Decoding Of Space-time Block Codes Research Articles

Low computational complexity methods for decoding of STBC in the uplink of a massive MIMO system

Reducing the computational complexity of the modern wireless communication systems such as massive MIMO configurations is of utmost interest. In this paper, we propose algorithms which can be used to accelerate matrix inversion and reduce the complexity of common spatial multiplexing schemes in massive MIMO systems. Here, we specifically investigate the performance of the proposed methods in systems that utilize STBC (Space-Time Block Code) in the uplink of dynamic massive MIMO systems for different scenarios. A multi-user system in which the base station is equipped with a large number of antennas and each user has two antennas is considered. In addition, users can enter or exit the system dynamically. For a given space-time block coding/decoding scheme, the computational complexity of the receiver will be significantly reduced by employing the proposed methods. The first approach is utilizing Neumann series to approximate the inverse matrix for linear decoders. The second tactic is reducing the computational complexity of the STBC decoders when a user is added to system or removed from it. In the proposed schemes, the matrix inversion for ZF and MMSE decoding is derived from inversing a partitioned matrix and Woodbury matrix identity. Furthermore, the suggested techniques can be utilized when the number of users is fixed but the CSI changes for a particular user. The mathematical equations for both approaches are derived and the complexity of the suggested methods is compared to the direct computation of the inverse matrix. Moreover, the performance of the proposed algorithms is evaluated in terms of the system BER (bit error rate). Evaluations confirm the effectiveness of the proposed approaches.

Efficient Soft Video MIMO Design to Combine Diversity and Spatial Multiplexing Gain

How to strike a balance between diversity gain and spatial multiplexing gain in a soft video delivery system is an open problem. Due to the power limit, it is especially important to achieve the optimal balance during video transmission in the Internet of Things. In this paper, taking the multisimilarity feature of a soft video system into account, we design an adaptive multiple-input, multiple-output (MIMO) receiver that can utilize nearly optimally either diversity gain or multiplexing gain. At the transmitter, we arrange multisimilar video data according to the space-time coding style and transmit them through multiple antennas. At the receiver, we propose using two decoders, i.e., the multisimilar space-time block coding (Ms-STBC) decoder and the soft MIMO decoder. The decoder to be chosen is determined by the predicted performance gain. We show that the proposed Ms-STBC transmission scheme can be considered a joint source-channel design, which is proposed for a soft video multiantenna delivery system. The relationship between intracodewords similarity and the channel signal-to-noise ratio (SNR) gain is derived. The experimental results demonstrate that the proposed designs can achieve a significant improvement over either individual soft MIMO multiplexing decoding or individual space-time block coding decoding in terms of peak SNR (PSNR) under the condition of a time-varying channel and a wide range of SNR. We can obtain at most 4-dB PSNR gain compared with the soft MIMO system.

Compressed sensing image reconstruction by low density parity check codes and soft decoding of space time block codes

To meet the demand of the energy and bandwidth efficient transmission of image/video data in 5G with an improved visual quality at the receiver end, this work suggests an integration of compressed sensing (CS) with low density parity check (LDPC) codes and space time block codes (STBC). An algorithm for soft decision decoding of STBC followed by performance comparison with zero and no-zero entry STBCs is also reported. Upper bounds of error for a CS–LDPC and a CS–STBC system are also developed. The proposed soft decision algorithm gives a bit error rate (BER) of ∼10−3 at around −2 dB for 8 antenna STBC.

Multiple-input multiple-output underwater acoustic communications by using a quasi-orthogonal group space-time architecture

A Quasi-orthogonal Group Space-Time (QoGST) architecture is presented in this paper for better diversity and multiplexing tradeoff gains in Multiple-Input Multiple-Output (MIMO) underwater acoustic (UWA) communications. Both QoGST and Group Layered Space-Time (GLST) are the combination of space-time block coding (STBC) and layered space-time coding. For GLST, the STBC is taken just in each group. For QoGST, however, all groups are encoded together via inter-group STBC, which can effectively suppress the interference between groups with the orthogonal STBC. At the receivers, the STBC decoding is performed and thus we have the higher diversity gains for the group detection. A statistical model of UWA channel which is presented by Milica Stojanovic and contains variations caused by small- and large-scale effects is considered. Simulation results show that the frame error rate (FER) of QoGST is much lower than that of GLST, which means the QoGST has the higher diversity gains. Furthermore, the lower bound diversity and multiplexing tradeoff of QoGST is coincides with that of GLST and the upper bound diversity and multiplexing tradeoff of QoGST is closer to the optimal values.

The nonassociative algebras used to build fast-decodable space-time block codes

Let $K/F$ and $K/L$ be two cyclic Galois field extensions and $D=(K/F,\sigma,c)$ a cyclic algebra. Given an invertible element $d\in D$, we present three families of unital nonassociative algebras over $L\cap F$ defined on the direct sum of $n$ copies of $D$. Two of these families appear either explicitly or implicitly in the designs of fast-decodable space-time block codes in papers by Srinath, Rajan, Markin, Oggier, and the authors. We present conditions for the algebras to be division and propose a construction for fully diverse fast decodable space-time block codes of rate-$m$ for $nm$ transmit and $m$ receive antennas. We present a DMT-optimal rate-3 code for 6 transmit and 3 receive antennas which is fast-decodable, with ML-decoding complexity at most $\mathcal{O}(M^{15})$.

Minimizing the Complexity of Fast Sphere Decoding of STBCs

Decoding of linear space-time block codes (STBCs) with sphere-decoding (SD) is well known. A fast-version of the SD known as fast sphere decoding (FSD) was introduced by Biglieri, Hong and Viterbo. Viewing a linear STBC as a vector space spanned by its defining weight matrices over the real number field, we define a quadratic form (QF), called the Hurwitz-Radon QF (HRQF), on this vector space and give a QF interpretation of the FSD complexity of a linear STBC. It is shown that the FSD complexity is only a function of the weight matrices defining the code and their ordering, and not of the channel realization (even though the equivalent channel when SD is used depends on the channel realization) or the number of receive antennas. It is also shown that the FSD complexity is completely captured into a single matrix obtained from the HRQF. Moreover, for a given set of weight matrices, an algorithm to obtain an optimal ordering of them leading to the least FSD complexity is presented. The well known classes of low FSD complexity codes (multi-group decodable codes, fast decodable codes and fast group decodable codes) are presented in the framework of HRQF.

Efficient FPGA implementation of a STBC-OFDM combiner for an IEEE 802.16 software radio receiver

In this paper, an efficient FPGA implementation of a 4×4 Space-Time Block Coding (STBC) combiner for MIMO-OFDM software radio receivers is considered. The proposed combiner is based on a low-complexity algorithm which reduces the interference due to the Quasi-Orthogonality of the STBC decoding. In the literature, feedback techniques have been proposed to solve this problem. However, the algorithm introduced in this paper has been conceived in order to avoid the transmission feedback, by estimating the interference factors and removing them. The proposed algorithm exhibits a low computational complexity and complies with the requirements of HW feasibility, considering the execution time/area occupation trade-off.

On the Sphere Decoding Complexity of High-Rate Multigroup Decodable STBCs in Asymmetric MIMO Systems

A space-time block code (STBC) is said to be multigroup decodable if the information symbols encoded by it can be partitioned into two or more groups such that each group of symbols can be maximum-likelihood (ML) decoded independently of the other symbol groups. In this paper, we show that the upper triangular matrix R encountered during the sphere decoding of a linear dispersion STBC can be rank-deficient even when the rate of the code is less than the minimum of the number of transmit and receive antennas. We then show that all known families of high-rate (rate greater than 1) multigroup decodable codes have rank-deficient R matrix even when the rate is less than the number of transmit and receive antennas, and this rank-deficiency problem arises only in asymmetric MIMO systems when the number of receive antennas is strictly less than the number of transmit antennas. Unlike the codes with full-rank R matrix, the complexity of the sphere decoding-based ML decoder for STBCs with rank-deficient R matrix is polynomial in the constellation size, and hence is high. We derive the ML sphere decoding complexity of most of the known high-rate multigroup decodable codes, and show that for each code, the complexity is a decreasing function of the number of receive antennas.

Review of Parallel Decoding of Space-time Block Codes toward 4G Wireless and Mobile Communications

This paper presents a review of recent developments in the area of STBC decoding particularly parallel decoding of full-rate full-diversity STBCs toward real-time 4G wireless communications. After reviewing some parallel STBC decoding techniques and presenting one of the most promising types of parallel processors suitable for the 4G SDR the SIMD processor, the paper shows that parallel decoding of the Golden Code on the ClearSpeed CSX700 SIMD processor achieves a speedup of up to 30 times. The paper highlights the potential to achieve real-time decoding of high-rate STBCs with the use of robust parallel processors.

A Novel Construction of Multi-Group Decodable Space-Time Block Codes

Complex Orthogonal Design (COD) codes are known to have the lowest detection complexity among Space-Time Block Codes (STBCs). However, the rate of square COD codes decreases exponentially with the number of transmit antennas. The Quasi-Orthogonal Design (QOD) codes emerged to provide a compromise between rate and complexity as they offer higher rates compared to COD codes at the expense of an increase of decoding complexity through partially relaxing the orthogonality conditions. The QOD codes were then generalized with the so called g-symbol and g-group decodable STBCs where the number of orthogonal groups of symbols is no longer restricted to two as in the QOD case. However, the adopted approach for the construction of such codes is based on sufficient but not necessary conditions which may limit the achievable rates for any number of orthogonal groups. In this paper, we limit ourselves to the case of Unitary Weight (UW)-g-group decodable STBCs for 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sup> transmit antennas where the weight matrices are required to be single thread matrices with non-zero entries ∈{± 1,± j} and address the problem of finding the highest achievable rate for any number of orthogonal groups. This special type of weight matrices guarantees full symbol-wise diversity and subsumes a wide range of existing codes in the literature. We show that in this case an exhaustive search can be applied to find the maximum achievable rates for UW-g-group decodable STBCs with g>;1. For this purpose, we extend our previously proposed approach for constructing UW-2-group decodable STBCs based on necessary and sufficient conditions to the case of UW-g-group decodable STBCs in a recursive manner.

Single-Symbol Maximum Likelihood Decodable STBCs with Fewer Zero-Entries

Two generalized constructions of single-symbol maximum likelihood (ML) decodable space-time block codes (SSDCs), the coordinate interleave orthogonal design (CIOD) and the generalized CIOD (GCIOD), have been proposed by Khan et al. Their main disadvantage is that there are too many zero entries in the codeword matrix. The transmission of these zero-valued symbols causes switching off some of the transmit antennas resulting in a high peak-to-average power ratio and also imposing a severe constraint on hardware implementation of the code. Based on the orthogonal construction of orthogonal space-time block codes and coordinate interleaving, a new generalized construction of SSDCs is proposed. Our proposed codes not only maintain the desirable properties of high rate, full transmit diversity and single-symbol ML decoding similar to CIODs and GCIODs, but also have fewer zero entries in its codeword matrix than CIODs and GCIODs.

New design of single-symbol decodable STBCs for MIMO communication system

Single-symbol maximum-likelihood (ML) decodable space-time block codes (SSDCs) can achieve a maximal symbol rate of 6/7 for multiple-input multiple-output (MIMO) communication system with five or six transmit antennas by using rate-efficient generalized coordinate interleaved orthogonal designs (RE-GCIODs). Unfortunately, there are many zero entries in the codeword matrix of RE-GCIODs. The zero entries result in high peak-to-average power ratio (PAPR) and also impose a severe constraint on hardware implementation. In this paper, for MIMO communication systems with five or six transmit antennas and one receive antenna, a new SSDC is proposed. By combining Alamouti code and orthogonal space-time block code (OSTBC), desirable properties like RE-GCIODs can be achieved and are derived, including maximal symbol rate up to 6/7, full diversity and single-symbol ML decodability. Moreover, by reducing the number of zero entries in the codeword matrix, the peak-to-average power ratio (PAPR) of our proposed code is lower than RE-GCIODs. Simulation results show that the proposed codes outperform RE-GCIODs under peak power constraint while performing almost same under average power constraint.

Collocated and Distributed STBCs with Partial Interference Cancellation Decoding, Part II: Code Construction

In this second part of a two part series of papers, we construct a new class of Space-Time Block Codes (STBCs) for point-to-point MIMO channel and Distributed STBCs (DSTBCs) for the amplify-and-forward relay channel that give full-diversity with Partial Interference Cancellation (PIC) and PIC with Successive Interference Cancellation (PIC-SIC) decoders. The proposed class of STBCs include most of the known full-diversity low complexity PIC/PIC-SIC decodable STBCs as special cases. We also show that a number of known full-diversity PIC/PIC-SIC decodable STBCs that were constructed for the point-to-point MIMO channel can be used as full-diversity PIC/PIC-SIC decodable DSTBCs in relay networks. For the same decoding complexity, the proposed STBCs and DSTBCs achieve higher rates than the known low decoding complexity codes. Simulation results show that the new codes have a better bit error rate performance than the low ML decoding complexity codes available in the literature.

Collocated and Distributed STBCs with Partial Interference Cancellation Decoding, Part I: Full-Diversity Criterion

Low complexity decoders called Partial Interference Cancellation (PIC) and PIC with Successive Interference Cancellation (PIC-SIC), which include the Zero Forcing (ZF) and ZF-SIC receivers as special cases, were given by Guo and Xia along with sufficient conditions for a Space-Time Block Code (STBC) to achieve full diversity with PIC/PIC-SIC decoding for point-to-point MIMO channels. In Part-I of this two part series of papers, we give new conditions for an STBC to achieve full diversity with PIC and PIC-SIC decoders, which are equivalent to Guo and Xia's conditions, but are much easier to check. We then show that PIC and PIC-SIC decoders are capable of achieving the full cooperative diversity available in wireless relay networks and give sufficient conditions for a Distributed Space-Time Block Code (DSTBC) to achieve full diversity with PIC and PIC-SIC decoders. In Part-II, we construct new low complexity full-diversity PIC/PIC-SIC decodable STBCs and DSTBCs that achieve higher rates than the known full-diversity low complexity ML decodable STBCs and DSTBCs.

A new result on turbo coded QO-STBC schemes

In this letter, we present a new result on turbo coded quasi orthogonal space time block coding (QO-STBC) schemes. Proper utilization of soft decision information is one of the important factors affecting the performance of turbo codes. If a space time block coding (STBC) scheme is used with turbo codes, the output of the STBC decoder must be fed into a turbo code decoder as soft decision information. Therefore, the performance of turbo codes depends on how the STBC scheme generates soft decision information from its detection process. In this letter, we investigate the performance of turbo coded QO-STBC schemes, and present the optimum soft decision metrics.

Fast method for precoding and decoding of distributive multi-input multi-output channels in relay-based decode-and-forward cooperative wireless networks

It is well-known that the performance of the relay-based decode-and-forward (DF) cooperative networks outperforms the performance of the amplify-and-forward cooperative networks. However, this performance improvement is accomplished at the expense of adding more signal processing complexity (precoding/decoding) at each relay node. In this study, the authors tackle this signal processing complexity issue by proposing a Jacket-based fast method for reducing the precoding/decoding complexity in terms of time computation. Jacket transforms have shown to find applications in signal processing and coding theory. Jacket transforms are defined to be n×n matrices A=(ajk) over a field ℱ with the property AA†=nIn, where A† is the transpose matrix of the element-wise inverse of A, that is, A†=(akj−1), which generalise Hadamard transforms and centre weighted Hadamard transforms. In particular, exploiting the Jacket transform properties, the authors propose a new eigenvalue decomposition (EVD) method with application in precoding and decoding of distributive multi-input multi-output channels in relay-based DF cooperative wireless networks in which the transmission is based on using single-symbol decodable space-time block codes. The authors show that the proposed Jacket-based method of EVD has significant reduction in its computational time as compared to the conventional-based EVD method. Performance in terms of computational time reduction is evaluated quantitatively through mathematical analysis and numerical results.

Achieving Full Frequency and Space Diversity in Wireless Systems via BICM, OFDM, STBC, and Viterbi Decoding

Orthogonal frequency-division multiplexing (OFDM) is known as an efficient technique to combat frequency-selective channels. In this paper, we show that the combination of bit-interleaved coded modulation (BICM) and OFDM achieves the full frequency diversity offered by a frequency-selective channel with any kind of power delay profile (PDP), conditioned on the minimum Hamming distance dfree of the convolutional code. This system has a simple Viterbi decoder with a modified metric. We then show that by combining such a system with space-time block coding (STBC), one can achieve the full space and frequency diversity of a frequency-selective channel with N transmit and M receive antennas. BICM-STBC-OFDM achieves the maximum diversity order of NML over L-tap frequency-selective channels regardless of the PDP of the channel. This latter system also has a simple Viterbi decoder with a properly modified metric. We verify our analytical results via simulations, including channels employed in the IEEE 802.11 standards

A very low-complexity space-time block decoder (STBD) ASIC for wireless systems

This paper presents a computationally efficient application-specific integrated circuit (ASIC) implementation for the decoding of space-time block codes (STBCs) . Alternative methods of evaluating the originally proposed maximum-likelihood decision metrics are explored at the algorithm and architectural level. At the algorithm level, unique decoding techniques are developed that result in computation savings of as much as 65%. At the architectural level, a low-computation symmetrical approach for the implementation of the proposed algorithm is presented. The proposed ASIC architecture offers considerable computation reductions leading to substantial power and area savings compared to a direct implementation of the original algorithm. The proposed architecture was realized in an ASIC referred to as the ST block decoder ASIC. The chip was fabricated using 0.18-/spl mu/m CMOS technology and occupies a core area of 0.25 mm/sup 2/. The ASIC architecture is highly scalable and can implement 2 /spl times/ 2, 8 /spl times/ 3, and 8 /spl times/ 4 STBCs with modulation formats ranging from binary-phase shift keying (BPSK) to 16 quadrature amplitude modulation (QAM), and can operate at any symbol rate up to 20 Mbaud. Depending on the mode of operation, the decoder power consumption ranges from 0.54 mW for 2 /spl times/ 2 BPSK systems to 1.89 mW for 8 /spl times/ 4 16-QAM systems.

Low-Complexity Decoding of Block Turbo-Coded System with Antenna Diversity

The goal of this paper is to reduce the decoding complexity of space-time block turbo-coded system with low performance degradation. Two block turbo-coded systems with antenna diversity are considered. These include the simple serial concatenation of error control code with space-time block code, and the recently proposed transmit antenna diversity scheme using forward error correction techniques. It is shown that the former performs better when compared to the latter in terms of bit error rate (BER) under the same spectral efficiency (up to 7 dB at the BER of 10-5 for quasistatic channel with two transmit and two receive antennas). For the former system, a computationally efficient decoding approach is proposed for the soft decoding of space-time block code. Compared to its original maximum likelihood decoding algorithm, it can reduce the computation by up to 70% without any performance degradation. Additionally, for the considered outer code block turbo code, through reduction of test patterns scanned in the Chase algorithm and the alternative computation of its extrinsic information during iterative decoding, extra 0.3 dB to 0.4 dB coding gain is obtained if compared with previous approaches with negligible hardware overhead. The overall decoding complexity is approximately ten times less than that of the near-optimum block turbo decoder with coding gain loss of 0.5 dB at the BER of 10-5 over AWGN channel.

Nonlinear space-time block codes designed for iterative decoding

Iterative decoding of space-time block codes (STBCs) and channel codes have shown to achieve very good performance. Using tools such as EXIT charts, the performance can be predicted and also used for design. However almost all work so far has concentrated on linear STBCs. Therefore nonlinear STBCs that are designed to work well with iterative decoding are investigated. It is shown that they can outperform linear STBCs since their characteristics are quite different when supplying a priori information from a channel decoder. Analysis, design rules and simulation results for the nonlinear codes are presented.