Abstract—In this paper, we present a low-complexity algorithm for detection in high-rate, non-orthogonal space–time block coded (STBC) large-multiple-input multiple-output (MIMO) systems that achieve high spectral efficiencies of the order of tens of bps/Hz. We also present a training-based iterative detection/channel estimation scheme for such large STBC MIMO systems. Our simulation results show that excellent bit error rate and nearness-to-capacity performance are achieved by the proposed multistage likelihood ascent search (-LAS) detector in conjunction with the proposed iterative detection/channel estimation scheme at low complexities. The fact that we could show such good results for large STBCs like 16 16 and 32 32 STBCs from Cyclic Division Algebras (CDA) operating at spectral efficiencies in excess of 20 bps/Hz (even after accounting for the overheads meant for pilot based training for channel estimation and turbo coding) establishes the effectiveness of the proposed detector and channel estimator. We decode perfect codes of large dimensions using the proposed detector. With the feasibility of such a low-complexity detection/channel estimation scheme, large-MIMO systems with tens of antennas operating at several tens of bps/Hz spectral efficiencies can become practical, enabling interesting high data rate wireless applications. Index Terms—Channel estimation, high spectral efficiencies, large-multiple-input multiple-output (MIMO) systems, low-complexity detection, non-orthogonal space–time block codes. I.

Abstract — 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. Keywords – Non-orthogonal STBCs, large dimensions, low-complexity decoding, belief propagation, Markov random fields, high spectral efficiencies. I.

In this paper, we propose a partial interference cancellation (PIC) group decoding strategy/scheme for linear dispersive space-time block codes (STBC) and a design criterion for the codes to achieve full diversity when the PIC group decoding is used at the receiver. A PIC group decoding decodes the symbols embedded in an STBC by dividing them into several groups and decoding each group separately after a linear PIC operation is implemented. It can be viewed as an intermediate decoding between the maximum likelihood (ML) receiver that decodes all the embedded symbols together, i.e., all the embedded symbols are in a single group, and the zero-forcing (ZF) receiver that decodes all the embedded symbols separately and independently, i.e., each group has and only has one embedded symbol, after the ZF operation is implemented. The PIC group decoding provides a framework to adjust the complexity-performance tradeoff by choosing the sizes of the information symbol groups. Our proposed design criterion (group independence) for the PIC group decoding to achieve full diversity is an intermediate condition between the loosest ML full rank criterion of codewords and the strongest ZF linear independence condition of the column vectors in the equivalent channel matrix. We also propose asymptotic optimal (AO) group decoding algorithm which is an intermediate decoding between the MMSE decoding algorithm and the ML decoding algorithm. The design criterion for the PIC group decoding can be applied to the AO group decoding algorithm because of its asymptotic optimality. It is well-known that the symbol rate for a full rank linear STBC can be full, i.e., nt, for nt transmit antennas. It has been recently shown that its rate is upper bounded by 1 if a code achieves full diversity with a linear receiver. The intermediate criterion proposed in this paper provides the possibility for codes of rates between nt and 1 that achieve full diversity with the PIC group decoding. This therefore provides a complexity-performance-rate tradeoff. Some design examples are given.

Abstract—In most of the existing space–time code designs, achieving full diversity is based on maximum-likelihood (ML) decoding at the receiver that is usually computationally expensive and may not have soft outputs. Recently, Zhang–Liu–Wong introduced Toeplitz codes and showed that Toeplitz codes achieve full diversity when a linear receiver, zero-forcing (ZF) or minimum mean square error (MMSE) receiver, is used. Motivated from Zhang–Liu–Wong’s results on Toeplitz codes, in this paper, we propose a design criterion for space–time block codes (STBC), in which information symbols and their complex conjugates are linearly embedded, to achieve full diversity when ZF or MMSE receiver is used. The (complex) orthogonal STBC (OSTBC) satisfy the criterion as one may expect. We also show that the symbol rates of STBC under this criterion are upper bounded by 1. Subsequently, we propose a novel family of STBC that satisfy the criterion and thus achieve full diversity with ZF or MMSE receiver. Our newly proposed STBC are constructed by overlapping the 2 2 2 Alamouti code and hence named overlapped Alamouti codes in this paper. The new codes are close to orthogonal and their symbol rates can approach 1 for any number of transmit antennas. Simulation results show that overlapped Alamouti codes significantly outperform Toeplitz codes for all numbers of transmit antennas and also outperform OSTBC when the number of transmit antennas is above 4. Index Terms—Full diversity, linear receivers, multiple-input multiple-output (MIMO) systems, minimum mean square error (MMSE), orthogonal space–time block codes, overlapped Alamouti codes, space–time block codes, Toeplitz codes, zero-forcing (ZF). I.

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Differential space–time modulation (DSTM) has been recently proposed by Hughes, and Hochwald and Sweldens when the channel information is not known at the receiver, where the demodulation is in fact the same as the coherent demodulation of space–time block coding by replacing the channel matrix with the previously received signal matrix. On the other hand, the DSTM also needs a recursive memory of a matrix block at the encoder and therefore provides a trellis structure when the channel information is known at the receiver, which is the interest of this paper. This recursive structure of the DSTM has been adopted lately by Schlegel and Grant in joint with a conventional binary code and joint iterative decoding/demodulation with a superior performance. The number of states of the trellis from the recursive structure depends on both the memory size, which is fixed in this case, and the unitary space–time code (USTC). When a USTC for the DSTM forms a

Abstract — For an nt transmit, nr receive antenna system (nt× nr system), a full-rate space time block code (STBC) transmits min(nt,nr) complex symbols per channel use. In this paper, a scheme to obtain a full-rate STBC for 4 transmit antennas and any nr, with reduced ML-decoding complexity is presented. The weight matrices of the proposed STBC are obtained from the unitary matrix representations of a Clifford Algebra. By puncturing the symbols of the STBC, full rate designs can be obtained for nr < 4. For any value of nr, the proposed design offers the least ML-decoding complexity among known codes. The proposed design is comparable in error performance to the well known Perfect code for 4 transmit antennas while offering lower ML-decoding complexity. Further, when nr < 4, the proposed design has higher ergodic capacity than the punctured Perfect code. Simulation results which corroborate these claims

The aim of this note is to bring to the attention of a wide mathematical audience the recent application of division algebras to wireless communication. The application occurs in the context of communication involving multiple transmit and receive antennas, a context known in engineering as MIMO, short for multiple input, multiple output. While the use of multiple receive antennas goes back to the time of Marconi, the basic theoretical framework for communication using multiple transmit antennas was only published about ten years ago. The progress in the field has been quite rapid, however, and MIMO communication is widely credited with being one of the key emerging areas in telecommunication. Our focus here will be on one aspect of this subject: the formatting of transmit information for optimum reliability. Recall that a division algebra is an (associative) algebra with a multiplicative identity in which every nonzero element is invertible. The center of a division algebra is the set of elements in the algebra that commute with every other element in the algebra; the center is itself just a commutative field, and the division algebra