Set-partitioning based forward/backward soft decision algorithms for MIMO detection

Abstract: Ever since the adoption of the single carrier frequency division multiple access (SC-FDMA) scheme for the uplink in the Long Term Evolution (LTE) standard, there has been much interest in improved receiver algorithms for the same. Successive interference cancelation (SIC) based turbo receivers (Turbo SIC) have been proposed to tackle the multi-stream interference (MSI) for transmission modes such as spatial multiplexing (SM) and multiuser (MU) multiple input multiple output (MIMO). In addition, decision feedback equalizers (DFE) have been discussed as an alternative to the simple linear minimum mean square error (LMMSE) based receivers to suppress intersymbol interference (ISI) caused by the frequency selective multi-path channel. This paper proposes a DFE receiver variant based on parallel interference cancelation (PIC) with maximum likelihood detection (MLD) and ordered SIC (OSIC) principles to suppress ISI and MSI. Simulations show that the proposed receiver performs better than the existing SIC and DFE based receivers and achieves the matched filter bound (MFB) for both coded and uncoded systems.

Abstract: A multi-dimensional set-partitioning scheme is proposed for joint reduced-state sequence detection (JRSSD) of vector sequences corrupted by intersymbol interference (ISI) and additive white Gaussian noise (AWGN). The existing multi-dimensional set-partitioning schemes result in complexity exponential in the dimensionality of the vectors in the vector sequence. The proposed set-partitioning scheme allows the construction of reduced-state trellises with very few states even when the vectors are of high dimensionality. One of the key requirements of the JRSSD algorithm is an efficient algorithm for spatial multi-symbol detection, for which we propose the reduced-state tree (RST) detection algorithm. In addition to performance improvement, the inclusion of RST algorithm for spatial multi-symbol detection provides a common framework for designing receivers for both flat-fading and frequency-selective fading MIMO channels.

Abstract: A reduced complexity soft-output joint equalization scheme is proposed for MIMO-ISI systems employing Higher Order Modulation (HOM). Multi-dimensional set partitioning proposed by Zhang et.al. [1] is applied to form a reduced-state trellis or the subset trellis. The Max-Log-MAP algorithm is modified to operate on the subset trellis in order to generate soft information at reduced complexity. The backward recursion can often be avoided since the forward recursion of the Max-LogMAP algorithm is capable of providing reliable soft information when some fixed decision delay is introduced. This idea is leveraged in the equalization scheme proposed in this paper. It generates soft information using only the forward recursion of the Max-Log-MAP algorithm and is referred to as the Forward-Only algorithm. A key requirement of reduced-state equalization is the ability to decide winners of parallel transitions using low-complexity slicing operations, which is accomplished via a novel flexible-complexity algorithm, viz., Reduced-State Tree Detection. Due to set partitioning, soft decision failure can occur in the forward-only algorithm and in such an event, a general approach to regenerate soft information using delayed decision feedback is proposed. The low complexity and memory requirements of the forward-only algorithm makes it attractive for MIMO-ISI equalization.

Abstract: Not only to reduce the candidates but also to maintain detection performance in multiple-input multiple-output (MIMO) detection, an adaptive overlapped cluster (AOC) scheme to balance detection error and computing cost is built for $4\times 4$ and $8\times 8$ MIMO-OFDM systems with up to 256 quadrature amplitude modulation (QAM). The constellations are partitioned into several clusters. A cluster with size decided by channel status is chosen for signal decoding. Different partition schemes are combined to minimize the numbers of clusters required to cover a candidate symbol as the pre-estimated signal falls at cluster edges, namely overlapped clustering. The simulations of a $4\times 4$ MIMO OFDM with 64 QAM and $8\times 8$ MIMO OFDM with 256 QAM hint that the AOC-based detection requires an additional 0.57 dB and 1.02 dB compared to maximum likelihood (ML). Compared with K-best sphere decoding (SD), it is reduced the computing complexity to 24.50% ~ 56.25% in $4\times 4$ MIMO OFDM and, 35.00% ~ 56.25% in $8\times 8$ MIMO OFDM. In addition, the proposed scheme is ported to a reconfigurable frequency-domain (FD) modem, which is designed and implemented via TSMC 45-nm technology, with multi-rate clocking and processing elements (PEs) upgrading for supporting the proposed MIMIO detection. The results show that the throughput is 1077.8 Mbps with $4\times 4\,\,64$ -QAM modulations.

Abstract: In this paper, we develop a detection algorithm at the receiver, for a wireless system employing multiple antennas at both the transmitter and receiver, where the knowledge of channel is not available at the transmitter (a.k.a open-loop system). The proposed algorithm offers a very good trade-off between implementation complexity and bit-error-rate (BER) performance. In the literature, the fixed complexity sphere decoding (FSD) is known to be state-of-the art decoding algorithm for open-loop multiple input and multiple output (MIMO) systems. The reduced state maximum aposteriori (RS-MAP) algorithm is an extension of FSD where reduced state (RS) receiver delivers bit level soft decisions using maximum aposteriori (MAP) Bahl, Cocke, Jelinek and Raviv (BCJR) recursions that are implemented on the reduced state tree. While RS-MAP employs state dependent hard decision feedback, the proposed algorithm uses a) a state dependent soft/hard symbol feedback b) a scaling of the branch metric with the assumption that soft decision feedback is employed, to obtain a performance improvement over standard RS-MAP algorithm. The proposed modifications to the branch metric are general and can be applied to a number of other sequence estimators such as maximum likelihood soft output viterbi algorithm (ML-SOVA), FSD-SOVA, RS-MAP with forward only recursion etc.

Abstract: The general problem of estimating the a posteriori probabilities of the states and transitions of a Markov source observed through a discrete memoryless channel is considered. The decoding of linear block and convolutional codes to minimize symbol error probability is shown to be a special case of this problem. An optimal decoding algorithm is derived.

Abstract: A coding technique is described which improves error performance of synchronous data links without sacrificing data rate or requiring more bandwidth. This is achieved by channel coding with expanded sets of multilevel/phase signals in a manner which increases free Euclidean distance. Soft maximum--likelihood (ML) decoding using the Viterbi algorithm is assumed. Following a discussion of channel capacity, simple hand-designed trellis codes are presented for 8 phase-shift keying (PSK) and 16 quadrature amplitude-shift keying (QASK) modulation. These simple codes achieve coding gains in the order of 3-4 dB. It is then shown that the codes can be interpreted as binary convolutional codes with a mapping of coded bits into channel signals, which we call "mapping by set partitioning." Based on a new distance measure between binary code sequences which efficiently lower-bounds the Euclidean distance between the corresponding channel signal sequences, a search procedure for more powerful codes is developed. Codes with coding gains up to 6 dB are obtained for a variety of multilevel/phase modulation schemes. Simulation results are presented and an example of carrier-phase tracking is discussed.

Abstract: Information theory research has shown that the rich-scattering wireless channel is capable of enormous theoretical capacities if the multipath is properly exploited In this paper, we describe a wireless communication architecture known as vertical BLAST (Bell Laboratories Layered Space-Time) or V-BLAST, which has been implemented in real-time in the laboratory Using our laboratory prototype, we have demonstrated spectral efficiencies of 20-40 bps/Hz in an indoor propagation environment at realistic SNRs and error rates To the best of our knowledge, wireless spectral efficiencies of this magnitude are unprecedented and are furthermore unattainable using traditional techniques

Abstract: Random matrix theory has found many applications in physics, statistics and engineering since its inception. Although early developments were motivated by practical experimental problems, random matrices are now used in fields as diverse as Riemann hypothesis, stochastic differential equations, condensed matter physics, statistical physics, chaotic systems, numerical linear algebra, neural networks, multivariate statistics, information theory, signal processing and small-world networks. This article provides a tutorial on random matrices which provides an overview of the theory and brings together in one source the most significant results recently obtained. Furthermore, the application of random matrix theory to the fundamental limits of wireless communication channels is described in depth.