Abstract-In this paper, we deal with low-complexity near-optimal detection/equalization in large-dimension multiple-input multiple-output inter-symbol interference (MIMO-ISI) channels using message passing on graphical models. A key contribution in the paper is the demonstration that near-optimal performance in MIMO-ISI channels with large dimensions can be achieved at low complexities through simple yet effective simplifications/approximations, although the graphical models that represent MIMO-ISI channels are fully/densely connected (loopy graphs). These include 1) use of Markov random field (MRF)-based graphical model with pairwise interaction, in conjunction with message damping, and 2) use of factor graph (FG)-based graphical model with Gaussian approximation of interference (GAI). The per-symbol complexities are ( 2 2 ) and ( ) for the MRF and the FG with GAI approaches, respectively, where and denote the number of channel uses per frame, and number of transmit antennas, respectively. These low-complexities are quite attractive for large dimensions, i.e., for large . From a performance perspective, these algorithms are even more interesting in large-dimensions since they achieve increasingly closer to optimum detection performance for increasing . Also, we show that these message passing algorithms can be used in an iterative manner with local neighborhood search algorithms to improve the reliability/performance of -QAM symbol detection.Index Terms-Factor graphs, graphical models, large dimensions, low-complexity detection, Markov random fields, multiple-input multiple-output inter-symbol interference (MIMO-ISI) channels, pairwise interaction, severe delay spreads.
Orthogonal time frequency space (OTFS) is a 2dimensional (2D) modulation technique designed in the delay-Doppler domain. A key premise behind OTFS is the transformation of a time varying multipath channel into an almost nonfading 2D channel in delay-Doppler domain such that all symbols in a transmission frame experience the same channel gain. It has been suggested in the recent literature that OTFS can extract full diversity in the delay-Doppler domain, where full diversity refers to the number of multipath components separable in either the delay or Doppler dimension, but without a formal analysis. In this paper, we present a formal analysis of the diversity achieved by OTFS modulation along with supporting simulations. Specifically, we prove that the asymptotic diversity order of OTFS (as SNR → ∞) is one. However, in the finite SNR regime, potential for a higher order diversity is witnessed before the diversity one regime takes over. Also, the diversity one regime is found to start at lower BER values for increased frame sizes. We also propose a phase rotation scheme for OTFS using transcendental numbers and show that OTFS with this proposed scheme extracts full diversity in the delay-Doppler domain.
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 {\em GSM for large-scale multiuser MIMO communications on the uplink}. Our contributions in this paper include: ($i$) 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 ($ii$) 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.Comment: IEEE Trans. on Wireless Communications, accepte
Abstract-In this paper, we propose low-complexity algorithms based on Monte Carlo sampling for signal detection and channel estimation on the uplink in large-scale multiuser multiple-input-multiple-output (MIMO) systems with tens to hundreds of antennas at the base station (BS) and a similar number of uplink users. A BS receiver that employs a novel mixed sampling technique (which makes a probabilistic choice between Gibbs sampling and random uniform sampling in each coordinate update) for detection and a Gibbs-sampling-based method for channel estimation is proposed. The algorithm proposed for detection alleviates the stalling problem encountered at high signal-to-noise ratios (SNRs) in conventional Gibbs-sampling-based detection and achieves near-optimal performance in large systems with M -ary quadrature amplitude modulation (M -QAM). A novel ingredient in the detection algorithm that is responsible for achieving near-optimal performance at low complexity is the joint use of a mixed Gibbs sampling (MGS) strategy coupled with a multiple restart (MR) strategy with an efficient restart criterion. Nearoptimal detection performance is demonstrated for a large number of BS antennas and users (e.g., 64 and 128 BS antennas and users). The proposed Gibbs-sampling-based channel estimation algorithm refines an initial estimate of the channel obtained during the pilot phase through iterations with the proposed MGS-based detection during the data phase. In time-division duplex systems where channel reciprocity holds, these channel estimates can be used for multiuser MIMO precoding on the downlink. The proposed receiver is shown to achieve good performance and scale well for large dimensions.
In this paper, we propose a multiple-input multiple output (MIMO) receiver algorithm that exploits channel hardening that occurs in large MIMO channels. Channel hardening refers to the phenomenon where the off-diagonal terms of the matrix become increasingly weaker compared to the diagonal terms as the size of the channel gain matrix increases. Specifically, we propose a message passing detection (MPD) algorithm which works with the real-valued matched filtered received vector (whose signal term becomes , where is the transmitted vector), and uses a Gaussian approximation on the off-diagonal terms of the matrix. We also propose a simple estimation scheme which directly obtains an estimate of (instead of an estimate of), which is used as an effective channel estimate in the MPD algorithm. We refer to this receiver as the channel hardening-exploiting message passing (CHEMP) receiver. The proposed CHEMP receiver achieves very good performance in large-scale MIMO systems (e.g., in systems with 16 to 128 uplink users and 128 base station antennas). For the considered large MIMO settings, the complexity of the proposed MPD algorithm is almost the same as or less than that of the minimum mean square error (MMSE) detection. This is because the MPD algorithm does not need a matrix inversion. It also achieves a significantly better performance compared to MMSE and other message passing detection algorithms using MMSE estimate of. Further, we design optimized irregular low density parity check (LDPC) codes specific to the considered large MIMO channel and the CHEMP receiver through EXIT chart matching. The LDPC codes thus obtained achieve improved coded bit error rate performance compared to off-the-shelf irregular LDPC codes.
Y. Guan and Z. Liu are with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 (e-mail: EYLGuan@ntu.edu.sg; zilongliu@ntu.edu.sg).S. Sugiura is with the Department of Computer and Information Sciences, Tokyo University of Agriculture and Technology, Koganei,
Orthogonal time frequency space (OTFS) modulation is a 2-dimensional (2D) modulation scheme designed in the delay-Doppler domain, unlike traditional modulation schemes which are designed in the time-frequency domain. Through a series of 2D transformations, OTFS converts a doubly-dispersive channel into an almost non-fading channel in the delay-Doppler domain. In this domain, each symbol in a frame experiences an almost constant fade, thus achieving significant performance gains over existing modulation schemes such as OFDM. The sparse delay-Doppler impulse response which reflects the actual physical geometry of the wireless channel enables efficient channel estimation, especially in high-Doppler fading channels. This paper investigates OTFS from a signal detection and channel estimation perspective, and proposes a Markov chain Monte-Carlo sampling based detection scheme and a pseudo-random noise (PN) pilot based channel estimation scheme in the delay-Doppler domain.
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