This paper evaluates and compares the performance of single- user (SU) and multi-user (MU) transmission for downlink multiple-input multiple-output (MIMO) channels in terms of system energy efficiency (EE). We introduce power control algorithms to maximize EE. Specifically, to optimize the power allocation, we consider the problem of EE maximization with the satisfaction of the minimum spectral efficiency (SE) gain. Antenna selection is taken into account to further enhance the EE performance for both SU and MU systems. Our results reveal that we should turn off extra antennas at the transmitter, which are originally used for diversity gain but incur large circuit power consumption. Our comparisons between SU and MU differ from conventional comparisons, which focus on SE. Jointly considering EE and SE, we show that SU is more desirable when the transmit power is low, while MU is favored in the case of high transmit power.

We study the problem of multi-stream joint maximum sum-rate precoder and minimum mean-squared error equalizer design for interference alignment in the multi-input multi-output interference channel. Joint precoder and equalizer optimization requires alternation between the forward and reverse links and assumes perfect synchronization at each network node between the transmitters and receivers, resulting in extensive overhead and spectral efficiency loss. To overcome this serious drawback, we propose a new design approach based on weighted-sum-rate maximization assuming a virtual equalizer type at the transmitter to limit the optimization process to the transmitter side. Furthermore, we examine the achievable weighted-sum-rate when the virtual equalizer type is either matched or mismatched to the actual equalizer type used at the receivers. In addition, we quantify the performance loss due to mismatched equalizer types and demonstrate the robustness of our proposed sum-rate weighting strategy to such mismatches. Finally, we derive asymptotic performance expressions and verify their accuracy numerically, even for a moderate number of users.

In this paper, we study the problem of per-stream maximum sum-rate joint precoder and minimum mean-squared error equalizer design for the multi-input multi-output interference channel. We consider the general case of more than three users with more than one stream per user. We propose a generalized iterative algorithm which directly maximizes the sum-rate without assuming the signal-to-noise ratio to be infinite. To reduce complexity, which can become prohibitive for large network size, we examine the performance-complexity tradeoffs involved in a sparse equalizer design. Joint precoder and equalizer optimization requires alternation between the forward and reverse links and assumes perfect synchronization between the transmitters and receivers at each network node, resulting in extensive overhead and spectral efficiency loss. To overcome this serious drawback, we propose a new design approach based on weighted-sum-rate maximization assuming a virtual equalizer type at the transmitter to limit the optimization process to the transmitter side. In addition, we quantify the sum-rate loss due to mismatched equalizer types and demonstrate the robustness of our proposed sum-rate weighting strategy to such mismatches with perfect or imperfect channel knowledge. Finally, we derive asymptotic performance expressions and verify their accuracy numerically even for a moderate number of users.

We study the problem of per-stream joint maximum sum-rate (MSR) precoder and minimum mean-squared error (MMSE) equalizer design for interference alignment in the multi-input multi-output interference channel. We consider the general case of more than three users with more than one stream per user. We propose a new generalized iterative algorithm which directly maximizes the average overall sum-rate without assuming the signal-to-noise ratio to be infinite. The receivers' implementation complexity increases proportional to the square of the number of equalizer taps which becomes prohibitive as the network size increases. To address this issue, we examine the performance-complexity tradeoffs involved in a sparse equalizer design. Our numerical results demonstrate that, for the full-complexity MMSE equalizer design, our proposed algorithm achieves higher overall sum-rate compared to previously proposed interference alignment algorithms. In addition, we reduce the MMSE linear equalizer complexity by 30% while limiting the sum-rate loss to about 10%, at most, compared to the full-complexity design.

A user scheduling problem for downlink multiuser-multiple-input-multiple-output (MU-MIMO) systems is investigated. Unlike in theoretical analysis, users are usually equipped with different numbers of antennas in practical downlink systems, which we call receive antenna heterogeneity. We propose a scheduling algorithm which utilizes the property of receiver antenna heterogeneity to improve the system's throughput. The algorithm consists of two strategies: (1) divide the whole set of users into several groups where each group contains multiple users served simultaneously; (2) allocate spatial streams to users in each group such that sum rate is maximized. Simulation results are provided to show that our algorithm outperforms the homogeneous scheduling algorithm which does not take the heterogeneity into account.

Performance of coding and modulation systems in fading channels is usually analysed under the assumption that the receiver has perfect knowledge of channel condition. However, various shortcomings in practical channel estimation techniques lead to imperfections, resulting in channel estimation errors. The authors analyse a practical coding and modulation scheme for multiple-antenna systems considering channel estimation errors. The novelty of this study resides in providing error probability bounds for concatenated trellis coded modulation (TCM) or bit-interleaved coded modulation (BICM) schemes with orthogonal space–time block codes (OSTBC) under imperfect channel estimation assumption. Moreover, our analytical results quantify the performance degradation associated with various levels of channel estimation error variance. The authors also show that if channel estimation quality does not improve sufficiently with SNR, there would be error floor in performance, such that the coded system could get outperformed by a system with differential signalling that requires no channel estimation. Simulation results are presented, which confirm the validity of the analytical results.

The authors analyse concatenated bit-interleaved coded modulation and orthogonal space-time block codes (OSTBC) over fading channels in the absence and presence of channel state information (CSI) in receiver. The authors derive analytical expressions for bit and frame error probabilities based on which corresponding designing rules are proposed. The analytical results are for arbitrary rate of constituent STBC and arbitrary convolutional code, and for CSI-aware receiver is for any number of transmit and receive antennas. Simulation results are presented to confirm the validity of the proposed designing rules. Moreover, the simulation results show that the proposed system outperforms concatenated trellis coded modulation and OSTBC.

In this letter, we analyze the performance of a class of multiple-antenna systems which concatenate channel codes, e.g., trellis coded modulation (TCM), and differential orthogonal space-time block codes (DOSTBC). Assuming no channel state information (CSI), tight performance bounds for bit and frame error rates are provided under block Rayleigh fading channel. Simulation results are also provided which confirm the accuracy of analytical findings.

Concatenation of orthogonal space-time block codes (OSTBC) with an outer trellis has led to simple and powerful codes, known as superorthogonal codes or space-time block trellis-coded modulation. In this letter, we generalize these codes by finding new code supersets and corresponding set partitioning, resulting in improved coding gain. We provide design guidelines for the labeling of the generalized code trellises and demonstrate the gains by several example designs for two and four transmit antennas

The keyhole condition, where the MIMO channel has only one degree of freedom, impairs the performance of MIMO systems. Thus, one may wish to design codes that are robust to this condition. So far, a general analysis of space-time codes in keyhole conditions has not been available (except in the special case of orthogonal space-time block codes). This work provides pairwise error probabilities for general space-time codes in keyhole condition. We present design criteria in high SNR, providing guidelines for codes that are robust to keyhole conditions. Also included is the proof of the intuitive result that the diversity under keyhole condition is min (M, N), where M and N are the number of transmit and receive antennas, with a slightly unexpected twist in the case of M=N.

In this paper we analyze the performance of an important class of MIMO systems that of orthogonal space-time block codes concatenated with channel coding. This system configuration has an attractive combination of simplicity and performance. We study this system under spatially independent fading as well as correlated fading that may arise from the proximity of transmit or receive antennas or unfavorable scattering conditions. We consider the effects of time correlation and present a general analysis for the case where both spatial and temporal correlations exist in the system. We present simulation results for a variety of channel codes, including convolutional codes, turbo codes, trellis coded modulation (TCM), and multiple trellis coded modulation (MTCM), under quasi-static and block-fading Rayleigh as well as Rician fading. Simulations verify the validity of our analysis

We consider linear detectors for MIMO systems, i.e., multi-antenna systems where linear equalizers are employed to remove spatial interference. We analyze the behavior of linear equalizers through outage probability. The MMSE equalizer was found to behave in unexpected ways. Contrary to the usual intuition, the performance of MMSE and zero-forcing equalizers may not coincide at high-SNR. This is especially true at low spectral efficiencies, where the MMSE equalizer may achieve full spatial diversity.

The performance of space-time codes under channel correlation has been studied in detail recently, and a variety of results have been produced. In this work, we simplify some of the existing derivations as well as present some new results. One of the novel issues raised in this investigation is the loss of the uniform error probability (UEP) property of many codes in the presence of transmit side correlation. Also our error expressions for the general case of jointly spatio-temporally correlated Rayleigh and Rician fading are new, to the best of our knowledge. We also apply our analysis to some of the more recently developed codes for the MIMO channel, including the super-orthogonal codes and the linear dispersion codes.

Antenna spacing and the properties of a scattering environment can create correlation between channel coefficients. Temporal correlation between fading coefficients may also be present, because one may be unable or unwilling to fully interleave the channel symbols. This paper presents a comprehensive analysis of multiple-input multiple-output systems under correlated fading. We calculate pairwise-error-probability (PEP) expressions under quasi-static fading, fast fading, block fading, as well as arbitrarily temporally correlated fading, under Rayleigh and Rician conditions. We use the PEP expressions to calculate union bounds on the performance of trellis space-time codes, super orthogonal space-time codes, linear-dispersion codes, and diagonal algebraic space-time codes.

Orthogonal space-time block codes (OSTBC) enjoy simple decoding, but have limited coding gain, if any. By concatenating OSTBC with an outer trellis, simple and powerful codes have been constructed, known as super-orthogonal codes or STB-TCM. In this work, we generalize these codes by exploring new code supersets, through mappings that do not induce any instantaneous modulation constellation expansion. By finding new mappings and establishing the properties of the resulting set partitions, we provide design guidelines for the labeling of the generalized code trellises. Simulations demonstrate significant coding gains resulting from our codes.

The keyhole condition, where the MIMO channel has only one degree of freedom, impairs the performance of MIMO systems. In cases that this condition is likely, one may wish to design codes that are robust to this condition. So far, a general analysis of space-time codes in keyhole conditions has not been available (except in the special case of orthogonal space-time block codes). In this work, we provide pairwise error probabilities for general space-time codes in the keyhole condition. We present design criteria in high SNR, providing guidelines for codes that are robust to keyhole conditions. We also prove the intuitive result that the diversity under the keyhole condition is min(M,N), with a slightly unexpected twist in the case of M=N.

Efficient compression of finite-alphabet sources requires variable-length codes (VLCs). However, in the presence of noisy channels, error propagation in the decoding of VLCs severely degrades performance. To address this problem, redundant entropy codes and iterative source-channel decoding have been suggested, but to date, neither performance bounds nor design criteria for the composite system have been available. We calculate performance bounds for the source-channel system by generalizing techniques originally developed for serial concatenated convolutional codes. Using this analysis, we demonstrate the role of a recursive structure for the inner code and the distance properties of the outer code. We use density evolution to study the convergence of our decoders. Finally, we pose the question: Under a fixed rate and complexity constraint, when should we use source-channel decoding (as opposed to separable decoding)? We offer answers in several specific cases. For our analysis and design rules, we use union bounds that are technically valid only above the cutoff rate, but interestingly, the codes designed with union-bound criteria perform well even in low signal-to-noise ratio regions, as shown by our simulations as well as previous works on concatenated codes.

We propose a general class of concatenated error-correcting entropy codes and channel codes. In this way we extend and generalize the existing body of work on iterative decoding of entropy and channel codes. Using the structure and properties of serial concatenated codes, we employ error-correcting entropy codes as the outer code, and a convolutional codes as the inner code. The generalization from entropy codes to redundant entropy codes allows powerful error correction similar to turbo codes. We provide upper bounds for the concatenated entropy code and channel code. We also show that iterative decoding of the proposed concatenated code outperforms iterative decoding of previously reported entropy and channel codes that operate at the same overall rate.

In progressive joint source-channel coding of images, experiments show that optimizing rate allocation according to PSNR criteria and according to rate criteria produce essentially similar results-a very important observation because optimization by rate is often much easier. This paper presents analysis to uncover the reason for-and the generality of-these empirical results. We first examine the typical shape of the distribution of PSNR in light of the distribution of the first uncorrectable error in the bitstream. Then we analyze the sensitivity of rate allocation to the operational R-D curve, via parametric modeling of the source and the channel. We demonstrate that rate allocation is locally insensitive to variations in the R-D characteristics. This analysis provides a justification for low-complexity rate allocation algorithms, such as the one by Chande and Farvardin (2000), that work independently of the operational R-D curve.