This paper proposes an interleaved transceiver design method for a multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system utilizing orthogonal frequency division multiplexing (OFDM). We consider a continuous transmission system and focus on transceiver design for alternate symbols to mitigate the interference to the radar from reflections of adjacent OFDM symbols. Constructive interference (CI) is incorporated into the optimization to improve communication performance, while the integrated mainlobe-tosidelobe ratio (IMSR) of the transmission beampattern ensures directivity. A time-domain radar receive filter is designed to reduce the range sidelobes and retain loss-in-processing gain, while also mitigating the interference to the radar and eliminating spurious peaks induced by distant targets. Given the high peak-to-average power ratio (PAPR) in OFDM systems, we constrain the power of each transmitted sample. The optimization problem is addressed using alternating optimization (AO), with the subproblem of transmitted waveform design being solved via successive convex approximation (SCA). Numerical simulations validate the effectiveness of our transceiver design in achieving desirable performance in both radar sensing and communication.

Mobile edge computing systems provide computational resources at the network access point that can be shared among the attached devices. Effective utilization of these resources requires careful selection of the offloading devices and joint allocation of the computing and communication resources. We develop an efficient resource allocation technique that exploits the temporal structure of computation offloading. Our initial formulation is combinatoric, but insight into the energy required to communicate a given message reveals effective heuristics for the allocation of computing resources, and a reduced-dimension convex formulation for the communication resources. Our numerical results demonstrate that the proposed approach provides performance that is close to that of the jointly optimal solution.

When multiple users seek to offload computational tasks to their access point, the nature of the multiple access scheme, and the optimization of its parameters, play a critical role in the system performance. For a system with heterogeneous tasks, we adopt a time-slotted signaling structure in which different numbers of users transmit in each slot, subject to individual power constraints. We consider the problem of optimizing the rates and powers of the users transmitting in each time slot, and the time slot lengths, so as to minimize the energy expended by the users. For time-division multiple access (TDMA) and "rate optimal" multiple access, we obtain reduced-dimension convex formulations, while for (suboptimal) non-orthogonal multiple access (NOMA) with independent decoding (ID) or fixed-order sequential decoding (FOSD), we develop a successive convex approximation algorithm with feasible point pursuit. These formulations are then embedded in a customized tree search algorithm for the set of offloading users. Our results demonstrate how the NOMA-FOSD schemes bridge the performance gap between TDMA and the rate-optimal schemes.

Multi-user computation offloading inherently involves the allocation of communication resources among the offloading devices. Since the devices require timely results, that allocation ought to be guided by the fundamental rate limits for finite block lengths, rather than the classical (asymptotic) limits. We develop an efficient algorithm for such an allocation. It includes a relaxation-rounding approach that is based on a customized incremental rounding scheme for the block lengths. A special feature is that the relaxation is tightened in such a way that rounding a feasible solution to the relaxed problem is guaranteed to generate a feasible integer block length. By exploiting a closed-form approximation of the transmission powers, our design approach reduces to successively solving convex approximation problems over the transmission rates alone.

This paper addresses joint design of the transmitting waveform and the receivers of a dual-function radar-communication (DFRC) system that enables both multiple-input multiple-output (MIMO) radar sensing and multi-user multiple-input single-output (MU-MISO) communications. The proposed approach incorporates the design of the communication receiving (Rx) coefficients, in addition to the radar Rx filters. We seek to maximize the minimum radar signal-to-interference-plus-noise ratio (SINR) over multiple targets, subject to per-antenna power constraints, peak-to-average-power ratio (PAPR) constraints and a communication SINR constraint for each user. A successive convex approximation algorithm is developed to find a good solution for the resultant nonconvex design problem. Numerical results show that by incorporating the communication Rx coefficients into the joint design, the radar and communication capabilities of the DFRC system can be significantly enhanced over the state-of-the-art designs.

Abstract A design technique is developed for the probing signals of a Multi‐Input Multi‐Output (MIMO) radar. The concentration of the energy of the signal in its essential duration and essential bandwidth is achieved through the use of a class of time‐frequency concentrated functions called the WLJ functions as the synthesizing signal set. The goal is to design a signal vector having a pre‐specified desired covariance (CoV) matrix while ensuring that the side‐lobes of the ambiguity functions are small. Since CoV matrices are structurally constrained, they form a manifold in the signal space. Hence, we argue that the difference between these matrices should not be measured in terms of the conventional Euclidean distance (ED); rather, the distance should be measured along the surface of the manifold, that is, in terms of a Riemannian distance (RD). In either case, the signal optimisation problem is non‐convex in the design variables, involving, respectively, a quartic and a square‐root objective function. An efficient algorithm based on successive convex approximation is developed in which the original non‐convex problems are transformed so that they can be approximated by a convex quadratically constrained quadratic problem at each stage, resulting in good approximate solutions. Comparing the designs using ED and RD, we find that the convergence of the algorithm can be significantly faster when optimising over the manifold (RD) than when optimising over the whole space (ED). More importantly, for tight constraints, the use of RD yields solutions which satisfy the constraints far better than the use of ED.

Computation offloading expands the range of computationally-intensive and latency-constrained tasks that mobile users can execute. In a multi-user setting, the system selects the offloading users and allocates resources to them so that the overall energy consumption is minimized. We show herein that when the users have different latencies, the appropriate signalling architecture has a time-slotted structure with different subsets of the offloading users transmitting in each time slot. Furthermore, for multiple access schemes that exploit the full capabilities of the channel we analytically determine the optimal signalling architecture and we develop a highly-efficient algorithm for the power and rate allocations in each time slot. Our numerical results illustrate the advantages of the proposed system over those that employ a single-slot architecture and over time division multiple access.

In this paper, the sum rate of opportunistic interference alignment (OIA) is analyzed in multiple-input-multiple-output interfering broadcast channels. The alignment metric upon which users are scheduled is based on the chordal distance between certain interfering subspaces at each receiver, and the closed-form expressions for the rates of the scheduled users are derived. Furthermore, we show that for a system in which each user has$N$receive antennas and the$j$th base station transmits$d_{j}$data streams, where$\sum _{j=1}^{I}d_{j}={N}+1$and${N}\ge 2$, the rate for each user can be approximated by the mean of a Gumbel random variable. Further analysis reveals that if the number of users in cell$i$scales as$\rho ^{\alpha }$, where$\rho $is the normalized transmit power and$\alpha \in [{0,1}]$, then cell$i$can achieve$\alpha d_{i}$degrees of freedom. The simulation results confirm the validity of the theoretical analysis and the accuracy of the approximation. Thus, the sum rate analysis provided herein is an effective performance evaluation method for multi-cell OIA.

The opportunity to offload computational tasks to computing resources embedded in the network infrastructure enables mobile users to expand the scope of the applications that can be processed and to reduce the energy required to complete them. In this paper we seek insight into the impact of the choice of the multiple access scheme that is employed when each of two users has a divisible task that they wish to complete with partial assistance from a computing resource at the access point. In particular, we obtain quasi-closed-form solutions for the partitioning of the problem, the transmission powers and the transmission rates that minimize the sum of the transmission energy and the local computation energy for each user, subject to latency, transmission power and achievable rate constraints. We consider both the case in which the multiple access scheme is unrestricted, and the case of time division multiple access. Our numerical results demonstrate that exploiting the full capabilities of the multiple access channel enables a substantial reduction in the energy expended by the users, especially when the users have significantly different channel gains.

This paper develops low-complexity design techniques for robust linear precoders suitable for various multi-cell multiple-input single-output (MISO) downlink systems. The goal is to satisfy pre-specified SINR requirements for users in multiple cells under some base station power constraints, in the absence of perfect channel state information (CSI). First, we consider the case of full cooperation between base stations and derive a simple iterative algorithm that achieves the required SINRs with high probability despite the presence of channel uncertainties. Then we consider the case of distributed coordination between base stations and develop a simple iterative algorithm that requires only very limited communication among the base stations. Our simulation results demonstrate that substantial robustness can be obtained at a low computational cost.

In this paper, we consider the problem of optimal opportunistic spectrum access using full-duplex (FD) radios in presence of uncertain primary user (PU) channel statistics and propose a Sensing-and-Selectively-Transmit protocol (SaST). To optimize its throughput, the SU sensing period has to be carefully tuned. However, in absence of the exact knowledge of PU activity statistics, under SaST, the PU's performance may be adversely affected. A learning strategy is devised to update the estimated statistics based on spectrum sensing observations. Simulation studies demonstrate that the resulting robust solution provides a good trade-off between optimizing the SU's throughput and protecting the PU.

A linear precoding scheme is developed for unbounded MIMO downlink networks with quasi-static channels that have a hexagonal cell architecture. In the scheme developed herein, the equivalent channel model is structured to be decomposable, and the linear precoders at the base stations are designed to be decomposable as well. The proposed scheme is based the principles of fractional spatial reuse precoding. Spatial reuse precoding (SRP) is a precoding scheme that exploits the fact that interfering sources that employ the same structured precoder arrive in the same subspace, regardless of the particular channel matrices between the interfering sources and the receiver. The proposed scheme is fractional in the sense that each cell is partitioned and different precoders, with different power levels, are assigned in each partition. The proposed fractional SRP scheme enables the elimination of the dominant sources of interference without requiring cooperation between base stations.

We consider the design of the linear precoder for a multiple-input single-output (MISO) downlink in a system that employs limited feedback using Grassmannian quantization. The goal is to minimize the outage probability of a target signal-to-interference-and noise ratio (SINR) under a transmitted power constraint. By approximating the outage constraint by a zero-outage region, employing a semidefinite relaxation, and applying an extension of the S-Lemma, the problem is converted into a quasi-convex problem. Insights into the structure of the solution of that problem generate an alternate design formulation that provides greater robustness in the presence of significant uncertainties and has a quasi-closed form solution.

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.

In this paper we propose a structured low-latency interference alignment scheme for the two-user single-input single-output (SISO) time-invariant X channel. The scheme is based on asymmetric (non-circular) complex signals generated by linear precoders and linear zero-forcing receivers. In addition to achieving the optimal (sum) degrees of freedom (DoF) of 4/3, the precoders are balanced in the sense that for pairs of symbols the signal-to-noise ratio at the input to the decoder is the same. Furthermore, the sum rate is shown to have a small power offset-in one simple scenario that offset is at least 6 dB smaller than the offset of an existing scheme. The principles that underlie this scheme are extended to a time-varying channel with delayed feedback in which either asymmetric symmetric signalling is used.

We consider the problem of power allocation for the multiple-input single-output (MISO) downlink with uncertain channel state information at the transmitter. The uncertainty is modeled probabilistically and the receivers specify quality-of-service (QoS) constraints in terms of a target signal-to-interference-and-noise ratio that is to be achieved with a given outage probability. The proposed approach is based on a deterministic characterization of the outage probability, and mildly conservative approximations thereof. Although the resulting optimization problems are not convex, the good solutions that we obtain using straightforward coordinate update algorithms provide significantly better performance than the existing convex approaches because the approximations are less conservative.

This paper considers a Gaussian broadcast channel with two unmatched degraded components, three individual messages, and a common message that is intended for all three receivers. It is shown that for this channel, superposition coding with Gaussian signalling is sufficient to achieve every point in the capacity region.

An effective strategy for transmitter adaptation on slow block-fading multiple-input multiple-output (MIMO) links is for the receiver to inform the transmitter of the subspace over which transmission should take place, and for the transmitter to allocate power uniformly over that subspace. The design of a feedback scheme to implement this strategy can be viewed as a (lossy) source compression problem on a Grassmannian manifold. Memoryless vector quantization on each fading block is one approach to that problem, but it neglects any correlation between blocks. In some recent work, several approaches have been proposed to take advantage of this correlation. In this paper we propose an alternative technique that leverages existing Grassmannian codebooks from memoryless schemes and employs a quantized form of geodesic interpolation. Distinguishing features of the proposed technique include the fact that it only requires a single codebook, and the fact that it enables the step length of the geodesic interpolation to be adapted to the channel realization, rather than the channel statistics. In some straightforward simulation experiments, the proposed approach provides better performance than an existing scheme.

We consider the problem of minimizing the cost of the power required to achieve a specified level of quality-of-service (QoS) on a point-to-point link that may be assisted by an orthogonal amplify-and-forward (AF) relay. We consider a scenario in which only the distribution of the channel states is available for the design, and the QoS is specified in terms of a target rate that is to be achievable with a specified probability of outage. We assign prices to the power expended by the source and the relay, and we seek to minimize the cost of the power required to achieve the specified QoS. This chance-constrained problem appears to be difficult to solve in its direct form. Instead, we employ the Chebyshev inequality to obtain a deterministic formulation whose solution is guaranteed to provide the required QoS. Although that problem is non-convex, its structure enables the development of an effective algorithm. We apply this design methodology to a system with imperfect channel estimation and illustrate its performance.

This paper presents two polynomial-complexity techniques for assigning Gray-like binary labels to arbitrary Grassmannian constellations. In the first technique, the constellation of interest, C, is matched directly to an auxiliary constellation that can be readily Gray labelled. The optimal matching in this technique can be obtained efficiently, but its application is limited to cases in which an auxiliary constellation with a geometric structure that resembles that of C can be identified. In the second technique no auxiliary constellation is required and the labels are generated by matching the distance spectrum of C with that of a hypothetical constellation that is assumed to be perfectly Gray labelled. Optimal matching in this case is computationally prohibitive. Instead, an efficient suboptimal matching algorithm is proposed. When compared with several existing schemes, the proposed labellings provide better performance in both uncoded and BICM-based non-coherent MIMO systems with iterative demapping and decoding (IDD). Furthermore, with the proposed labels, the Grassmannian-based BICM-IDD scheme performs better than a training-based counterpart that employs the Golden code and optimal demapping.

In many half-duplex cooperative systems, the direct formulation of the problem of finding the jointly optimal power and channel resource allocation that maximizes a weighted sum of the achievable rates can be difficult to solve. In this paper, we provide an efficient algorithm to solve this problem for a class of systems with convex achievable rate regions. For those systems, we show that the weighted-sum-rate problem can be solved using a bisection-based search in which a “target rate” problem is solved at each step. The target rate problem involves maximizing one of the achievable rates subject to target values for the other rates, and can be efficiently solved in a number of cases. We show that the proposed technique can be applied to orthogonal multiple access relay systems and that joint optimization can result in significantly larger weighted sum rates than optimization over the powers alone with a fixed channel resource allocation.

One of the advantages of relaying is that it offers the potential for a reduction the power required to achieve a specified level of quality-of-service (QoS). However, the problem of optimizing the available resources so as to minimize this power is often difficult to solve. In this paper we consider the case of a point-to-point link assisted by an orthogonal non-regenerative decode-and-forward (NDF) relay that is allocated a fraction of the time block. We assign prices to the powers of the source and the relay, and we consider the problem of jointly optimizing the source power, the relay power and the fraction of the time block so as to minimize the total cost of the power required to achieve a specified target rate. The natural formulation of that problem is not convex, but by analyzing the structure of the constraints we obtain a quasi-closed-form expression for the optimal solution that, at most, requires the solution of a simple one-dimensional zero-crossing problem for a monotonic function. This enables the problem to be efficiently solved, and clearly identifies when relaying is superior to direct transmission. Our numerical results illustrate the extent of the gains over regenerative decode-and-forward relaying, in which the resource allocation is, by definition, constrained to be equal.

This paper considers a Gaussian broadcast channel with two unmatched degraded components, three particular messages, and a common message that is intended for all three receivers. It is shown that for this channel superposition coding and Gaussian signalling is sufficient to achieve every point in the capacity region.

This paper addresses the problem of designing optimum full-symbol-rate linear space-time block codes (STBC) for a multi-input multi-output (MIMO) communication system with M transmitter and N ≥ M receiver antennas and a linear minimum mean square error (MMSE) receiver. By analyzing the detection error probability expression for the optimized STBC, it is shown that for QAM signaling, the maximum diversity gain for such a system is N - M + 1. The minimum probability of error STBC design is then extended to systems in which the transmission spans L independent realizations from a block fading channel model, and a (multiblock) linear MMSE receiver is employed. Necessary and sufficient conditions for the optimality of the code are obtained, and a systematic design method for generating codes that satisfy these conditions is presented. The detection error probability and diversity gain of this optimized linear multiblock transceiver are analyzed. It is proved that the error probability decreases with L, and it is shown numerically that the diversity gain increases with L. Thus, if the corresponding latency can be accommodated, for sufficiently large L an optimally designed multiblock system with a linear receiver can exploit the temporal diversity provided by the block-fading channel and achieve higher diversity gain than that of any single-block system of the same symbol rate with a maximum likelihood (ML) receiver. The optimized multiblock linear system achieves this diversity at a substantially lower computational cost. In fact, the structure of the optimal codes can be exploited to significantly reduce the cost of the multiblock linear receiver.

We consider a broadcast channel with multiple antennas at the base station and single-antenna receivers, and we study transceiver design with quality of service (QoS) requirements in the presence of uncertain channel state information (CSI) at the transmitter. Each user's QoS requirement is formulated as an upper bound on the outage probability of the mean square error (MSE), and we demonstrate that these constraints imply bounds on the outage of the received signal-to-interference-plus-noise-ratio. Using this MSE framework, we provide a unified approach to the design of non-linear and linear transceivers that minimize the transmitted power required to satisfy the QoS constraints. We present three conservative design approaches that yield (deterministic) convex and efficiently-solvable design formulations that guarantee the satisfaction of the QoS constraints, and we propose computationally-efficient algorithms that can reduce the level of conservatism in the initial formulations.

Three computationally-efficient List-based soft MIMO demodulators are developed, each of which generates its list using the randomization procedure associated with the semidefinite relaxation (SDR) of a particular hard demodulation problem. The structure of this SDR depends on the signaling scheme, and we will focus on 16-QAM signaling. The key step in the development of the first two demodulators is the derivation of polynomial expressions for the extrinsic information provided by the decoder. These expressions enable this information to be incorporated into the SDR framework. The resulting "List-SDR" demodulators require one semidefinite program (SDP) to be solved at each demodulation-decoding iteration. In the proposed "Single-SDR" demodulator this requirement is reduced to one SDP per channel use by deriving an approximation of the randomization procedure used by the List-SDR demodulator and showing that this approximation enables the decoupling of the processing of the channel measurement from that of the extrinsic information from the decoder. Simulation results show that the proposed demodulators provide considerable reductions in computational cost over several existing soft demodulators, and that these reductions are obtained without incurring a substantial degradation in performance.

This paper considers the design of both a transmitter and a receiver for noncoherent communication over a frequency-flat, richly scattered multiple-input multiple-output (MIMO) channel. The design is guided by the fact that at high signal-to-noise ratios (SNRs), the ergodic capacity of the channel can be achieved by input signals that are isotropically distributed on the (compact) Grassmann manifold. The first part of the paper considers the design of Grassmannian constellations that MIMIC the isotropic distribution. A subspace perturbation analysis is used to determine an appropriate metric for the distance between Grassmannian constellation points, and using this metric, greedy, direct and rotation-based techniques for designing constellations are proposed. These techniques offer different tradeoffs between the minimum distance of the constellation and the design complexity. In addition, the rotation-based technique results in constellations that have lower storage requirements and admit a natural ldquoquasi-set-partitioningrdquo binary labeling.

A bit-interleaved coded modulation (BICM) scheme with iterative (soft) demapping and decoding (IDD) is developed for non-coherent communication over a multiple-input multiple-output (MIMO) channel. The scheme exploits the underlying Grassmannian geometry of the signalling scheme that approaches the ergodic capacity of the non-coherent model at high signal-to-noise ratios. In particular, this geometry guides the construction of the constellation and the mapper at the transmitter, and gives rise to a computationally-efficient list-based demapping algorithm. The incorporation of a scheme that enables the decoder to augment the demapping list virtually eliminates the mild performance degradation of the efficient demapper. Simulation results demonstrate that at high data rates the proposed scheme can provide significantly better performance than several training-based BICM-IDD schemes.

We consider a single-user multiple-input multiple-output (MIMO) communication system in which the transmitter has access to both the channel covariance and the channel mean. For this scenario, we provide an explicit second-order approximation of the ergodic capacity of the channel, and we use this approximation to show that when the channel has a non-zero mean, the basis of the optimal input covariance matrix depends on the input signal power. (This basis is independent of the signal power in the zero-mean case.) The second-order approximation also provides insight into the way in which the low-signal-to-noise-ratio (SNR) optimal input covariance matrix is related to the optimal input covariance matrix at arbitrary SNRs. Furthermore, we show that the design of the input covariance matrix that optimizes the second-order approximation can be cast as a convex optimization problem for which the Karush-Kuhn-Tucker (KKT) conditions completely characterize the optimal solution. Using these conditions, we provide an efficient algorithm for obtaining second-order optimal input covariance matrices. The resulting covariances confirm our theoretical observation that, in general, the low-SNR optimal signal basis does not coincide with the optimal basis at higher SNRs. Finally, we show how our second-order design algorithm can be used to efficiently obtain input covariance matrices that provide ergodic rates that approach the ergodic capacity of the system.

We consider a multiple-input multiple-output (MIMO) wireless communication scenario in which the channel follows a general spatially-correlated complex Gaussian distribution with non-zero mean. We derive an explicit characterization of the optimal input covariance from an ergodic rate perspective for systems that operate at low SNRs. This characterization is in terms of the eigen decomposition of a matrix that depends on the mean and the covariance of the channel, and typically results in a beamforming strategy along the principal eigenvector of that matrix. Simulation results show the potential impact of (jointly) exploiting the mean and the covariance of the channel on the ergodic achievable rate at both low and moderate- to-high SNRs.

We consider the jointly optimal allocation of transmission power and channel resources (such as time and bandwidth) for an orthogonal amplify-and-forward (AF) pairwise cooperation scheme. In particular, we derive a simple efficient algorithm for determining the joint allocations required to operate at any point on the boundary of the achievable rate region. The algorithm is based on a closed-form solution, derived herein, for the optimal power allocation for a given channel resource allocation, and on showing that the channel resource allocation problem is quasi-convex.

We develop a computationally efficient and memory efficient approach to (near) maximum a posteriori probability demodulation for MIMO systems with QPSK signalling, based on semidefinite relaxation. Existing approaches to this problem require either storage of a large list of candidate bit-vectors, or the solution of multiple binary quadratic problems. In contrast, the proposed demodulator does not require the storage of a candidate list, and involves the solution of a single (efficiently solvable) semidefinite program per channel use. Our simulation results show that the resulting computational and memory efficiencies are obtained without incurring a significant degradation in performance.

We consider the design of linear precoders for broadcast channels with quality of service (QoS) constraints for each user, in scenarios with uncertain channel state information at the transmitter. Given a total power constraint on the transmission power, our goal is to design a robust fair precoder that maximizes the minimum QoS over all users that can be guaranteed for every channel within a specified uncertainty region around the estimate of each user's channel. Since this problem is not known to be computationally tractable, we will derive three conservative design approaches that yield quasi-convex and computationally-efficient restrictions of the original design problem. The three approaches yield formulations that offer different trade-offs between the degree of conservatism and the size of the design problem. Our simulations indicate that the proposed approaches can significantly increase the minimum QoS of all users when the available channel knowledge at the transmitter is imperfect.

We study the problem of jointly allocating power and the channel resource of an orthogonal multiple access relay systems in order to maximize the achievable rate region. Four relaying strategies are considered: regenerative decode-and- forward (RDF), non-regenerative decode-and-forward (NDF), amplify-and-forward (AF), and compress-and-forward (CF). For RDF and NDF we show that the problem can be formulated as a quasi-convex problem, while for AF and CF we show that the problem can be made quasi-convex if the signal to noise ratios of the direct channels are at least -3 dB. Therefore, efficient algorithms can be used to obtain the jointly optimal power and channel resource allocation. Furthermore, we show that the convex subproblems in those algorithms admit a closed-form solution. Our numerical results show that the joint allocation of power and the channel resource achieves significantly larger achievable rate regions than those achieved by power allocation alone with fixed channel resource allocation. We also demonstrate that assigning different relaying strategies to different users together with the joint allocation of power and the channel resources can further enlarge the achievable rate region.

Motivated by some observations regarding the structure of the optimal power allocation for an existing orthogonal amplify-and-forward (AF) pairwise cooperation scheme, we propose a modified orthogonal AF cooperation scheme that uses the channel resources more efficiently and hence provides a larger achievable rate region. We consider the jointly optimal allocation of the transmission power and the channel resource for that scheme. In particular, we derive a simple efficient algorithm for determining the allocations required to operate at any point on the boundary of the achievable rate region. The algorithm is based on a closed-form solution, derived herein, for the optimal power allocation for a given channel resource allocation, and on showing that the channel resource allocation problem is quasi-convex.

We consider the design of linear transceivers for multiuser communication systems in the presence of uncertain channel state information (CSI), with an emphasis on the downlink. We consider a deterministically-bounded model for the channel uncertainty, and we study the design of robust downlink transceivers that minimize the worst-case MSE over all admissible channels. While we show that the design problem is NP-hard, we also propose an iterative local optimization algorithm that is based on efficiently-solvable convex conic formulations. Our framework is quite flexible, and can incorporate different bounded uncertainty models as well as a variety of power constraints. In particular, we study a "system-wide" uncertainty model, and although the resulting design problem is still NP hard, it does result in a significantly simpler iterative local design algorithm than the "per-user" uncertainty model. Our approaches to the minimax design for the downlink can be extended to the uplink, and we provide explicit formulations for the resulting uplink designs. Simulation results indicate that the proposed designs can significantly reduce the sensitivity of the downlink to uncertain CSI.

We consider joint transceiver design for point-to-point Multiple-Input Multiple-Output communication systems that implement interference (pre-)subtraction; i.e., Decision Feedback Equalization (DFE) or Tomlinson-Harashima precoding (THP). We develop a unified framework for joint transceiver design of these two dual systems by considering design criteria that are expressed as functions of the (logarithm of the) Mean Square Error (MSE) of the individual data streams. By deriving two inequalities that involve the logarithms of the individual MSEs, we obtain optimal designs for two broad classes of communication objectives, namely those that are Schur-convex and Schur-concave functions of these logarithms. These two classes embrace several design criteria for which the optimal transceiver design has remained an open problem. For Schur-convex objectives, the optimal design results in data streams with equal MSEs. In addition to other desirable properties, this design simultaneously minimizes the total MSE and the average bit error rate, and maximizes the Gaussian mutual information; a property that is not achieved by a linear transceiver. Moreover, we show that the optimal design yields objective values that are superior to the corresponding optimal objective value for a linear transceiver. For Schur-concave objectives, the optimal DFE design results in linear equalization and the optimal THP design results in linear precoding. The proposed design framework can be regarded as a counterpart of the existing framework for linear transceiver design.

We consider the design of linear transceivers for multiuser communication systems in the presence of uncertain channel state information (CSI), with an emphasis on downlink systems with a single antenna at each receiver. For systems with uplink-downlink reciprocity, we consider a stochastic model for the channel uncertainty, and we propose an efficient algorithm for the joint design of the linear preceding matrix at the base station and the equalizing gains at the receivers so as to minimize the average mean-square-error (MSE) over the channel uncertainty. The design is based on a generalization, derived herein, of the MSE duality between the broadcast and multiple access channels (MAC) to scenarios with uncertain CSI, and on a convex formulation for the design of robust transceivers for the dual MAC. For systems in which quantized channel feedback is employed, we consider a deterministically-bounded model for the channel uncertainty, and we study the design of robust downlink transceivers that minimize the worst- case MSE over all admissible channels. While we show that the design problem is NP-hard, we also propose an iterative local optimization algorithm that is based on efficiently-solvable convex conic formulations. Our framework is quite flexible, and can incorporate different bounded uncertainty models as well as a variety of power constraints. In particular, we study a "system-wide" uncertainty model, and although the resulting design problem is still NP hard, it does result in a significantly simpler iterative local design algorithm than the "per-user" uncertainty model. Our approaches to the minimax design for the downlink can be extended to the uplink, and we provide explicit formulations for the resulting uplink designs. Simulation results indicate that the proposed approaches to robust linear transceiver design can significantly reduce the sensitivity of the downlink to uncertain CSI, and can provide improved performance over that of existing robust designs.

We consider the design of multiple-input multiple-output communication systems with a linear precoder at the transmitter, zero-forcing decision feedback equalization (ZFDFE) at the receiver, and a low-rate feedback channel that enables communication from the receiver to the transmitter. The channel state information (CSI) available at the receiver is assumed to be perfect, and based on this information the receiver selects a suitable precoder from a codebook and feeds back the index of this precoder to the transmitter. Our approach to the design of the components of this limited feedback scheme is based on the development, herein, of a unified framework for the joint design of the precoder and the ZF-DFE under the assumption that perfect CSI is available at both the transmitter and the receiver. The framework is general and embraces a wide range of design criteria. This framework enables us to characterize the statistical distribution of the optimal precoder in a standard Rayleigh fading environment. Using this distribution, we show that codebooks constructed from Grassmann packings minimize an upper bound on an average distortion measure, and hence are natural candidates for the codebook in limited feedback systems. Our simulation studies show that the proposed limited feedback scheme can provide significantly better performance at a lower feedback rate than existing schemes in which the detection order is fed back to the transmitter.

We consider the jointly optimal allocation of the radio resources for a two-user orthogonal amplify-and-forward (AF) cooperation scheme. In particular, we derive a simple efficient algorithm for determining the power and channel resource allocations required to operate at any point on the boundary of the achievable rate region. The algorithm is based on two results derived herein: a closed-form solution for the optimal power allocation for a given channel resource allocation; and the fact that the channel resource allocation problem is quasiconvex. The structure of the optimal power allocation reveals that at optimality at most one user acts as a relay, and hence a fraction of the channel resource will be idle. We propose a modified orthogonal AF cooperation scheme that uses the channel resources more efficiently and hence provides a larger achievable rate region.

Bit-interleaved coded-modulation (BICM) with iterative demodulation and decoding (IDD) is a popular architecture for the development of practical communication schemes that operate at rates close to capacity. In multiple-input multiple-output (MIMO) BICM-IDD schemes, a key computational bottleneck is the demodulation step; that is, the extraction of "soft" information about the transmitted bits from the channel output. The concept of list-based demodulation provides a convenient framework for managing the trade-off between accuracy and computational cost in the extraction of this soft information, especially when tree-search techniques are used to construct the list. In this paper, we will propose several list-based demodulators based on modifications of the stack algorithm for searching a tree. The modifications partition the stack in ways that enable efficient and effective searching of the tree from the perspective of list-based demodulation. Simulation results show that the proposed demodulators achieve desirable trade-offs between complexity and performance.

We consider joint transceiver design for general multiple-input multiple-output communication systems that implement interference (pre-)subtraction, such as those based on decision feedback equalization (DFE) or Tomlinson-Harashima precoding (THP). We develop a unified framework for joint transceiver design by considering design criteria that are expressed as functions of the mean square error (MSE) of the individual data streams. By deriving two inequalities that involve the logarithms of the individual MSEs, we obtain optimal designs for two classes of communication objectives, namely those that are Schur-convex and Schur-concave functions of these logarithms. For Schur-convex objectives, the optimal design results in data streams with equal MSEs. This design simultaneously minimizes the total MSE and maximizes the mutual information for the DFE-based model. For Schur-concave objectives, the optimal DFE design results in linear equalization and the optimal THP design results in linear preceding. The proposed framework embraces a wide range of design objectives and can be regarded as a counterpart of the existing framework of linear transceiver design.

We consider a broadcast scenario in which a single transmitter wishes to send common, partially common and particular messages to several receivers over the product of unmatched parallel scalar Gaussian subchannels with a total power constraint. This scenario is a generalization of the 2-user 2-subchannel scenario that was studied earlier in the literature. In order to expose the signal structure and the difficulties that arise in generalizing the results on the 2-user 2-subchannel case to the case of K users and N subchannels, we consider a representative scenario with 3 users and 2 subchannels. For this case, we characterize the achievable rate region, and express the boundary points thereof as the solution of an optimization problem. This problem is not convex in the general case, but it provides insight that leads to tight inner and outer bounds on the capacity region that can be obtained efficiently via the solution of a convex Geometric Program (GP). (The GP also generates the corresponding power loads and partitions.) In addition to these bounds, we provide a (precise) GP formulation for the optimal power allocation problem for the 2-user 2-subchannel case.

We consider point-to-point multiple antenna communication systems in which multiple data streams are transmitted simultaneously. We consider systems which use Tomlinson-Harashima (TH) precoding to pre-subtract the interference among these data streams at the transmitter. In a conventional Tomlinson-Harashima precoding system, transmitter feedback and receiver feedforward processing matrices are used for interference pre-subtraction and channel spatial equalization. In addition to these matrices, we consider a transmitter precoding matrix that generalizes the permutation matrix used for ordering the precoded symbols in existing designs. This extra degree of freedom offers the potential for improved performance. In particular, under a mild signal to noise ratio (SNR) constraint, we find an optimum zero-forcing preceding matrix that minimizes the average symbol error rate (SER) of the data streams subject to a transmitter power constraint. We also show that the proposed design is optimal from an average bit error rate (BER) perspective. Simulation studies show significant improvement over conventional zero-forcing Tomlinson-Harashima precoders.

We consider the design of Tomlinson-Harashima (TH) precoders for broadcast channels in the presence of channel uncertainty. For systems in which uplink-downlink reciprocity is used to obtain a channel estimate at the transmitter, we present a robust design based on a statistical model for the channel uncertainty. We provide a convex formulation of the design problem subject to two types of power constraints: a set of constraints on the power transmitted from each antenna and a total power constraint. For the case of the total power constraint, we present a closed-form solution for the robust TH precoder that incurs essentially the same computational cost as the corresponding designs that assume perfect channel knowledge. For systems in which the receivers feed back quantized channel state information to the transmitter, we present a robust design based on a bounded model for the channel uncertainty. We provide a convex formulation for the TH precoder that maximizes the performance under the worst-case channel uncertainty subject to both types of power constraints. We also present a conservative robust design for this type of channel uncertainty that has reduced computational complexity for the case of power constraints on individual antennas and leads to a closed-form solution for the total power constraint case. Simulation studies verify our analytical results and show that the robust TH precoders can significantly reduce the rather high sensitivity of broadcast transmissions to errors in channel state information.

We consider linear precoding for the downlink of a multiuser communication system in the presence of uncertain channel state information (CSI) at the base station. We consider systems in which the base station has multiple antennas and each user has a single antenna and the channel estimate at the receivers is quantized and fed back to the base station. For these systems we propose a deterministically bounded model for the channel uncertainty and a convex optimization formulation for the precoder that maximizes the worst-case performance under constraints on the power transmitted from each antenna. We also derive a closed-form expression for the precoder that maximizes the worst-case performance under a constraint on total transmitted power. The cost of computing this closed-form solution is the same as that of computing the solution to the corresponding method that assumes perfect channel knowledge. An interesting property of the proposed robust precoders is that they do not necessarily use all the allowable transmission power. Our simulations indicate that the proposed approach can significantly reduce the sensitivity of the linearly precoded downlink to uncertainty in the CSI.

Multiple access schemes in which the transmitting nodes are allowed to cooperate have the potential to provide higher quality of service than conventional schemes. In the class of pairwise cooperative multiple access schemes in which channel state information is available at the transmitters, the allocation of transmission power plays a key role in the realization of these quality of service gains. Unfortunately, the natural formulation of the power allocation problem for full-duplex cooperative schemes is not convex, but it is shown herein that this non-convex formulation can be simplified and re-cast in a convex form. In fact, in most scenarios a closed form expression for the optimal power allocation for each point on the boundary of an achievable rate region can be obtained

We consider linear precoding for the downlink of a multiuser communication system in the presence of uncertain channel state information (CSI) at the base station. We consider systems in which the base station has multiple antennas and each user has a single antenna; i.e. multiple-input single-output (MISO) systems. For systems with uplink-downlink reciprocity we propose a statistical model for the channel uncertainty and provide a convex optimization formulation for the precoder that maximizes an average mean square performance measure. For systems in which the channel measurements are quantized and fed back to the base station we propose a deterministically bounded model for the channel uncertainty and a convex formulation for the precoder that maximizes the worst-case performance. Both formulations allow the incorporation of power constraints on individual antennas in addition to the overall power constraint. Our simulations indicate that the proposed approach can significantly reduce the sensitivity of the linearly preceded downlink to uncertainty in the CSI

A bit-interleaved coded modulation (BICM) scheme with iterative demapping and decoding (ID) is developed for non-coherent communication over a multiple-input multiple-output (MIMO) channel. The scheme exploits the underlying Grassmannian geometry of the signalling scheme that achieves the ergodic capacity of the non-coherent model at high signal-to-noise ratios. In particular, this geometry gives rise to an efficient list-based demapping algorithm that substantially reduces the computational complexity of the receiver. By allowing the decoder to augment the demapping list, the performance degradation of this efficient algorithm can be rendered insignificant. We compare the performance of the proposed scheme with that of a training-based BICM-ID scheme and show, via simulation, that the proposed scheme can provide significantly better performance at high data rates.

Multiple access schemes in which the transmitting nodes are allowed to cooperate have the potential to provide higher quality of service than conventional schemes. In the class of half-duplex pairwise cooperative multiple access schemes in which channel state information is available at the transmitters, the allocation of transmission power and communication resources plays a key role in the realization of these quality of service gains. In this paper we propose a half-duplex cooperative multiple access scheme and develop an efficient algorithm for the joint allocation of power and the communication resources. We demonstrate that the new scheme can attain a significantly larger fraction of the achievable rate region for the full duplex case than an existing scheme that does not employ resource allocation.

We consider a multi-input multi-output (MIMO) communication system equipped with a linear minimum mean-square error (MMSE) receiver. We design a full-rate linear space-time block code (STBC) for blocks of data that span several realizations of a block-static fading channel to achieve high diversity gain. The proposed code structures are necessary and sufficient to minimize the detection error probability. They also enable the detection computations to be partitioned into separate blocks such that the normalized complexity is reduced to little more than that for a single block. The additional complexity grows only linearly with L, the number of blocks for which the code design covers. Analysis shows that the diversity gain achieved by the code also grows linearly with L. This is confirmed by simulation results

An efficient channel-independent design method for the prototype filter of a filtered multitone (FMT) transceiver is proposed, along with an iterative power-loading algorithm for FMT. The insight gained from this design is used to choose the number of subchannels in an FMT system.

We consider the problem of blind maximum-likelihood (ML) detection for the orthogonal space-time block code (OSTBC) scheme. Our previous work has shown that the problem can be simplified to a Boolean quadratic program (BQP). This sequel focuses on effective optimization methods for that BQP, which, from an optimization viewpoint, is still a computationally hard problem. First, we consider semidefinite relaxation (SDR), a high-precision BQP approximation algorithm with a computational cost that is polynomial in the problem size. We also propose a simple method that can significantly reduce the average complexity of the SDR technique. Second, we consider sphere decoding, an exact BQP solver that can be computationally expensive in the worst case, but generally incurs a reasonable average complexity particularly at high SNRs. Simulation results indicate that these two blind ML algorithms provide very similar bit error rate performance. Moreover, numerical studies show that SDR provides better complexity performance than sphere decoding in the worst-case sense, while sphere decoding provides better complexity performance in the average sense.

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 derive analytic expressions for the boundaries of the search region of a recently proposed efficient detector for non-coherent reception of Grassmannian constellations. These boundaries are designed to ensure that the restriction of the detection search space to the enclosed region does not incur significant performance degradation. In addition, we show that the cardinality of the set of candidate constellation points, that is the number of constellation points that lie within the search space, approaches one at least as fast as the inverse of the square root of the received signal SNR

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, a design method is developed for the class of linear-dispersion (LD) codes - a diverse set of space-time codes that subsumes several standard designs. The development begins by showing that for systems that employ a large number of transmit antennas, LD codes constructed from unitary coding matrices are asymptotically optimum from different design perspectives, viz., minimum mean square error (MMSE), mutual information, and average pairwise error probability (PEP). Those measures have a direct impact on the detection complexity, data rate, and error performance that a space-time code can achieve. Using the insight generated by the asymptotic result, a structured design technique for the LD coding matrices, that suits a broad class of configurations is provided. The resulting codes can support high data rates and provide performance advantages over current designs when decoded with a standard detector. Based on the asymptotic results, a row interleaving scheme is proposed, and it is shown to result in significant performance enhancement.

This paper addresses the blind symbol identifiability of the orthogonal space-time block code (OSTBC) scheme. That is, the conditions under which OSTBC symbols can be identified without ambiguity when channel state information is not available. In many space-time communication schemes, achieving unique blind symbol identification requires certain assumptions on the number of receiver antennas and the rank of the channel matrix. In this paper, we show that unique blind symbol identification of OSTBCs is possible for any number of receiver antennas and for any (nonzero) channel matrix. This attractive unique identifiability result is shown to be achieved by a class of OSTBCs that exhibit certain matrix non-rotational properties. Using these properties, we validate the identifiability of a number of commonly used OSTBCs.

Realizing the benefits of ultra-wideband (UWB) communications hinges critically on judicious pulse shape design to enable UWB spectral mask compatibility, and co-existence with and adaptation to other wireless devices. To this end, we propose a convex optimization based waveform design method for UWB radios. By casting the pulse design problem as a (convex) semidefinite program (SDP) over the pulse autocorrelation, globally optimal waveform designs can be efficiently obtained. While the focus of this paper is on the design of waveforms that optimally utilize the bandwidth and power allowed by the spectral mask, the flexibility of the SDP framework also allows the optimization of several other system objectives.

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.

Filtered multitone (FMT) modulation is a filter bank based modulation scheme that is a candidate for the next generation of digital subscriber line (DSL) technology. The high level of spectral containment provided by FMT schemes offers the potential for larger achievable bit rates than more conventional discrete multitone (DMT) schemes in typical DSL environments. In this paper we provide an effective design method for the prototype filter in the FMT filter bank. Our method allows efficient evaluation of the inherent trade-off between the subchannel spectral containment provided by the prototype filter and the intersymbol interference that the filter generates. An appropriate operating point on this trade-off curve is then identified by computing the achievable bit rate for FMT systems with prototype filters which lie on the curve. Our numerical results indicate that careful exploration of the filter design trade-off results in a significant gain in the achievable bit rate.

We propose a greedy algorithm for designing Grassmannian constellations that mimic the distribution that achieves the high SNR capacity of a noncoherent MIMO fading channel. We also introduce a reduced complexity suboptimum detector whose performance is comparable to that of the optimal detector.

Two strategies for improving the (uncoded) bit error rate (BER) performance of practical rate-adaptive block-by-block communication schemes, such as discrete multitone modulation (DMT) is proposed. Our strategies are inspired by some recent work which showed that for uniformly bit-loaded schemes, the transmission strategy which minimizes the BER for a linear receiver involves allocating power to the subchannels that are implicit in the block-by-block framework in a minimum mean square error (MMSE) fashion and linearly combining these subchannels using a normalized discrete Fourier transform (DFT) matrix. This combining equalizes the decision point signal-to-noise ratios (SNRs) of the subchannels. Given a nonuniformly bit-loaded scheme, our first design strategy simply performs a DFT-based linear combination within the groups of subchannels which share the same constellation. Our second strategy provides further reduction in the BER by reallocating power within these groups in a MMSE fashion prior to DFT combining. Our examples indicate that our design strategies can provide significant reductions in the BER, and give rise to substantial SNR gains (of the order of several decibels).

We consider the problem of determining an optimal transmission scheme for broadcasting a common message over vector channels, given (perfect) channel knowledge at both the receive and transmit ends. We provide an efficient method for jointly designing a linear transmitter and and a set of linear receivers so as to minimize a weighted mean square error (WMSE) of the data estimates. The computational efficiency follows from the convex formulations that we develop. These formulations enable utilization of highly efficient interior point methods. For diagonal channel matrices, which appear in multicarrier systems that employ cyclic prefixing, we show that the optimal transmitter is obtained by subcarrier allocation and power loading. The set of minimum MSE transceivers for a vector broadcast system is parametrized by a unitary matrix degree of freedom. For the case of diagonal systems, we show how this unitary matrix can be chosen so that the symbol error rate is minimized (over the given set). This optimal unitary matrix ensures that, for each receiver, the subcarrier signal-to-noise ratios (SNRs) are all the same. Simulations indicate that our designs can provide significantly improved performance over standard designs.

Orthogonal space-time block codes (OSTBCs) have attracted much attention because they provide an effective and simple scheme for fully utilizing the diversity gain in multi-antenna systems. We address the problem of decoding OSTBCs without channel state information. We place our emphasis on the blind maximum-likelihood (ML) method with the BPSK constellation, and show that blind ML decoding requires the solution of a computationally hard optimization problem. To overcome this computational difficulty, we propose using a high-precision and efficient approximation algorithm, called semidefinite relaxation (SDR), to implement blind ML decoding suboptimally. The resultant SDR-ML blind decoder is efficient in that its complexity is approximately cubic in the number of symbols processed, and is promising for its appealing theoretical worst-case approximation accuracy. Simulation results show that the bit error performance of the SDR-ML blind decoder is substantially better than that of several other blind decoders including the cyclic ML method and the subspace method.

We propose a new approach to solving the problem of blind separation of BPSK signals. Using the constant modulus property of the signal, we formulate this problem as a constrained minimization problem that can be solved efficiently using an extended Newton's method on the Stiefel manifold. Compared with the existing separation methods, the proposed method is quite robust to additive noise, achieves a low bit error rate, and enjoys a quadratic convergence rate and a low computational complexity. Simulation results show that our method is a competitive blind separation method.

We present a flexible, efficient design technique for the prototype filter of an oversampled near perfect reconstruction (NPR) generalized discrete Fourier transform (GDFT) filter bank. Such filter banks have several desirable properties for subband processing systems that are sensitive to aliasing; e.g., subband adaptive filters. Our design criteria for the prototype filter are explicit bounds on the aliased components in the subbands, the aliased components in the output, and the distortion induced by the filter bank. It is shown that the design of an optimal prototype filter can be transformed into a convex optimization problem that can be efficiently solved. Our design technique provides an efficient and effective tool for exploring many of the inherent trade-offs in the design of the prototype filter, including the trade-off between aliasing in the subbands and the distortion induced by the filter bank. In our examples we calculate several of these trade-offs and demonstrate that our method can generate filters with significantly better performance than filters obtained using current design methods.

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.

Maximum-likelihood (ML) multiuser detection provides attractive bit error rate performance, but it is computationally prohibitive to implement (except in certain restricted cases). Recently, it has been shown that ML detection for synchronous CDMA can be efficiently and accurately approximated using the semi-definite relaxation (SDR) method. In this work, we consider the application of SDR to the more general scenario of asynchronous CDMA. To make this application computationally feasible, we incorporate a block coordinate ascent (BCA) technique into our detector. Simulation studies show that the resulting BCA-SDR detector has significantly better BER performance than several typical suboptimal multiuser detectors.

The design of a finite impulse response filter often involves a spectral 'mask' which the magnitude spectrum must satisfy. This constraint can be awkward because it yields an infinite number of inequality constraints (two for each frequency point). In current practice, spectral masks are often approximated by discretization, but we show that piecewise constant masks can be precisely enforced in a finite and convex manner via linear matrix inequalities. This facilitates the formulation of a diverse class of filter and beamformer design problems as semidefinite programmes. These optimization problems can be efficiently solved using recently developed interior point methods. Our results can be considered as extensions to the well-known positive-real and bounded-real lemmas from the systems and control literature.

We formulate the blind equalization of constant modulus (CM) signals as a convex optimization problem. This is done by performing an algebraic transformation on the direct formulation of the equalization problem and then restricting the set of design variables to a subset of the original feasible set. In particular, we express the blind equalization problem as a linear objective function subject to some linear and semidefiniteness constraints. Such semidefinite programs (SDP) can be efficiently solved using interior point methods. Simulations indicate that our method performs better than the standard methods, whilst requiring significantly fewer data samples.

In multiuser detection, maximum-likelihood detection (MLD) is optimum in the sense of minimum error probability. Unfortunately, MLD involves a computationally difficult optimization problem for which there is no known polynomial-time solution (with respect to the number of users). In this paper, we develop an approximate maximum-likelihood (ML) detector using semi-definite (SD) relaxation for the case of anti-podal data transmission, SD relaxation is an accurate and efficient approximation algorithm for certain difficult optimization problems. In MLD, SD relaxation is efficient in that its complexity is O(K/sup 3.5/), where K stands for the number of users. Simulation results indicate that the SD relaxation ML detector has its bit error performance close to the true ML detector, even when the cross-correlations between users are strong or the near-far effect is significant.

The design of a pulse shaping filter which provides maximal robustness to an unknown frequency-selective channel has previously been formulated as a convex optimization problem from which an optimal filter can be efficiently obtained. Robustness was measured by the worst-case 'peak' intersymbol interference over a class of deterministically bounded channels, and the optimization was subject to a constraint on the bandwidth of the filter. The purpose of the present paper is to show that the design trade-offs between bandwidth, performance in an ideal channel and robustness to unknown channel distortion can be efficiently evaluated using this convex optimization problem. In the design examples, these trade-offs are used to select chip waveforms with superior performance to those specified in standards for digital mobile telephony.

Redundant multirate filter bank transceivers have been proposed for block-based transmission over channels whose characteristics are known at both the receiver and the transmitter. We propose a criterion for the design of such transceivers for applications in which the channel is not known at the transmitter. The design objective is the minimization of the average mean square error of the data estimates produced by a zero-forcing equalizer over a statistically modelled class of channels. Two solution methods are proposed, one of which appears to be amenable to modification for the solution of certain other robust performance problems. It is shown that the optimal transmitter provides substantially improved performance over a scheme based on multicarrier modulation.

Wavelet packet-division multiplexing (WPDM) is a high-capacity, flexible, and robust multiple-signal transmission technique in which the message signals are waveform coded onto wavelet packet basis functions for transmission. We derive an expression for the probability of error for a WPDM scheme in the presence of both impulsive and Gaussian noise sources and demonstrate that WPDM can provide greater immunity to impulsive noise than both a time-division multiplexing scheme and an orthogonal frequency-division multiplexing scheme.

In digital communications, orthogonal pulse shapes are often used to represent message symbols for transmission through a channel. The design of such pulse shapes is formulated as a convex semidefinite programming problem, from which a globally optimal pulse shape can be efficiently found using interior point methods. The formulation is used to design filters which achieve the minimal bandwidth for a given filter length, and the minimal filter length for a given bandwidth. The effectiveness of the method is demonstrated by the design of waveforms with substantially improved performance over the 'chip' waveforms specified in the standards for digital mobile telecommunications.

We propose a simple algorithm for the blind separation of m synchronous co-channel BPSK signals by an array of n receiving antennas. We exploit the geometric implications of the finite alphabet property of BPSK signals. After a standard channel whitening step, the noiseless received data vectors describe an m-cube, which is a rotated version of the hypercube defined by the 2/sup m/ distinct vectors of /spl plusmn/1s corresponding to all the possible combinations of the states of the sources. We provide a simple procedure to estimate the vertices of this rotated hypercube in the noisy case and then show how the rotation matrix can be determined up to a sign and permutation of its columns. De-rotation of the channel-whitened data results in source separation. Simulations show the good performance of our proposed technique.

Wavelet packet division multiplexing (WPDM) is a high-capacity, flexible and robust orthogonal multiplexing technique in which wavelet packet basis functions are chosen as the coding waveforms. By analogy with frequency-hopped communication schemes, incorporation of time variation into the WPDM scheme offers the potential for further performance improvements, especially in frequency-selective fading channels. We consider a 'branch-hopped' WPDM scheme which employs an efficient modular switched transmultiplexer structure to induce the time variation. We determine classes of 'slow' and 'fast' hopping schemes analogous to their frequency-hopped counterparts, and evaluate several switching strategies for the transmultiplexer. For a given switching strategy we then design the filters within the transmultiplexer modules to provide further robustness to frequency-selective fading channels.