high signal-to-noise ratio regime, MIMO-OWC offers both large-scale diversity gain, governing the exponential decay of the error curve, and small-scale diversity gain, producing traditional power-law decay. Particularly for a two by two MIMO-OWC system with unipolar pulse amplitude modulation, a closed-form solution to the design problem of a linear FDSC optimizing both diversity gains is attained by taking advantage of the available properties on the successive terms of Farey sequences in number theory as well as by developing new properties on the disjoint intervals formed by the Farey sequence terms to attack the continuous and discrete variables mixed max-min design problem. In fact, this specific design not only proves that a repetition code is the optimal linear FDSC optimizing both the diversity gains but also uncovers a significant difference between MIMO radio frequency communications and MIMO-OWC that space dimension alone is sufficient for a full large-scale diversity achievement. Computer simulations demonstrate that FDSC substantially outperforms uncoded spatial multiplexing with the same total optical power and spectral efficiency, and the latter provides only the small-scale diversity gain.

This paper investigates the design of optimal space signaling for an intensity modulated direct detection multi-input-multi-output optical wireless communication system with independent and non-identically log-normal distributed channel coefficients. In order to optimize both large-scale diversity and small-scale diversity gains with a maximum likelihood detector, the design problem is formulated into a max-min optimization problem with continuous-discrete mixed design variables. Two techniques are proposed to solve the problem: 1) by taking advantage of the full large scale diversity condition, all spatial codewords are properly sorted to simplify the inner minimization problem with the discrete design variables; and 2) a novel geometrically weighted inequality is established to carefully deal with a specific objective function of the power products in the outer maximization problem with the continuous variables. Among all the high dimensional nonnegative space signaling vectors, we rigorously prove that the spatial repetition signaling (RS) with an optimal power allocation is optimal under an average optical power constraint. Simulation results indicate that in a high signal to noise ratio regime, our optimally designed space signaling has better error performance than RS, which is the best space signaling available in literature for this application.

For any binary-input channel with perfect state information at the decoder, if the mutual information between the noisy state observation at the encoder and the true channel state is below a positive threshold determined solely by the state distribution, then the capacity is the same as that with no encoder side information. A complementary phenomenon is revealed for a similarly defined quantity.

This paper considers the asymptotic analysis of symbol error probability (SEP) for either optimally precoded or uniformly precoded large correlated MIMO fading channels using the zero-forcing (ZF) detector. For such systems, we reveal some very nice structures which naturally lead us to the exploration of two very strong and very useful mathematical tools for the systematic study of asymptotic behaviors on their error performance. The first tool is the Szegö's theorem on large Hermitian Toeplitz matrices and the second tool is the well known limit: limx→∞(1 + 1/x)x= e. This new approach enables us to attain a very simple expression for the SEP limit as the number of the transmitter antennas goes to infinity. One of the major advantages for this method is that its convergence rate is very fast. Hence, this expression is very efficient and effective SEP approximation for the large MIMO systems. Due to the constraint on allowable space and limited (sparse) multi-path scattering, fading correlation between neighbouring antenna elements is almost inevitable in a large MIMO architecture. By specifically examining an exponential correlation matrix model, we show that channel fading correlation can lead to significant performance loss. The optimal precoding technique can yield substantial power gain over the uniform power allocation strategy.

In this paper, we consider a multiple-input-multiple-output optical wireless communication (MIMO-OWC) system suffering from log-normal fading. In this scenario, a general criterion for the design of full large-scale diversity space code (FLDSC) with the maximum likelihood (ML) detector is developed. Based on our criterion, FLDSC is attained if and only if all the entries of the space coding matrix are positive. Particularly for 2×2 MIMO-OWC with unipolar pulse amplitude modulation (PAM), a closed-form linear FLDSC satisfying this criterion is attained by smartly taking advantage of some available properties as well as by developing some new interesting properties on Farey sequences in number theory to rigorously attack the continuous and discrete variables mixed max-min problem. In fact, this specific design not only proves that a repetition code (RC) is the best linear FLDSC, but also uncovers a significant difference between MIMO radio frequency (RF) communications and MIMO-OWC that space-only transmission is sufficient for a full diversity achievement. Computer simulations demonstrate that FLDSC substantially outperforms spatial multiplexing with the same total optical power and spectral efficiency and the latter obtains only the small-scale diversity gain.

This paper develops a power allocation strategy for multiple networks of Poisson-distributed single-antenna nodes that share the available spectrum in a spectrum underlay scenario. This strategy aims to maximize the overall throughput obtained by sharing the spectrum while limiting the degradation of the successful transmission probability of each network. In its original form, this joint power allocation problem is difficult to solve. However, we demonstrate that the problem can be transformed into a convex optimization formulation, which can be efficiently solved. Furthermore, we obtain a quasi-closed-form solution that has a water-filling interpretation by analyzing the optimality conditions. Numerical results indicate that, when a spectrum-sharing scheme employs the proposed optimal strategy of power allocation, the throughput substantially improves over that obtained by exclusively allocating the spectrum to the primary network. Moreover, when the number of spectrum-sharing networks increases, the enhancement is significant, being up to the limit imposed by the maximum allowable degradation in the performance of each network.

Mutual interference is the main bottleneck on the throughput of large random spectrum sharing networks. This work examines the extent to which the performance of such networks can be improved by employing multiple transmitting antennas, without degrading the average performance of individual users. By extending partial zero-forcing beamforming to spectrum sharing networks, the aggregate interference towards primary receivers is reduced, and the desired signals at both primary and secondary receivers are boosted. Considering randomly distributed users and spatially independent Rayleigh fading channels, this work provides upper and lower bounds on the maximum permissible density of secondary transmitters with respect to the numbers of primary and secondary transmitting antennas. The simulation results show that substantial increase in the density of secondary transmitters can be obtained while meeting the outage requirements of the spectrum sharing users.

This paper develops a power control strategy for multiple spectrum-sharing networks of single antenna nodes in a spectrum underlay scenario. A distinguishing feature of the proposed strategy is that it requires only knowledge of the spatial distribution of the nodes, rather than instantaneous channel state information. The strategy seeks to maximize a weighted sum of the throughput of each network while guaranteeing specified successful transmission probabilities. In its native form, this joint power allocation problem is difficult to solve. However, we show that the problem can be transformed into a convex optimization formulation that can be efficiently solved using general purpose tools. Furthermore, we analyze the optimality conditions and obtain a quasi-closed form solution reminiscent of waterfilling. Numerical results demonstrate that spectrum sharing employing the proposed optimal power yields a substantial throughput gain over allocating the spectrum to a single network.

The direct application of orthogonal space-time block coding (OSTBC) for multiple input and multiple output (MIMO) systems to distributed cooperative relay networks makes the equivalent channel matrix for maximum likelihood (ML) detection lose its orthogonality. Hence, this paper proposes a new design that makes the channel matrix be orthogonally distributed (OD) for a suboptimal symbol-by-symbol detector (SBSD). Using ODSTBC, an asymptotic symbol error probability (SEP) formula with SBSD is derived, showing the optimal diversity gain function is achieved. In addition, two kinds of ODSTBC designs for the distributed relay networks are presented, which interestingly renders that SBSD is equivalent to the ML detector. Numerical results verify the diversity analysis and indicate competitive error performance to currently available orthogonal distributed STBC designs with much simpler complexity.

This paper develops a novel uniquely-factorable constellation pair (UFCP) by carefully factorizing phase-shift keying (PSK) constellation. With this unique factorization, a new distributed concatenated Alamouti code is proposed for a one-way relaying network consisting of two single-antenna terminals and one relay having two antennas. This design allows the relay to transmit its own information while forwarding the source information which it has received to the destination. By making use of the Alamouti coding scheme twice and jointly processing the signals from the two antennas at the relay node, such a code design also renders the equivalent channel between source and destination be a product of the two Alamouti channels and therefore, is called distributed concatenated Alamouti space-time block code (STBC). In addition, the asymptotic symbol error probability (SEP) formula is derived with the maximum likelihood (ML) detector, showing that the optimal diversity gain function is achieved and proportional to ln SNR/SNR2.

In this paper, we consider a half-duplex amplify-and-forward two-way relaying network consisting of two sources with each having a single antenna and N relays with each having two antennas. For such a system with a general distributed linear dispersion code, a tight lower bound of pairwise error probability (PEP) of the maximum likelihood (ML) detector is derived, showing that diversity gain function cannot decay faster than lnNSNR/SNR2N, where SNR is signal to noise ratio. Particularly for N = 2b, a new distributed concatenated space-time block code (STBC) is proposed and its asymptotic PEP formula is attained, showing that the code presented in this paper achieves the maximum diversity gain, i.e., meeting the lower bound of the diversity gain function, as well as the maximum coding gain.

Utilizing the recently-developed unique factorization of signals and distributed Alamouti coding scheme, a distributed collaborative Alamouti space-time block code design is presented for a two-way amplify-and-forward (AF) relaying network, where both two sources and the relay are equipped with a single antenna. For such system, two asymptotic pairwise error probability (PEP) formulae are first derived for both fixed-gain AF and variable-gain AF over Rayleigh channels with the maximum likelihood detector. Then, subject to the constraints on a fixed transmission bit rate and unity average transmission energy, the optimal constellation combinations with the optimal energy-scales as the coefficients are attained by minimizing the dominant term of PEP. It is shown that the PEP and the average block error rate of the newly-designed code are superior to those of the conventional distributed Alamouti code.

Utilising the recently‐developed unique factorisation of signals and distributed Alamouti coding, a distributed collaborative space‐time block code design is presented for a two‐way amplify‐and‐forward (AF) relaying network, where all nodes are equipped with a single antenna. Two asymptotic pairwise error probability (PEP) formulae are firstly derived for both fixed‐gain AF and variable‐gain AF over Rayleigh channels with the maximum‐likelihood detector. Then, subject to the constraints on a fixed transmission bit rate and unity average transmission energy, the optimal constellation combinations with the optimal coefficients are attained by minimising the dominant term of PEP. It is shown that the PEP and the average block error rate of the newly‐designed code are superior to those of the conventional distributed Alamouti code while the prior still has linear‐decoding complexity.

In this paper, a novel concept called a uniquely factorable constellation pair (UFCP) is proposed for the systematic design of a noncoherent full diversity collaborative unitary space-time block code by normalizing two Alamouti codes for a wireless communication system having two transmitter antennas and a single receiver antenna. It is proved that such a unitary UFCP code assures the unique identification of both channel coefficients and transmitted signals in a noise-free case as well as full diversity for the noncoherent maximum likelihood receiver in a noise case. To further improve error performance, an optimal unitary UFCP code is designed by appropriately and uniquely factorizing a pair of energy-efficient cross quadrature amplitude modulation (QAM) constellations to maximize the coding gain subject to a transmission bit rate constraint. After a deep investigation of the fractional coding gain function, a technical approach developed in this paper to maximizing the coding gain is to carefully design an energy scale to compress the first three largest energy points in the corner of the QAM constellations in the denominator of the objective as well as carefully design a constellation triple forming two UFCPs, with one collaborating with the other two so as to make the accumulated minimum Euclidean distance along the two transmitter antennas in the numerator of the objective as large as possible, and at the same time, to avoid as many corner points of the QAM constellations with the largest energy as possible to achieve the minimum of the numerator. In other words, the optimal coding gain is attained by intelligent constellations collaboration and efficient energy compression. Computer simulations demonstrate that error performance of the optimal unitary UFCP code presented in this paper outperforms those of the differential code and the signal-to-noise-ratio-efficient training code.

A half-duplex amplify-and-forward two-way relay network consisting of two single-antenna sources and N relays with each having two antennas is considered in this paper. For such a system, a tight lower bound of pairwise error probability (PEP) of a maximum likelihood (ML) detector for any distributed linear dispersion code with a fixed average amplifier is derived, revealing that diversity gain function cannot decay faster than lnNSNR/SNR2N, where rm SNR is signal to noise ratio. Particularly for the network having two relays, a novel distributed quasi-orthogonal space-time block code (QO-STBC) is proposed with two significant advantages. One is that the equivalent channel matrices at both source nodes turn out to be the block-circulant matrices, with each block being a product of the two Alamouti channel matrices. The other is that the equivalent noises at the both source nodes are Gaussian and white. Therefore, like QO-STBC for a multi-antennas system, the proposed code for the relay system still maintains low-decoding complexity for the ML detector. Asymptotic PEP formula is attained to show that the proposed code enables the optimal diversity gain function, i.e., meeting the lower bound of diversity gain, and the optimal coding gain. In addition, a near optimal power allocation that maximizes the received SNR of the worse link is presented and examined through comprehensive computer simulations for various kinds of asymmetric relay channels.

Space-time block code designs based on algebraic field extension for full rate, large diversity product, and nonvanishing minimum determinant of codewords have received great attention. There are many different types of codes available for two-transmitter antennas, such as cyclotomic space-time block codes, the golden space-time block code, and rotation-based space-time block codes. In this paper, a more general space-time block code design scheme, which is called quadratic space-time block coding, is proposed for the two-transmitter antennas using quadratic field extension. The optimal design of the quadratic space-time block codes in terms of a diversity product criterion is also presented. It is shown that the optimal quadratic space-time block codes designed in this paper do not belong to the existing space-time block code family such as the cyclotomic, golden, and rotation-based space-time block codes. The simulation results demonstrate that the average codeword error rate of the optimal quadratic space-time block code attains about 0.5 dB signal to noise ratio gain over those of the optimal cyclotomic and golden space-time block codes.

This paper considers the blind detection for a two-way relay system in which two source nodes exchange information via a relay node by amplify-and-forward relaying. An efficient transmission scheme is first proposed to achieve unique identifications of both the transmitted symbols and channel coefficients at a noise-free receiver using the M-ary phase shift keying modulation. Blind receivers based on the generalized likelihood ratio test are then derived for both the reciprocal and nonreciprocal channels with additive Gaussian noise. The least square error-based receiver is also studied for the case without prior knowledge of the noise power for detection. Moreover, constellation selection algorithms are proposed to achieve a uniform transmission bit rate for the ease of implementation. Finally, numerical results are provided to validate the proposed schemes.

In this paper, the systematic design of a space-time block code is considered for a wireless communication system with multiple transmitter-receiver antennas and flat fading, in which channel state information is completely unknown. From the viewpoint of blind signal processing, a necessary and sufficient condition is given for the unique identification of the multi-input multi-output flat fading channel and transmitted signal. Then, some novel unique factorizations for a pair of coprimeP-ary andQ-ary phase shift keying (PSK) constellations are established. With this and currently available coherent space-time block code designs, a method is developed to systematically construct full diversity blind nonunitary space-time block codes as well as unitary codes by just performing the QR decomposition of the nonunitary codes. It is proved that under a noise-free environment, the code design proposed in this paper can guarantee that the transmitted signals and the channel coefficients are uniquely identified, and that under a complex Gaussian noise environment in whichPth-order andQth-order statistics (PandQare co-prime) of the received signals are available, the channel coefficients can be still uniquely identified. In addition, a closed-form solution to determine the channel coefficients is obtained.

In this letter, we consider a coherent communication system equipped with multiple transmitter antennas and a single receiver antenna, i.e., a MISO system. For such a system, quasi-orthogonal STBC designs with fast maximum likelihood (ML) decoding have been proposed. However, full diversity cannot be achieved by such codes. The rotated quasi-orthogonal STBC overcomes such shortcomings and enables full diversity and optimal coding gain. However, for large constellations, the performance of such codes deteriorates due to the increase of the number of the nearest neighbor per symbol. In this letter, we propose to add the number of nearest neighbor as a design criterion. We show that for the rotated quasi-orthogonal code proposed in, the number of nearest neighbor tends to infinity when the size of constellation becomes infinite. Furthermore, we propose to have a particular value of rotation and show that this value not only achieves full diversity and maximum coding gain, but also has only a small number of nearest neighbors even for very large constellations.

In this letter, a necessary and sufficient condition is developed to check whether a set of polynomial equations is solvable. Furthermore, under the sufficient condition, a closed-form solution is attained using linear Diophantine equation theory. With this, a novel signal design and a row-circular transmission scheme of phase shift keying (PSK) constellations for MIMO flat fading channels are proposed so that the channel coefficients can be uniquely identified. When certain high-order moments of the received signals are available, a closed-form solution to uniquely determine the channel coefficients is given. When only finite received data are available, a numerical algorithm is provided to efficiently and effectively estimate the channel.

Recently, various space-time block coding (STBC) schemes have been developed to take advantage of the MIMO communication channel. The code designs using the pair-wise error probability of the maximum likelihood (ML) detector are based mainly on the rank and the determinant criteria. In particular, the current STBC designs focus on full diversity and the non-vanishing determinant, since such codes enable the optimal tradeoff of diversity and multiplexing gains. In this paper, we consider a coherent communication system equipped with multiple transmitter antennas and a single receiver antenna, i.e., a MISO system. For such systems, Afarkhani, Tirkkonen-Boariu-Hottinen, and Papadias-Foschini proposed the quasi-orthogonal STBC designs with fast ML decoding. Su and Xia designed the rotated quasi-orthogonal STBCs enabling full diversity and optimal coding gain. However, the nearest neighbor number per symbol for this code tends to infinity when the size of constellation is infinity. Here, we explore a novel criterion to design rotated quasi-orthogonal STBCs. In addition to both maximizing the rank and the coding gain, our design attempts to make the average number of the nearest neighbors as small as possible.

In this paper, we develop two kinds of novel closed-form decompositions on phase shift keying (PSK) constellations by exploiting linear congruence equation theory: the one for factorizing a pq-PSK constellation into a product of a p-PSK constellation and a q-PSK constellation, and the other for decomposing a specific complex number into a difference of a p-PSK constellation and a q-PSK constellation. With this, we propose a simple signal design technique to blindly and uniquely identify frequency selective channels with zero-padded block transmission under noise-free environments by only using the first two block received signal vectors. Furthermore, a closed-form solution to determine the transmitted signals and the channel coefficients is obtained. In the Gaussian noise and Rayleigh fading environment, we prove that the newly proposed signaling scheme enables non-coherent full diversity for the Generalized Likelihood Ratio Test (GLRT) receiver.

In this paper, the ergodic channel capacities are established for the amplify-and-forward (AF) half-duplex cooperative systems, which consist of a source node, a destination, and multiple-relay nodes. The relay nodes assist the transmission from the source node to the destination. Since the channel matrices for the cooperative systems involve product of Gaussian random variables, which are no longer Gaussian, the approach in obtaining the ergodic channel capacity for conventional multiple-input-multiple-output (MIMO) Gaussian channels (Telatar, 1999) is not applicable. By using a novel approach, we have arrived at the following conclusions about the ergodic channel capacities for the AF cooperative systems. For the single antenna AF relay systems in which all nodes are equipped with one antenna, the optimal covariance matrix of the input signals to achieve the ergodic channel capacity is diagonal, and the diagonal elements are obtained by solving optimization problems of multidimensional integrals. These diagonal entries are not all equal even if all the channel gains in the cooperative systems are independent and identically distributed (i.i.d.) Gaussian with unit variance. Therefore, a white input signal for the AF cooperative system may not achieve the ergodic channel capacity of the system. This is in direct contrast to the case of conventional multiple-input-single-output (MISO) systems having i.i.d. Gaussian channel gains of unit variance, in which case, the ergodic capacity is achieved if the input covariance matrix is a scaled identity matrix. For the MIMO relay system in which the nodes have multiple antennas, the input covariance matrix to achieve the ergodic capacity is block diagonal and each block diagonalizes the autocorrelation of channel matrix from the source to the destination. This is different from the case of conventional MIMO systems, where the input covariance matrix to achieve the ergodic channel capacity diagonalizes the channel autocorrelation matrix of the MIMO system (Tulina, Lozano, and Verdu, 2006). If the channel gains in conventional MIMO systems are correlated Gaussian random variables, the input covariance matrix is a full matrix, not block diagonal; and if the channel gains are i.i.d. Gaussians, the optimal input covariance matrix is a scaled identity. The observations obtained in this paper reveal useful insights of how the AF cooperative systems ldquomimicrdquo the conventional MISO and MIMO systems from the ergodic channel capacity perspective.

We consider a flat fading wireless link having multiple M transmitter antennas and a single receiver antenna (MISO). This system is often useful in mobile downlink communications for which the mobile receiver may not be able to support multiple antennas. For such a system, we propose a novel and very simple design of full diversity two-group and four-group decodable block diagonal linear dispersion codes with rate one for any number of the transmitter antennas. For M = 2nand M = 2n− 1, we also prove that for K-ary Quadrature Amplitude Modulation (QAM) transmission equipped with a maximum likelihood (ML) detector, our proposed code minimizes the worst case average pair-wise error probability, i.e., it achieve optimal coding gain.

In this paper, a new robust downlink power control solution based on worst-case performance optimization is developed. Our approach depends on explicit modeling of uncertainties in the downlink channel correlation (DCC) matrices, worst-case performance optimization and guarantees that the quality of service (QoS) constraints are satisfied for all users using minimum amount of power. An iterative algorithm to find the optimum power allocation is proposed. The key to this algorithm is to solve an optimization problem to obtain worst-case uncertainty matrices. When the uncertainty is small enough to guarantee that the DCC matrices are positive semidefinite, we obtain a closed-form solution of the subproblem. When the uncertainty is large, we transform this intractable problem into a convex problem. Simulation results show that our proposed robust downlink power control using the approach of worst-case performance optimization reduces the transmission power effectively under imperfect knowledge of the channel condition.

We consider the design of the precoder for a multi-input multi-output (MIMO) communication system equipped with a decision feedback equalizer (DFE) receiver. For such design problems, perfect knowledge of the channel state information (CSI) at both the transmitter and the receiver is usually required. However, in the wireless communications environment, it is often difficult to provide sufficiently timely and accurate feedback of CSI from the receiver to the transmitter for such designs to be practically viable. In this paper, we consider the optimum design of a precoder for a wireless communication link having M transmitter antennas and N receiver antennas (M ≪ N), in which the channels are assumed to be flat fading and may be correlated. We assume that full knowledge of CSI is available at the receiver. At the transmitter however, only the second order statistics of the channels are available. Our goal here is to come up with an efficient design of the optimal precoder for such a MIMO system by minimizing the average arithmetic mean-squared error (MSE) of zero-forcing (ZF) decision feedback detection subject to a constraint on the total transmitting power. Applying some of the properties of the matrix parameters, this non-convex optimization problem can be transformed into a convex geometrical programming problem which can then be efficiently solved using an interior point method. The superior performance of our MIMO system equipped with the optimum precoder is verified by computer simulations.

In this paper, a general criterion for space-time block codes (STBC) to achieve full diversity with a linear receiver is proposed for a wireless communication system having multiple transmitter and single receiver antennas [multiple-input-single-output (MISO)]. Particularly, the STBC with Toeplitz structure satisfies this criterion, and therefore, enables full diversity. Further examination of this Toeplitz STBC reveals the following important properties: (1) the symbol transmission rate can be made to approach unity; (2) applying the Toeplitz code to any signalling scheme having nonzero distance between the nearest constellation points results in a nonvanishing determinant. In addition, if quadratic-amplitude modulation (QAM) is used as the signalling scheme, then for independent MISO flat-fading channels, the Toeplitz codes is proved to approach the optimal diversity-versus-multiplexing tradeoff with a zero-forcing (ZF) receiver when the number of channel uses is large. This is, so far, the first nonorthogonal STBC shown to achieve the optimal tradeoff for such a receiver. On the other hand, when maximum-likelihood (ML) detection is employed in a MISO system, the Toeplitz STBC achieves the maximum coding gain for independent channels. When the channel fading coefficients are correlated, the inherent transmission matrix in the Toeplitz STBC can be designed to minimize the average worst case pairwise error probability.

In this paper, an optimal unitary precoder is designed for an amplify-and-forward (AF) half-duplex relay system to obtain the maximum coding gain while the original ergodic channel capacity for the relay system is kept unchanged. A closed-form design is derived for quadrature amplitude modulation (QAM) signals by employing the properties of Farey sequence in number theory. Simulation results indicate that the proposed design greatly improves the bit error rate (BER) performance for the relay system.

Recently, distributed space-time code designs with high cooperative diversity for wireless communication networks, such as ad hoc and sensor networks, have received much attention. Amplify forward and decoding forward are widely used protocols for the cooperative diversity in the wireless communication networks. In both protocols, the information received by relay terminals are "forwarded" to destination or next relay terminals. Since the signals transmitted by relay terminals and those transmitted from the source terminal are correlated, there is information redundancy. To improve the energy efficiency of cooperative networks, we propose an encoding protocol, which is referred to as a nested cooperative encoding protocol. In our proposed protocol, the received signal at each relay terminal is divided into several sub-signals with the nest lattice structure of source information. Each of the sub-signals contains only a partial information with a smaller size of constellation compared to the original information sent by the source terminal. Do a new encoding or modulation by using these sub-signals before transmitting at relay terminals. It is shown that the proposed new protocols can achieve both high cooperative diversity and high energy efficiency.

In this paper, we design an optimal precoder for the amplify-and-forward (AF) half-duplex cooperative system. We first present asymptotic pairwise error probability (PEP) expression and identify the corresponding terms for diversity and coding gains. By employing the properties of the Farey sequence in number theory, we obtain a closed form optimal precoder to achieve both full diversity as well as maximum coding gain for square quadrature amplitude modulation (QAM) signals. Simulation results indicate that the proposed design significantly improves the BER performance of the relay system.

The design of a linear space-time code with full rate, large diversity product, and non-vanishing minimum determinant of codewords continues to attract great attention. However, in most available no-vanishing determinant space-time codes for three, four, and six transmitter antennas, the average power at each layer is different, which results in a high peak to average power ratio. In this paper, a new cyclic algebraic space-time design scheme is proposed and the optimal codes in this class are provided by using some specific cyclic field extensions. Our proposed codes not only include the available non-vanishing determinant cyclotomic space-time codes for three, four, and six transmitter antennas, but also have the desirable property that the optimal codes can be achieved with the same average power at each layer.

This paper presents a method for jointly designing the transmitter-receiver pair in a block-by-block transmission system that employs minimum mean square error intra-block decision feedback detection. We provide a recursive closed-form expression for a transceiver which maximizes the Gaussian mutual information and also minimizes the bit error rate at moderate-to-high signal-to-noise ratios (in the absence of error propagation). The proposed design generates uncorrelated inputs to the decision device with equal signal-to-interference-and-noise ratios. These properties suggest that one can approach the capacity of the block transmission system using (independent instances of) the same (Gaussian) code for each element of the block. Our simulation studies indicate that the proposed transceiver performs significantly better than standard transceivers, and that it retains its performance advantages in the presence of error propagation.

In this paper, we introduce the definitions of a full diversity integer generating matrix and the corresponding norm form space-time code for MIMO systems. Subject to a power constraint, we characterize all full diversity integer generating matrices with the first three largest gains in the Gaussian integer ring and the Eisenstein integer ring for two transmitter antennas. Using this generating matrix family to separately design space-time codes layer by layer for two transmitter antenna and two receiver antenna MIMO systems, we obtain the optimal norm form integer space-time codes both in the Gaussian integer ring and the Eisenstein integer ring in the sense of maximizing the minimum determinant of codeword matrices. As a consequence, we prove that the golden code constructed by Dayal and Varanasi, Belfiore, Rekaya and Viterbo is optimal in the Gaussian integer ring. Also, we find the optimal code in the Eisentein integer ring, the coding gain of which is greater than that of the golden code.

We consider efficient techniques for the design of a transceiver for a matrix channel with minimum mean square error (MMSE) decision-feedback (DF) detection when perfect channel information is available at both the transmitter and receiver. By combining the canonical property of the MMSE-DF detector and our recently developed equal-diagonal QRS decomposition of a matrix we obtain a uniform decomposition of mutual information in which each of the synthesized scalar subchannels has the same mutual information (under the assumption of error-free feedback). To assist our analysis of this uniform decomposition, we provide a new QR interpretation of the MMSE-DF receiver. This enables us to show that the natural detection order is optimal (in an SINR sense), and that for the proposed transmitter, the MMSE-DF detector is asymptotically equivalent to the maximum likelihood detector when the SNR is high. We also derive a low-complexity quadratic recursive algorithm for the characterization of all eligible S-factors in the QRS decomposition. When coupled with our QR interpretation of the MMSE-DF detector, this enables us to efficiently design the optimal transmitter and to efficiently implement the MMSE-DF receiver

In this paper we consider coherent flat fading wireless communication systems with multiple transmitter antennas and single receiver antenna (MISO). We propose a Toeplitz linear space time block code (STBC) that converts an original MISO flat fading channel into a Toeplitz virtual multiple inputs multiple outputs (MIMO) channel. We show that our proposed code has the following main features: (a) The symbol transmission rate is (T-M + 1)/T, where M is the number of transmitter antenna and T is the number of channel uses (T > M). (b) Linear receivers (zero-forcing and minimum mean square error) can extract full diversity. Moreover, when the channel coefficients are independent and the maximum likelihood (ML) detector is employed, our Toeplitz STBC minimizes the exact worst case average pair-wise error probability, (c) When channels are correlated, we design our Toeplitz STBC that minimizes the exact average worst case pair-wise error probability. By transforming this non-convex optimization problem into a convex one, the problem can be solved efficiently by employing an interior point method. In particular, when the design criterion in question is approximated by the Chernoff bound, we obtain a closed form solution, (d) Finally, for the independent MISO flat fading system, we prove that our proposed codes can approach the optimal diversity-vs-multiplexing tradeoff developed by Zheng and Tse with a linear zero-forcing receiver when the number of channel uses is large

In multiple-input multiple-output (MIMO) multiuser detection theory, the QR decomposition of the channel matrix H can be used to form the back-cancellation detector. In this paper, we propose an optimal QR decomposition, which we call the equal-diagonal QR decomposition, or briefly the QRS decomposition. We apply the decomposition to precoded successive-cancellation detection, where we assume that both the transmitter and the receiver have perfect channel knowledge. We show that, for any channel matrix H, there exists a unitary precoder matrix S, such that HS=QR, where the nonzero diagonal entries of the upper triangular matrix R in the QR decomposition of HS are all equal to each other. The precoder and the resulting successive-cancellation detector have the following properties. a) The minimum Euclidean distance between two signal points at the channel output is equal to the minimum Euclidean distance between two constellation points at the precoder input up to a multiplicative factor that equals the diagonal entry in the R-factor. b) The superchannel HS naturally exhibits an optimally ordered column permutation, i.e., the optimal detection order for the vertical Bell Labs layered space-time (V-BLAST) detector is the natural order. c) The precoder S minimizes the block error probability of the QR successive cancellation detector. d) A lower and an upper bound for the free distance at the channel output is expressible in terms of the diagonal entries of the R-factor in the QR decomposition of a channel matrix. e) The precoder S maximizes the lower bound of the channel's free distance subject to a power constraint. f) For the optimal precoder S, the performance of the QR detector is asymptotically (at large signal-to-noise ratios (SNRs)) equivalent to that of the maximum-likelihood detector (MLD) that uses the same precoder. Further, We consider two multiplexing schemes: time-division multiple access (TDMA) and orthogonal frequency-division multiplexing (OFDM). We d

In this paper, we present a design of linear codes which improves the bit error rate (BER) performance for multiple-input multiple-output (MIMO) communication systems, under a flat-fading environment, in which the channel information is unknown for the transmitter but known at the receiver. Recently, space-time codes have been designed to achieve capacity and/or minimize the overall mean square error. Our codes here simultaneously achieve the lower bound of BER, the upper bound of the overall signal to interference plus noise ratio (SINR) and the lower bound of substream minimum mean square error. Our code structure is orthogonal in both overall and individual senses.

It has recently been determined (by others) that one can construct full rate full diversity linear space-time block codes without a reduction in the achievable information rate. In this paper, we address two issues in those designs. One issue is whether the rotation matrix and the Diophantine number can be systematically and efficiently constructed for an arbitrary number of transmitter antennas and receiver antennas and whether the signal constellation is necessarily limited to PAM or QAM. The other issue is whether the currently available square designs can be generalized to a rectangular design and in particular, to a linear dispersion code design. This paper resolves these issues by proposing a trace-orthonormal linear space-time block code and linear dispersion code, and giving a systematic method to design such a code family. By carefully selecting V-structured matrices or conjugate V-structured matrices in this family, we can systematically and efficiently design information lossless full rate full diversity cyclotomic space-time codes.

In this paper we propose a trace-orthonormal linear dispersion code that is an extension of the generalized complex orthogonal space-time block codes and present a method to systematically design such code family. We prove that our proposed codes can minimize the average bit error probability for the QPSK modulation when the minimum mean square error (MMSE) detector is employed. Furthermore, we establish a unified framework to systematically and efficiently construct trace-orthonormal full diversity cyclotomic linear dispersion codes with any integer symbol transmission rate which is less than or equals to the number of transmitter antennas. This result generalizes the currently available linear space-time block code designs into a full diversity linear dispersion code design

In this paper we derive an analytic expression for the linear precoder which minimizes the bit error rate (BER) for block transmission systems with zero-forcing equalization and threshold detection. The design is developed for the two standard schemes for eliminating inter-block interference; viz, zero padding (ZP) and cyclic prefix (CP). The CP minimum BER precoder has a structure similar to that of the conventional water-filling discrete multitone (DMT) modulation scheme, but the diagonal water-filling power loading matrix is replaced by a full matrix consisting of a diagonal minimum mean square error (MMSE) power loading matrix post-multiplied by a Discrete Fourier Transform (DFT) matrix. The ZP minimum BER precoder has a corresponding structure. Performance evaluations indicate that the signal-to-noise ratio (SNR) gain of the ZP and CP minimum BER precoders over conventional water-filling DMT, MMSE, and orthogonal frequency division multiplexing (OFDM) schemes can be as much as several decibels.

Redundancy introduced using filterbank precoders at the transmitter builds a unified framework for modulation schems. Taking advantage of this diversity can offer a powerful tool for removing interblock interference and devising simple but effective precoders for suppressing the intersymbol interference (ISI) and being robust to frequency selective channels‥ In this paper, we assume that the transmitter knows the autocorrelation sequences of the channel impulse response. Under this assumption, we derive a lower and an upper bound on the free distance for a precoded channel and with this, design the precoder that maximizes the lower bound subject to a power constraint. It turns out that the optimal precoder is a unitary matrix which makes QR decomposition of its super-channel exhibit equal diagonal entries in R-factor and the lower and the upper bounds of its free distance equal. We show that for the optimal precoded channel, the detection performance using the decision feedback equalizer (DFE) based on QR decomposition is asymptotically equivalent to that of the mamximum likehood detector (MLD) when the signal to noise ratio (SNR) is large.

In this paper, two types of adaptive FREquency SHift filters are proposed. One is LMS adaptive FRESH filter. The other is blind adaptive FRESH filter. By exploiting the spectral correlation of cyclostationary signals, these adaptive filters can separate the signals which overlap in both frequency and time domain. Theoretical development and simulations of these filters are given in this paper. The results show that for signals which spectrally overlap, the adaptive FRESH filters can perform very well while ordinary adaptive filters fail.