High-Rate, Single-Symbol ML Decodable Precoded DSTBCs for Cooperative Networks

Space-time block codes from orthogonal designs proposed by Alamouti (1998), and Tarokh-Jafarkhani-Calderbank (199) have attracted much attention lately due to their fast maximum-likelihood (ML) decoding and full diversity. However, the maximum symbol transmission rate of a space-time block code from complex orthogonal designs for complex constellations is only 3/4 for three and four transmit antennas. Jafarkhani (see IEEE Trans. Commun., vol.49, no.1, p.1-4, 2001), and Tirkkonen-Boariu-Hottinen (see ISSSTA 2000, pp.429-432, September 2000) proposed space-time block codes from quasi-orthogonal designs, where the orthogonality is relaxed to provide higher symbol transmission rates. With the quasi-orthogonal structure, these codes still have a fast ML decoding, but do not have the full diversity. In this paper, we design quasi-orthogonal space-time block codes with full diversity by properly choosing the signal constellations. In particular, we propose that half symbols in a quasi-orthogonal design are from a signal constellation A and another half of them are optimal selections from the rotated constellation e/sup j/spl phi// A. The optimal rotation angles /spl phi/ are obtained for some commonly used signal constellations. The resulting codes have both full diversity and fast ML decoding.

Space-time block codes from orthogonal designs proposed by Alamouti, and Tarokh-Jafarkhani-Calderbank have attracted much attention lately due to their fast maximum-likelihood (ML) decoding and full diversity. However, the maximum symbol transmission rate of a space-time block code from complex orthogonal designs for complex constellations is only 3/4 for three and four transmit antennas. Recently, Jafarkhani,and Tirkkonen-Boariu-Hottinen proposed space-time block codes from quasi-orthogonal designs, where the orthogonality is relaxed to provide higher symbol transmission rates. With the quasi-orthogonal structure, these codes still have a fast ML decodng algorithm, but do not have the full diversity. The performance of these codes is better than that of the codes from orthogonal designs at low SNR, but worse at high SNR. This is due to the fact that the slope of the BER-SNR curve depends on the diversity. In this paper, we design quasi-orthogonal space-time block codes with full diversity by properly choosing the signal constellations. In particular, we propose that half of the symbols in a quasi-orthogonal design are from a signal constellation Α and another half of them are optimal selections from the rotated constellation ejφΑ . The optimal rotation angles φ are obtained for some commonly used signal contellations. The resulting codes have both full diversity and fast ML decoding. Simulation results show that the proposed codes outperform the codes from orthogonal designs at both low and high SNRs.© (2002) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Receiver complexity is an important performance metric in space time block coding (STBC). After comprehensive study and analysis of STBCs over complex domain, quaternion orthogonal designs (QODs) have been explored that can provide less decoder complexity. However, some researchers argue that existing maximum likelihood (ML) decoding rule for QODs does not yield optimal performance for quasi-orthogonal STBC-based QODs and, therefore, the design of optimal decoder for such designs remains a big challenge of this field. To counter this observation, we modify the system model slightly. In addition to this, we present a new generalized QOD construction that can generate QODs for any number of transmit antennas. These codes are quasi-orthogonal in complex domain and provide code rates higher than their respective complex orthogonal designs (CODs). We show that the proposed ML decoder provides optimal linear decoupled decoding solution for these codes because of their distinctive construction. Simulation results verify the optimal performance of the ML decoder for the proposed codes and also show that the diversity of the proposed quaternion-based codes is same as CODs, however, they provide better code rates.

It is well known that the performance of the wireless communication systems can be enhanced by using multiple transmit and receive antennas, which is generally referred to as the MIMO technique, and has been incorporated into the IEEE 802.11n standard, i.e. one of the Wi-Fi systems. The MIMO technique has also been adopted by the 3GPP Long Term Evolution (LTE) and the 3GPP2 Ultra Mobile Broadband (UMB) standards. The space-time coding is a promising way to realize the gain in the wireless communications system using MIMO. The space time block code, and the orthogonal space time block code in particular have been proposed in research and implemented in practical wireless communication systems due to their low computational complexity in maximum likelihood decoding implementation. However, the code rates of the orthogonal space time block codes are usually lower than $3/4$ when the number of transmit antennas is greater than two, which limit their throughput. To increase the code rate and the throughput of the orthogonal space time block code for more than two transmit antennas, a family of new space-time block codes (STBC) for 3 and 4 transmit antennas in a MIMO wireless communication system have been proposed in this Ph.D. research. These new codes are orthogonal and achieve full diversity, full rate using Triple QPSK'' modulation, which is proposed in this research. We investigated the performance of these STBCs when the channel state information (CSI) is perfectly known at the receiver. The CSI is not known to the transmitter in all of the studies in this dissertation. An analytical bound of the probability of bit error is developed and the Monte Carlo simulation is used when investigating these new STBC codes. In practical wireless communication system, the CSI is generally not available at the receiver and it is usually estimated by the receiver through the pilot signals or training signals known to the receiver. No matter what channel estimation method is used, the estimate of CSI will not match the CSI exactly and is noisy. The performance of these new STBCs using theTriple QPSK'' modulation when the estimate of the CSI is employed to detect the symbol is investigated in this dissertation. An upper bound of the bit error probability is developed when the noisy CSI is used to detect the symbols. The performance of the new STBCs using the Triple QPSK'' modulation is also evaluated using Monte Carlo simulation. When the CSI is not available to either the receiver or the transmitter, the differential encoding and decoding algorithm is applied to these new STBCs, which use theTriple QPSK'' modulation. The results showed that these orthogonal STBCs achieve full diversity full rate using ""Triple-QPSK"" modulation with differential detection. This provides a means of achieving space diversity and multiplexing gain without the CSI. A new differential encoding and decoding algorithm is proposed and analyzed for STBCs with 3 transmit antennas, whose transmission matrix is not square matrix, as part of this Ph.D. research. The STBCs using this algorithm achieve full diversity the MIMO system can possibly provide.

In this letter we examine the application of space-time block codes (STBC) to offset QPSK (OQPSK). We present the maximum-likelihood (ML) decoder for STBC-OQPSK as well as a simplified decoder. We show through analysis and simulation that the simplified decoder matches the performance of the ML decoder.

The maximum-likelihood (ML) decoder is derived for diagonal unitary space-time block code (STBC) matrices based double-differential modulation for multiple-input multiple-output systems. The ML decoder is obtained on the basis of maximising the joint probability density function of three consecutively received data matrices.

We consider an asynchronous cooperative communication system where two distributed transmitters are communicating with one destination. In this paper, a bounded delay-tolerant time interleave reversal Alamouti code (BDT-TIR AC) is proposed. BDT-TIR AC achieves full diversity, given that the path delay difference is within a tolerance limit. Furthermore, we design an efficient maximum-likelihood (ML) decoder. By employing a divide-and-conquer strategy, the original decoding problem is decoupled into several sub-problems in small size. In fact, these sub-problems contain either Alamouti code structure or only four symbols. By parallel decoding on the sub-problems, the proposed ML decoder exhibits low complexity advantage in large scale problems. Simulations of BDT-TIR AC confirm the full diversity gain. The bit error rate performance of BDT-TIR AC in the considered asynchronous scenarios is comparable with that of synchronized Alamouti code, and outperforms the latest delay-tolerant space-time code.

We consider an asynchronous two-way relay network, in which two double-antenna relays assist in the communication between two single-antenna terminals through analog network coding. The asynchronous transmission between relays and terminals causes symbol misalignments and results in diversity loss in space-time block code (STBC). We propose a zero-padded time-reversal quasi-orthogonal STBC that can achieve full diversity with low-complexity maximum likelihood (ML) decoding, given a bounded delay. With ML decoding, the proposed code is decomposed into several independent parts, which leads to single complex symbol decoding. Proof of full diversity is established, and the decoding complexity order is analyzed for the proposed design. Simulations confirm the full diversity gain. The bit error rate performance in asynchronous scenarios is almost the same as that in synchronous scenarios.

We consider an asynchronous two-way relay network in which a few distributed relays assist in the communication between two single-antenna terminals through analog network coding. The asynchronous transmission between relays and terminals causes symbol misalignments and results in diversity loss in space–time codes (STCs). We propose a family of zero-padded time-reversal STC that can achieve full diversity with low-complexity maximum likelihood (ML) decoding, given a bound for the path delay difference. With ML decoding, the proposed code is decomposed into several independent parts, which greatly facilitate the decoding process. For two-relay scenarios, three code designs based on Alamouti code, quasi-orthogonal space–time block code, and multigroup decodable STC are provided for each relay with one, two, and four antennas, respectively. For three-relay scenarios, one code design based on quasi-orthogonal space-time block code is provided for each relay with one antenna. Proof of full diversity is established, and the decoding complexity order is analyzed for all four designs. Simulations confirm the full diversity gain of all designs. The bit-error-rate performance in asynchronous scenarios is almost similar to that in synchronous scenarios.

Orthogonal space-time block codes (OSTBCs) have several desirable properties for delay limited communication over a coherent narrowband (/sub at/) fading multiple antenna channel. In particular, they provide full diversity, and maximum likelihood detection can be achieved via linear processing and symbol-by-symbol detection. As a result, the maximal symbol rate and minimal latencies of OSTBCs have been well studied. In this paper, we construct orthogonal block codes for frequency-selective multiple antenna channels, and study their symbol rate and latency properties. Our code construction is based on direct application of the orthogonality constraints. This enables us to show that the maximum symbol rate of an orthogonal block code for a channel with memory length L is 1/L times the maximum rate of an OSTBC for the same antenna configuration. Orthogonal codes that achieve this maximal rate can be simply constructed via the Kronecker product of a rate maximal OSTBC with an identity matrix of size L. This Kronecker design scheme can also be applied to construct orthogonal block codes for frequency-selective channels with other desirable properties, such as minimal latency.

Fast Maximum Likelihood Decodable Space-Time Block Codes (STBCs) have recently gained a lot of interest for use in wireless communication systems. Several strategies have been introduced in the literature to build such codes, among them we mention the conditional detection strategy, where the code matrix can be expressed as the sum of two Orthogonal STBCs by means of a unitary matrix. Thus, the decoder benefits from the orthogonality by estimating an orthogonal set of symbols assuming knowledge of the other set of symbols. Even if this strategy permits high rates, numerical optimization of the coding gain becomes unrealizable for high-order constellations. Another strategy has been proposed in the literature, the g-group decodable codes, where the minimization of the Maximum Likelihood (ML) metric can be made over several independent subsets of symbols. Moreover, the g-group decodability strategy enables us to optimize the coding gain for each subset of symbols separately which permits the optimization of the coding gain for high-order constellations. On the other hand, the rate of g-group decodable codes is limited. In this paper, we reformulate the problem of finding Unitary Weight (UW)-2-group decodable codes in a simpler way based on necessary and sufficient conditions. Then, a simple routine is used to search for the desired code. We determine the maximum achievable rate for a specified type of weight matrices.

Irregular LDPC codes can achieve better error rate performance than regular LDPC codes. However, irregular LDPC codes have higher error floors than regular LDPC codes. The Ordered Statistic Decoding (OSD) algorithm achieves approximate Maximum Likelihood (ML) decoding. ML decoding is effective to lower error floors. However, the OSD estimates satisfy the parity check equation of the LDPC code even the estimates are wrong. Hybrid decoder combining LLR-BP decoding algorithm and the OSD algorithm cannot also lower error floors, because wrong estimates also satisfy the LDPC parity check equation. We proposed the concatenated code constructed with an inner irregular LDPC code and an outer Cyclic Redundancy Check (CRC). Owing to CRC, we can detect wrong codewords from OSD estimates. Our CRC-LDPC code with hybrid decoder can lower error floors in an AWGN channel. In wireless communications, we cannot neglect the effects of the channel. The OSD algorithm needs the ordering of each bit based on the reliability. The Channel State Information (CSI) is used for deciding reliability of each bit. In this paper, we evaluate the Block Error Rate (BLER) of the CRC-LDPC code with hybrid decoder in a fast fading channel with perfect and imperfect CSIs where 'imperfect CSI' means that the distribution of channel and those statistical average of the fading amplitudes are known at the receiver. By computer simulation, we show that the CRC-LDPC code with hybrid decoder can lower error floors than the conventional LDPC code with hybrid decoder in the fast fading channel with perfect and imperfect CSIs. We also show that combining error detection with the OSD algorithm is effective not only for lowering the error floor but also for reducing computational complexity of the OSD algorithm.

Large MIMO systems with tens of antennas in each communication terminal using full-rate non-orthogonal space- time block codes (STBC) from cyclic division algebras (CDA) can achieve the benefits of both transmit diversity as well as high spectral efficiencies. Maximum-likelihood (ML) or near-ML decoding of these large-sized STBCs at low complexities, however, has been a challenge. In this paper, we establish that near-ML decoding of these large STBCs is possible at practically affordable low complexities. We show that the likelihood ascent search (LAS) detector, reported earlier by us for V-BLAST, is able to achieve near-ML uncoded BER performance in decoding a 32 times 32 STBC from CDA, which employs 32 transmit antennas and sends 32 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> = 1024 complex data symbols in 32 time slots in one STBC matrix (i.e., 32 data symbols sent per channel use). In terms of coded BER, with a 16 times 16 STBC, rate-3/4 turbo code and 4-QAM (i.e., 24 bps/Hz), the LAS detector performs close to within just about 4 dB from the theoretical MIMO capacity. Our results further show that, with LAS detection, information lossless (ILL) STBCs perform almost as good as full-diversity ILL (FD-ILL) STBCs. Such low-complexity detectors can potentially enable implementation of high spectral efficiency large MIMO systems that could be considered in wireless standards.

In this paper, we propose a near maximum likelihood (ML) decoding technique, which reduces the computational complexity of the exact ML decoding algorithm. The computations needed for the tree search in the ML decoding is simplified by reducing the dimension of the search space prior to the tree search. In order to compensate performance loss due to the dimension reduction, a list stack algorithm (LSA) is considered, which produces a list of the top K closest points. The combination of both approaches, called reduced dimension list stack algorithm (RD-LSA), is shown to provide flexibility and offers a performance-complexity trade-off. Simulations performed for V-BLAST transmission demonstrate that significant complexity reduction can be achieved compared to the sphere decoding algorithm (SDA) while keeping the performance loss below an acceptable level.

We study the maximum a posteriori (MAP) decoding of memoryless non-uniform sources over multiple-antenna channels. Our model is general enough to include space-time coding, BLAST architectures, and single-transmit multi-receive antenna systems which employ any type of channel coding. We derive a closed-form expression for the codeword pairwise error probability (PEP) of general multi-antenna codes using moment generating function and Laplace transform arguments. We then consider space-time orthogonal block (STOB) coding and prove that, similar to the maximum likelihood (ML) decoding case, detection of symbols is decoupled in MAP decoding. We also derive the symbol PEP in closed-form for STOB codes. We apply these results in several scenarios. First, we design a binary antipodal signaling scheme which minimizes the system bit error rate (BER) under STOB coding. At a BER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> , this constellation has a channel signal-to-noise ratio (CSNR) gain of 4.7 dB over conventional BPSK signaling for a binary nonuniform source with p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> Delta <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">=</sub> P(0) = 0.9. We next design space-time linear dispersion (LD) codes which are optimized for the source distribution under the criterion of minimizing the union upper bound on the frame error rate (FER). Two codes are given here: one outperforms V-BLAST by 3.5 dB and Alamouti's code by 12.3 dB at an FER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> for a binary source with p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> = 0.9, and the other outperforms V-BLAST by 4.2 dB at an FER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> for a uniform source. These codes also outperform the LD codes of constructed under a different criteria. Finally, the problem of bit-to-signal mapping is studied. It is shown that for a binary source with p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> = 0.9, 64-QAM signaling, and SER = 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> , a gain of 3.7 dB can be achieved using a better-than-Gray mapping. For a system with one transmit and two receive antennas that uses trellis coding with 16-QAM signaling, a 1.8 dB gain over quasi-Gray mapping and ML decoding is observed when MAP decoding is used for binary sources with p <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> = 0.9.