Pritam Som

Improved large-MIMO detection based on damped belief propagation

In this paper, we consider the application of belief propagation (BP) to achieve near-optimal signal detection in large multiple-input multiple-output (MIMO) systems at low complexities. Large-MIMO architectures based on spatial multiplexing (V-BLAST) as well as non-orthogonal space-time block codes(STBC) from cyclic division algebra (CDA) are considered. We adopt graphical models based on Markov random fields (MRF) and factor graphs (FG). In the MRF based approach, we use pairwise compatibility functions although the graphical models of MIMO systems are fully/densely connected. In the FG approach, we employ a Gaussian approximation (GA) of the multi-antenna interference, which significantly reduces the complexity while achieving very good performance for large dimensions. We show that i) both MRF and FG based BP approaches exhibit large-system behavior, where increasingly closer to optimal performance is achieved with increasing number of dimensions, and ii) damping of messages/beliefs significantly improves the bit error performance.

Low-Complexity Detection in Large-Dimension MIMO-ISI Channels Using Graphical Models

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 O(K2nt2) and O(Knt) for the MRF and the FG with GAI approaches, respectively, where K and nt 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 Knt. From a performance perspective, these algorithms are even more interesting in large-dimensions since they achieve increasingly closer to optimum detection performance for increasing Knt. 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 M-QAM symbol detection.

Spatial modulation and space shift keying in single carrier communication

Spatial modulation (SM) and space shift keying (SSK) are relatively new modulation techniques which are attractive in multi-antenna communications. Single carrier (SC) systems can avoid the peak-to-average power ratio (PAPR) problem encountered in multicarrier systems. In this paper, we study SM and SSK signaling in cyclic-prefixed SC (CPSC) systems on MIMO-ISI channels. We present a diversity analysis of MIMO-CPSC systems under SSK and SM signaling. Our analysis shows that the diversity order achieved by (n_t, n_r) SSK scheme and (n_t, n_r, Θ_M) SM scheme in MIMO-CPSC systems under maximum-likelihood (ML) detection is n_r, where n_t, n_r denote the number of transmit and receive antennas and Θ_M denotes the modulation alphabet of size M. Bit error rate (BER) simulation results validate this predicted diversity order. Simulation results also show that MIMO-CPSC with SM and SSK achieves much better performance than MIMO-OFDM with SM and SSK.

Performance Analysis of Space-Shift Keying in Decode-and-Forward Multihop MIMO Networks

In this paper, space-shift keying (SSK) is considered for multihop multiple-input-multiple-output (MIMO) networks. In SSK, only one among ns = 2m available transmit antennas, chosen on the basis of m information bits, is activated during transmission. We consider two different systems of multihop cooperation, where each node has multiple antennas and employs SSK. In system I, a multihop diversity relaying scheme is considered. In system II, a multihop multibranch relaying scheme is considered. In both systems, we adopt decode-and-forward (DF) relaying, where each relay forwards the signal only when it correctly decodes. We analyze the end-to-end bit error rate (BER) and diversity order of both the systems with SSK. For binary SSK (ns = 2), our analytical BER expression is exact, and our numerical results show that the BERs evaluated through the analytical expression overlap with those obtained through Monte Carlo simulations. For nonbinary SSK (ns > 2), we derive an approximate BER expression, where the analytically evaluated BER results closely follow the simulated BER results. We show the comparison of the BERs of SSK and conventional phase-shift keying (PSK) and also show the instances where SSK outperforms PSK. We also present the diversity analyses for SSK in systems I and II, which predict the achievable diversity orders as a function of system parameters.

Belief propagation based decoding of large non-orthogonal STBCs

In this paper, we present a belief propagation (BP) based algorithm for decoding non-orthogonal space-time block codes (STBC) from cyclic division algebras (CDA) having large dimensions. The proposed approach involves message passing on Markov random field (MRF) representation of the STBC MIMO system. Adoption of BP approach to decode non-orthogonal STBCs of large dimensions has not been reported so far. Our simulation results show that the proposed BP-based decoding achieves increasingly closer to SISO AWGN performance for increased number of dimensions. In addition, it also achieves near-capacity turbo coded BER performance; for e.g., with BP decoding of 24 × 24 STBC from CDA using BPSK (i.e., 576 real dimensions) and rate-1/2 turbo code (i.e., 12 bps/Hz spectral efficiency), coded BER performance close to within just about 2.5 dB from the theoretical MIMO capacity is achieved.

Bit Error Probability Analysis of SSK in DF Relaying with Threshold-Based Best Relay Selection and Selection Combining

In this letter, we analyze the end-to-end average bit error probability (ABEP) of space shift keying (SSK) in cooperative relaying with decode-and-forward (DF) protocol, considering multiple relays with a threshold based best relay selection, and selection combining of direct and relayed paths at the destination. We derive an exact analytical expression for the end-to-end ABEP in closed-form for binary SSK, where analytical results agree with simulation results. For non-binary SSK, approximate analytical and simulation results are presented.

End-to-end BER analysis of space shift keying in decode-and-forward cooperative relaying

Space shift keying (SSK) is a special case of spatial modulation (SM), which is a relatively new modulation technique that is getting recognized to be attractive in multi-antenna communications. Our new contribution in this paper is an analytical derivation of exact closed-form expression for the end-to-end bit error rate (BER) performance of SSK in decode-and-forward (DF) cooperative relaying. An incremental relaying (IR) scheme with selection combining (SC) at the destination is considered. In SSK, since the information is carried by the transmit antenna index, traditional selection combining methods based on instantaneous SNRs can not be directly used. To overcome this problem, we propose to do selection between direct and relayed paths based on the Euclidean distance between columns of the channel matrix. With this selection metric, an exact analytical expression for the end-to-end BER is derived in closed-form. Analytical results are shown to match with simulation results.

BER Analysis of Space Shift Keying in Cooperative Multi-Hop Multi-Branch DF Relaying

Space shift keying (SSK) is an attractive modulation technique for multi-antenna communications. In SSK, only one among the available transmit antennas is activated during one channel use, and the index of the chosen transmit antenna conveys information. In this paper, we analyze the performance of SSK in multi-hop, multi-branch cooperative relaying systems. We consider the decode-and-forward relaying protocol, where a relay forwards the decoded symbol if it decodes the symbol correctly from the received signal. We derive closed-form expressions for the end-to-end bit error rate of SSK in this system. Analytical and simulation results match very well.

Damped Belief Propagation Based Near-Optimal Equalization of Severely Delay-Spread UWB MIMO-ISI Channels

In this paper, we present a belief propagation (BP) based equalizer for ultrawideband (UWB) multiple-input multiple-output (MIMO) inter-symbol interference (ISI) channels characterized by severe delay spreads. We employ a Markov random field (MRF) graphical model of the system on which we carry out message passing. The proposed BP equalizer is shown to perform increasingly closer to optimal performance for increasing number of multipath components (MPC) at a much lesser complexity than that of the optimum equalizer. The proposed equalizer performs close to within 0.25 dB of SISO AWGN performance at 10^{-3} bit error rate on a severely delay-spread MIMO-ISI channel with 20 equal-energy MPCs. We point out that, although MIMO/UWB systems are characterized by fully/densely connected graphical models, the following two proposed features are instrumental in achieving near-optimal performance for large number of MPCs at low complexities: i) use of pairwise compatibility functions in densely connected MRFs, and ii) use of damping of messages.

Decode-and-Forward Cooperative Multicast with Space Shift Keying

In this paper, we consider space-shift keying (SSK) in dual-hop decode-and-forward (DF) cooperative multicast networks, where a source node communicates with multiple destination nodes with the help of relay nodes. We consider a topology consisting of a single source, two relays, and multiple destinations. For such a system, we propose a scheme to select a single relay among the two when SSK is used for transmission on each of the links in the cooperative system. We analyze the end-to-end average bit error probability (ABEP) of this system. For binary SSK, we derive an exact expression for the ABEP in closed-form. Analytical results exactly match the simulation results validating the analysis. For non-binary SSK, we derive an approximate ABEP expression, where the analytical ABEP results closely follow simulation results. We also derive the diversity order of the system through asymptotic ABEP analysis.