Multiple-input Multiple-output Block-fading Channels Research Articles

Learning-Based Near-Orthogonal Superposition Code for MIMO Short Message Transmission

Massive machine type communication (mMTC) has attracted new coding schemes optimized for reliable short message transmission. In this paper, a novel deep learning-based near-orthogonal superposition (NOS) coding scheme is proposed to transmit short messages in multiple-input multiple-output (MIMO) channels for mMTC applications. In the proposed MIMO-NOS scheme, a neural network-based encoder is optimized via end-to-end learning with a corresponding neural network-based detector/decoder in a superposition-based auto-encoder framework including a MIMO channel. The proposed MIMO-NOS encoder spreads the information bits to multiple near-orthogonal high dimensional vectors to be combined (superimposed) into a single vector and reshaped for the space-time transmission. For the receiver, we propose a novel looped <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -best tree-search algorithm with cyclic redundancy check (CRC) assistance to enhance the error correcting ability in the block-fading MIMO channel. For a comprehensive understanding of the proposed MIMO-NOS scheme, we further quantify the gain from individual components/modules in the framework, and analyze the decoding complexity measured by the floating point operations (FLOPs). Simulation results show the proposed MIMO-NOS scheme outperforms maximum likelihood (ML) MIMO detection combined with a polar code with CRC-assisted list decoding by 1 – 2 dB in various MIMO systems for short (32 – 64 bit) message transmission.

MIMO Block-Fading Channels With Mismatched CSI

We study transmission over multiple-input multiple-output block-fading channels with imperfect channel state information (CSI) at both the transmitter and receiver. In particular, based on mismatched decoding theory for a fixed channel realization, we investigate the largest achievable rates with independent and identically distributed inputs and the nearest neighbor decoder. We then study the corresponding information outage probability in the high signal-to-noise ratio (SNR) regime and analyze the interplay between estimation error variances at the transmitter and receiver to determine the optimal outage exponent, defined as the high-SNR slope of the outage probability plotted in a logarithmic-logarithmic scale against the SNR. We demonstrate that despite operating with imperfect CSI, power adaptation can offer substantial gains in terms of outage exponent.

Directional Estimation of Block-Fading MIMO Channels Using Spherical Harmonics Expansion and Tensor Analysis

The well-known benefits of multiple input multiple output (MIMO) wireless communication systems suppose an efficient use of spatial diversity at both the transmitter and receiver. An important and ...

Gallager's Exponent Analysis of STBC MIMO Systems over η-μ and κ-μ Fading Channels

In this paper, we analytically investigate Gallager's exponent for space-time block codes over multiple-input multiple-output block-fading channels with Gaussian input distribution. As a suitable metric of the fundamental tradeoff between communication reliability and information rate, Gallager's exponent can be used to determine the required codeword length to achieve a prescribed error probability at a given rate below the channel capacity. We assume that the receiver has full channel state information (CSI), while the transmitter has no CSI and performs equal power allocation across all transmit antennas. In the following, novel exact expressions for Gallager's exponent are derived for two well-known channel fading models, namely η-μ and κ-μ fading models. More importantly, the implications of fading parameters and channel coherence time on Gallager's exponent are investigated. In addition, we present new expressions for the Shannon capacity, cutoff rate and expurgated exponent for the above mentioned fading models, while in the high signal-to-noise ratio regime, simplified closed-form expressions are also derived. Finally, we highlight the fact that the presented analysis encompasses all previously known results on Nakagami-m, Rician, Rayleigh and Hoyt fading channels, as special cases.

On an Achievable Rate of Large Rayleigh Block-Fading MIMO Channels With No CSI

Training-based transmission over Rayleigh block-fading multiple-input multiple-output (MIMO) channels is investigated. As a training method a combination of a pilot-assisted scheme and a biased signaling scheme is considered. The achievable rates of successive decoding (SD) receivers based on the linear minimum mean-squared error (LMMSE) channel estimation are analyzed in the large-system limit, by using the replica method under the assumption of replica symmetry. It is shown that negligible pilot information is best in terms of the achievable rates of the SD receivers in the large-system limit. The obtained analytical formulas of the achievable rates can improve the existing lower bound on the capacity of the MIMO channel with no channel state information (CSI), derived by Hassibi and Hochwald, for all signal-to-noise ratios (SNRs). The comparison between the obtained bound and a high SNR approximation of the channel capacity, derived by Zheng and Tse, implies that the high SNR approximation is unreliable unless quite high SNR is considered. Energy efficiency in the low SNR regime is also investigated in terms of the power per information bit required for reliable communication. The required minimum power is shown to be achieved at a positive rate for the SD receiver with no CSI, whereas it is achieved in the zero-rate limit for the case of perfect CSI available at the receiver. Moreover, numerical simulations imply that the presented large-system analysis can provide a good approximation for not so large systems. The results in this paper imply that SD schemes can provide a significant performance gain in the low-to-moderate SNR regimes, compared to conventional receivers based on one-shot channel estimation.

Array Gain in the DMT Framework for MIMO Channels

Following the seminal work by Zheng and Tse on the diversity and multiplexing tradeoff (DMT) of multiple-input multiple-output (MIMO) channels, in this paper, we introduce the array gain to investigate the fundamental relation between transmission rate and reliability in MIMO systems. The array gain gives information on the power offset that results from exploiting channel state information at the transmitter or as a consequence of the channel model. Hence, the diversity, multiplexing, and array gain (DMA) analysis is able to cope with the limitations of the original DMT and provide an operational meaning in the sense that the DMA gains of a particular system can be directly translated into a parameterized characterization of its associated outage probability performance. In this paper, we derive the best DMA gains achievable by any scheme employing isotropic signaling in uncorrelated Rayleigh, semicorrelated Rayleigh, and uncorrelated Rician block-fading MIMO channels. We use these results to analyze the effect of important channel parameters on the outage performance at different points of the DMT curve.

Nearest Neighbor Decoding in MIMO Block-Fading Channels With Imperfect CSIR

This paper studies communication outages in multiple-input multiple-output (MIMO) block-fading channels with imperfect channel state information at the receiver (CSIR). Using mismatched decoding error exponents, we prove the achievability of the generalized outage probability, the probability that the generalized mutual information (GMI) is less than the data rate, and show that this probability is the fundamental limit for independent and identically distributed (i.i.d.) codebooks. Then, using nearest neighbor decoding, we study the generalized outage probability in the high signal-to-noise ratio (SNR) regime for random codes with Gaussian and discrete signal constellations. In particular, we study the SNR exponent, which is defined as the high-SNR slope of the error probability curve on a logarithmic-logarithmic scale. We show that the maximum achievable SNR exponent of the imperfect CSIR case is given by the SNR exponent of the perfect CSIR case times the minimum of one and the channel estimation error diversity. Random codes with Gaussian constellations achieve the optimal SNR exponent with finite block length as long as the block length is larger than a threshold. On the other hand, random codes with discrete constellations achieve the optimal SNR exponent with block length growing with the logarithm of the SNR. The results hold for many fading distributions, including Rayleigh, Rician, Nakagami- , Nakagami- and Weibull as well as for optical wireless scintillation distributions such as lognormal-Rice and gamma-gamma.

MIMO ARQ With Multibit Feedback: Outage Analysis

This paper studies the asymptotic outage performance of incremental redundancy automatic-repeat-request (INR-ARQ) transmission over multiple-input multiple-output (MIMO) block-fading channels with discrete input constellations. We first show that transmission with random codes using a discrete signal constellation across all transmit antennas achieves the optimal outage diversity given by the Singleton bound. The optimal SNR-exponent and outage diversity of INR-ARQ transmission over the MIMO block-fading channel are then analysed. We show that a significant gain in outage diversity is obtained by providing more than one bit feedback at each ARQ round. Thus, the outage performance of INR-ARQ transmission can be remarkably improved with minimal additional overhead. A practical feedback-and-power-adaptation rule is proposed for MIMO INR-ARQ, demonstrating the benefits provided by multibit feedback. Although the rule is sub-optimal in terms of outage performance, it achieves the optimal outage diversity.

Coded Modulation With Mismatched CSIT Over MIMO Block-Fading Channels

Reliable communication over delay-constrained multiple-input multiple-output (MIMO) block-fading channels with discrete inputs and mismatched (imperfect) channel state information at the transmitter (CSIT) is studied. The CSIT mismatch is modeled as Gaussian random variables, whose variances decay as a power of the signal-to-noise ratio (SNR). A special focus is placed on the large-SNR decay of the error and outage probabilities when power control with long-term power constraints is used. Without explicitly characterizing the corresponding power allocation algorithms, we derive the outage exponent as a function of the system parameters, including the CSIT noise variance exponent and the exponent of the peak power constraint. It is shown that CSIT, even if noisy, is always beneficial and leads to important gains in terms of exponents.

Throughput-reliability tradeoff in decode-and-forward cooperative relay channels: A network information theory approach

Cooperative transmission protocols are always designed to achieve the largest diversity gain and the network capacity simultaneously. The concept of diversity-multiplexing tradeoff (DMT) in multiple input multiple output (MIMO) systems has been extended to this field. However, DMT constrains a better understanding of the asymptotic interplay between transmission rate, outage probability (OP) and signal-to-noise ratio. Another formulation called the throughput-reliability tradeoff (TRT) was then proposed to avoid such a limitation. By this new rule, Azarian and Gamal well elucidated the asymptotic trends exhibited by the OP curves in block-fading MIMO channels. Meanwhile they doubted whether the new rule can be used in more general channels and protocols. In this paper, we will prove that it does hold true in decode-and-forward cooperative protocols. We deduce the theoretic OP curves predicted by TRT and demonstrate by simulations that the OP curves will asymptotically overlap with the theoretic curves predicted by TRT.

On the performance of golden space-time trellis coded modulation over MIMO block fading channels

The Golden space-time trellis coded modulation (GST-TCM) scheme was proposed for a high rate 2 times 2 multiple-input multiple-output (MIMO) system over slow fading channels. In this letter, we present the performance analysis of GST-TCM over block fading channels, where the channel matrix is constant over a fraction of the codeword length and varies from one fraction to another, independently. In practice, it is not useful to design such codes for specific block fading channel parameters and a robust solution is preferable. We then show both analytically and by simulation that the GST-TCM designed for slow fading channels are indeed robust to all block fading channel conditions.

Power minimization of central wishart MIMO block-fading channels

In this correspondence, a central Wishart multiple input multiple-output (MIMO) K-block fading channel with an information outage probability constraint is studied. Under this block-limited channel condition, we aim to minimize the transmit power required for attaining a given outage probability based on the statistical channel information at the transmitter (SCIT). Using Gaussian approximation to express the probability density function (pdf) of the instantaneous mutual information and by deriving analytically the mean and variance of the mutual information of the MIMO channel, the optimal power allocation can be obtained numerically by a simple one-dimensional sampling method such as dividing rectange (DIRECT).

Joint Source–Channel Codes for MIMO Block-Fading Channels

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We consider transmission of a continuous amplitude source over an <emphasis><formula formulatype="inline"><tex>$L$</tex></formula></emphasis>-block Rayleigh-fading <emphasis><formula formulatype="inline"><tex>$M_t \times M_r$</tex></formula></emphasis> multiple-input multiple-output (MIMO) channel when the channel state information is only available at the receiver. Since the channel is not ergodic, Shannon's source–channel separation theorem becomes obsolete and the optimal performance requires a joint source–channel approach. Our goal is to minimize the expected end-to-end distortion, particularly in the high signal-to-noise ratio (SNR) regime. The figure of merit is the distortion exponent, defined as the exponential decay rate of the expected distortion with increasing SNR. We provide an upper bound and lower bounds for the distortion exponent with respect to the bandwidth ratio among the channel and source bandwidths. For the lower bounds, we analyze three different strategies based on layered source coding concatenated with progressive superposition or hybrid digital/analog transmission. In each case, by adjusting the system parameters we optimize the distortion exponent as a function of the bandwidth ratio. We prove that the distortion exponent upper bound can be achieved when the channel has only one degree of freedom, that is <emphasis><formula formulatype="inline"><tex>$L=1$</tex></formula></emphasis>, and <emphasis><formula formulatype="inline"><tex>$\min\{M_t,M_r\}=1$</tex> </formula></emphasis>. When we have more degrees of freedom, our achievable distortion exponents meet the upper bound for only certain ranges of the bandwidth ratio. We demonstrate that our results, which were derived for a complex Gaussian source, can be extended to more general source distributions as well. </para>

The Throughput–Reliability Tradeoff in Block-Fading MIMO Channels

We build on Zheng and Tse's elegant formulation of diversity-multiplexing tradeoff (DMT) to provide a better understanding of the asymptotic interplay between transmission rate, error probability, and signal-to-noise ratio (SNR) in block-fading multiple-input multiple-output (MIMO) channels. In particular, we identify the limitation imposed by the notion of multiplexing gain and develop a new formulation called the throughput-reliability tradeoff (TRT), that avoids this limitation. The new characterization is then used to elucidate the asymptotic trends exhibited by the outage probability curves of block-fading MIMO channels.

Outage Theorems for MIMO Block-Fading Channels

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

Optimization and Performance Analysis of Zero Forcing Decision Feedback Detector for MIMO Block-Fading Channels with Per-Antenna Power Control

In multiple-input multiple-output (MIMO) antenna systems, the zero forcing decision feedback detector (ZF-DFD) is used to recover transmit signals. In this paper, we propose a per-antenna power control (PAPC) scheme based on ZF-DFD for MIMO block-fading channels. The optimal power controlled ZF-DFD can minimize the block error rate (BLER) and maximize the lower bound of the channel's free distance at high signal-to-noise ratio (SNR) region subject to a power constraint. Additionally, the optimal power controlled ZF-DFD can achieve this BLER performance without any ordering operation at the receiver. The performance analysis among the conventional ZF-DFD without feedback, the optimal power controlled ZF-DFD with power feedback, and the ZF-DFD with full channel state information feedback shows that the optimal ZF-DFD achieves a tradeoff between performance and feedback overhead. We compare the bit error rate (BER) and BLER performance of the optimal ZF-DFD with other detectors without power feedback by simulation. In simulations, the execution times required by these detectors are also reported to compare their complexity. It comes straight that the optimal power controlled ZF-DFD proposed in this paper can achieve good performance with small feedback overhead and have low complexity.

A New Class of Iterative Equalizers for Space–Time BICM Over MIMO Block Fading Multipath AWGN Channel

This paper addresses the issue of advanced equalization methods for space-time communications over multiple-input multiple-output block fading channel with intersymbol interference. Instead of resorting to conventional multiuser detection techniques (based on the straightforward analogy between antennas and users), we adopt a different point of view, and separate time equalization from space equalization, thus introducing a higher degree of freedom in the overall space-time equalizer design. Time-domain equalization relies on minimum mean-square error criterion and operates on multidimensional modulation symbols, whose individual components can be detected in accordance with another criterion. In particular, when the optimum maximum a posteriori criterion is chosen, substantial performance gains over conventional space-time turbo equalization have been observed for different transmission scenarios, at the price of an increased, albeit manageable, computational complexity.

Optimization of irregular repeat accumulate codes for MIMO systems with iterative receivers

This paper takes into account the design optimization of the random-like ensemble of irregular repeat accumulate (IRA) codes for multiple-input multiple-output (MIMO) communication systems employing iterative receivers. First, the density evolution-based procedure for optimizing the IRA code ensemble is presented. An approximation method based on linear programming is adopted to design an IRA code with the extrinsic information transfer (EXIT) chart matched to that of the soft MIMO demodulator. The authors then reveal the relationship between the IRA codes and the low-density parity-check (LDPC) codes. With a code ensemble mapping relationship between an IRA code and an LDPC code, a quasi-optimal IRA code can be obtained by transforming an optimal LDPC code designed for MIMO systems. Two types of soft MIMO detectors are treated, namely, the maximum a posteriori (MAP) detector and the soft interference canceller with linear MMSE filtering (SIC-MMSE). The results show that with the MAP receiver the designed IRA codes can perform within 1 dB from the ergodic capacities of the MIMO systems under consideration. The authors also treat the short-length IRA code design for block fading MIMO channels. They adopt design techniques for short-length LDPC codes to improve the performance of the short-length IRA code and to reduce the error floor.

An Analytical Comparison of Partial Power-Feedback Designs for MIMO Block Fading Channels

It has been shown that with perfect feedback (CSIT), the optimal multiple input/multiple output (MIMO) transmission strategy is a cascade of channel encoder banks, power control matrix, and eigen-beamforming matrix. However, the feedback capacity requirement for perfect CSIT is 2n/sub T//spl times/n/sub R/, which is not scalable with respect to n/sub T/ or n/sub R/. In this letter, we shall compare the performance of two levels of partial power-feedback strategies, namely, the scalar symmetric feedback and the vector feedback, for MIMO block fading channels. Unlike quasi-static fading, variable rate encoding is not needed for block fading channels to achieve the optimal channel capacity.