Generalized spatial modulation (GSM) uses $n_{t} $ transmit antenna elements but fewer transmit radio frequency (RF) chains, $n_{rf} $ . Spatial modulation (SM) and spatial multiplexing are special cases of GSM with $n_{rf}=1$ and $n_{rf}=n_{t} $ , respectively. In GSM, in addition to conveying information bits through $n_{rf} $ conventional modulation symbols (for example, QAM), the indices of the $n_{rf} $ active transmit antennas also convey information bits. In this paper, we investigate GSM for large-scale multiuser MIMO communications on the uplink. Our contributions in this paper include: 1) an average bit error probability (ABEP) analysis for maximum-likelihood detection in multiuser GSM-MIMO on the uplink, where we derive an upper bound on the ABEP, and 2) low-complexity algorithms for GSM-MIMO signal detection and channel estimation at the base station receiver based on message passing. The analytical upper bounds on the ABEP are found to be tight at moderate to high signal-to-noise ratios (SNR) . The proposed receiver algorithms are found to scale very well in complexity while achieving near-optimal performance in large dimensions. Simulation results show that, for the same spectral efficiency, multiuser GSM-MIMO can outperform multiuser SM-MIMO as well as conventional multiuser MIMO, by about 2 to 9 dB at a bit error rate of $10^{-3} $ . Such SNR gains in GSM-MIMO compared to SM-MIMO and conventional MIMO can be attributed to the fact that, because of a larger number of spatial index bits, GSM-MIMO can use a lower-order QAM alphabet which is more power efficient.

Generalized Spatial Modulation in Large-Scale Multiuser MIMO Systems

We propose iterative detection and decoding (IDD) algorithms with low-density parity-check (LDPC) codes for multiple-input multiple-output (MIMO) systems operating in block-fading and fast Rayleigh fading channels. Soft-input–soft-output minimum-mean-square-error (MMSE) receivers with successive interference cancelation are considered. In particular, we devise a novel strategy to improve the bit error rate (BER) performance of IDD schemes, which takes into account the soft a posteriori output of the decoder in a block-fading channel when root-check LDPC codes are used. A MIMO IDD receiver with soft information processing that exploits the code structure and the behavior of the log-likelihood ratios is also developed. Moreover, we present a scheduling algorithm for decoding LDPC codes in block-fading channels. Simulations show that the proposed techniques result in significant gains in terms of BER for both block-fading and fast-fading channels.

Iterative Detection and Decoding Algorithms for MIMO Systems in Block-Fading Channels Using LDPC Codes

This paper presents cost-effective low-rank techniques for designing robust adaptive beamforming (RAB) algorithms. The proposed algorithms are based on the exploitation of the cross-correlation between the array observation data and the output of the beamformer. First, we construct a general linear equation considered in large dimensions whose solution yields the steering vector mismatch. Then, we employ the idea of the full orthogonalization method (FOM), an orthogonal Krylov subspace based method, to iteratively estimate the steering vector mismatch in a reduced-dimensional subspace, resulting in the proposed orthogonal Krylov subspace projection mismatch estimation (OKSPME) method. We also devise adaptive algorithms based on stochastic gradient (SG) and conjugate gradient (CG) techniques to update the beamforming weights with low complexity and avoid any costly matrix inversion. The main advantages of the proposed low-rank and mismatch estimation techniques are their cost-effectiveness when dealing with high-dimension subspaces or large sensor arrays. Simulations results show excellent performance in terms of the output signal-to-interference-plus-noise ratio (SINR) of the beamformer among all the compared RAB methods.

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Robust Adaptive Beamforming Based on Low-Rank and Cross-Correlation Techniques

We propose iterative detection and decoding (IDD) algorithms with Low-Density Parity-Check (LDPC) codes for Multiple Input Multiple Output (MIMO) systems operating in block-fading and fast Rayleigh fading channels. Soft-input soft-output minimum mean-square error receivers with successive interference cancellation are considered. In particular, we devise a novel strategy to improve the bit error rate (BER) performance of IDD schemes, which takes into account the soft \textit{a posteriori} output of the decoder in a block-fading channel when Root-Check LDPC codes are used. A MIMO IDD receiver with soft information processing that exploits the code structure and the behavior of the log likelihood ratios is also developed. Moreover, we present a scheduling algorithm for decoding LDPC codes in block-fading channels. Simulations show that the proposed techniques result in significant gains in terms of BER for both block-fading and fast-fading channels.

Iterative Detection and Decoding Algorithms using LDPC Codes for MIMO Systems in Block-Fading Channels

In this work, we propose a novel adaptive reduced-rank receive processing strategy based on joint preprocessing, decimation and filtering (JPDF) for large-scale multiple-antenna systems. In this scheme, a reduced-rank framework is employed for linear receive processing and multiuser interference suppression based on the minimization of the symbol-error-rate (SER) cost function. We present a structure with multiple processing branches that performs a dimensionality reduction, where each branch contains a group of jointly optimized preprocessing and decimation units, followed by a linear receive filter. We then develop stochastic gradient (SG) algorithms to compute the parameters of the preprocessing and receive filters, along with a low-complexity decimation technique for both binary phase shift keying (BPSK) and $M$ -ary quadrature amplitude modulation (QAM) symbols. In addition, an automatic parameter selection scheme is proposed to further improve the convergence performance of the proposed reduced-rank algorithms. Simulation results are presented for time-varying wireless environments and show that the proposed JPDF minimum-SER receive processing strategy and algorithms achieve a superior performance than existing methods with a reduced computational complexity.

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Adaptive Reduced-Rank Receive Processing Based on Minimum Symbol-Error-Rate Criterion for Large-Scale Multiple-Antenna Systems

In this paper we propose a novel message passing algorithm which exploits the existence of short cycles to obtain performance gains by reweighting the factor graph. The proposed decoding algorithm is called variable factor appearance probability belief propagation (VFAP-BP) algorithm and is suitable for wireless communications applications with low-latency and short blocks. Simulation results show that the VFAP-BP algorithm outperforms the standard BP algorithm, and requires a significantly smaller number of iterations when decoding either general or commercial LDPC codes.

/pdf/low-latency-reweighted-belief-propagation-decoding-for-ldpc-1k1b6ijviu.pdf

Low-Latency Reweighted Belief Propagation Decoding for LDPC Codes

In this study, a novel low-complexity adaptive decision feedback (DF) detection with parallel DF (P-DF) and P-DF constellation constraints (P-DFCC) is proposed for multiuser multi-input–multi-output (MIMO) systems. The authors propose a constrained constellation map which introduces a number of selected points served as the feedback candidates for interference cancellation. By introducing a reliability checking, a higher degree of freedom is introduced to refine the unreliable estimates. The P-DFCC is followed by an adaptive receive filter to estimate the transmitted symbol. To reduce the complexity of computing the filters with time-varying MIMO channels, an adaptive recursive least squares algorithm is employed in the proposed P-DFCC scheme. An iterative detection and decoding (Turbo) scheme is considered with the proposed P-DFCC algorithm. Simulations show that the proposed technique has a complexity comparable to the conventional P-DF detector while it obtains a performance close to the maximum-likelihood detector at a low to medium signal-to-noise ratio range. .

Adaptive decision feedback detection with parallel interference cancellation and constellation constraints for multiuser multi-input-multi-output systems

In this paper, we present novel strategies for generating rate-compatible (RC) irregular low-density parity-check (LDPC) codes with short/moderate block lengths. We propose three puncturing and two extension schemes, which are designed to determine the puncturing positions that minimize the performance degradation and the extension that maximizes the performance. The first puncturing scheme employs a counting cycle algorithm and a grouping strategy for variable nodes having short cycles of equal length in the Tanner graph (TG). The second scheme relies on a metric called extrinsic message degree (EMD) and the third scheme is a simulation-based exhaustive search to find the best puncturing pattern among several random ones. In addition, we devise two layer-structured extension schemes based on a counting cycle algorithm and an EMD metric which are applied to design RC-LDPC codes. Simulation results show that the proposed extension and puncturing techniques achieve greater rate flexibility and good performance over the additive white Gaussian noise channel, outperforming existing techniques.

Rate-compatible LDPC codes with short block lengths based on puncturing and extension techniques

In this paper, we investigate rate-compatible (RC) short/ moderate length irregular low-density parity-check (LDPC) codes and propose three different novel puncturing schemes to determine the preferred puncturing positions so as to achieve less performance degradation. The first one is based on a short cycle counting algorithm as well as grouping variable nodes which have the equal length of short cycles in the Tanner Graph; the second scheme can be seen as an improved version of the first one by means of introducing another metric called Extrinsic Message Degree (EMD); and the last scheme relies on a simulation-based exhaustive search in order to find the best puncturing pattern among several random puncturing patterns. The simulation results show that all three proposed schemes can achieve the rate flexibility and minimize the performance loss over the additive white Gaussian noise (AWGN) channel.

Novel intentional puncturing schemes for finite-length irregular LDPC codes

We propose two innovative extension schemes for Rate-Compatible (RC) Low-Density Parity-Check (LDPC) codes with short/moderate block lengths. The proposed designs are based on the counting cycles algorithm and the Approximate Cycle Extrinsic Message Degree (EMD). Our layer-structured extension schemes enjoy a linear-time encodable ability and relatively low decoding complexity thanks to low degree profiles with limited decoding iterations, such that they intrinsically fit in a type-II hybrid automatic repeat-request (ARQ) system. Simulation results show that the proposed approaches manage to yield a performance gain of up to 0.3 dB when compared to the existing extension technique.

Jingjing Liu

Papers

Low-Latency Reweighted Belief Propagation Decoding for LDPC Codes

Adaptive decision feedback detection with parallel interference cancellation and constellation constraints for multiuser multi-input-multi-output systems

Rate-compatible LDPC codes with short block lengths based on puncturing and extension techniques

Novel intentional puncturing schemes for finite-length irregular LDPC codes

Finite-length rate-compatible LDPC codes based on extension techniques