Performance analysis and design of STBCs for frequency-selective fading channels

In this paper, space-time block-coded transmission over frequency-selective fading channels is investigated. A lower bound for the pairwise error probability for optimum detection is given. Also, an approximation for the bit-error rate is derived and compared with simulation results for maximum-likelihood sequence estimation (MLSE) for the GSM/EDGE (Enhanced Data Rates for GSM Evolution) system. Furthermore, a novel design rule for space-time block codes (STBCs) for frequency-selective fading channels is provided. A corresponding code is designed and shown to yield higher performance than Alamouti's code. It is demonstrated that for fading channels with L independent impulse response coefficients, STBCs designed for the flat fading channel can achieve at most a diversity order of (N/sub T/+L-1)N/sub R/ if N/sub T/ transmit antennas and N/sub R/ receive antennas are used. On the other hand, the maximum diversity order employing the proposed code design rule is LN/sub T/N/sub R/.     

Algebraic properties of space-time block codes in intersymbol interference multiple-access channels

In this paper, we study the multiple-access channel where users employ space-time block codes (STBC). The problem is formulated in the context of an intersymbol interference (ISI) multiple-access channel which occurs for transmission over frequency-selective channels. The algebraic structure of the STBC is utilized to design joint interference suppression, equalization, and decoding schemes. Each of the K users transmits using M/sub t/=2 transmit antennas and a time-reversed STBC suitable for frequency-selective channels. We first show that a diversity order of 2M/sub r/(/spl nu/+1) is achievable at full transmission rate for each user, when we have M/sub r/ receive antennas, channel memory of /spl nu/, and an optimal multiuser maximum-likelihood (ML) decoder is used. Due to the decoding complexity of the ML detector we study the algebraic structure of linear multiuser detectors which utilize the properties of the STBC. We do this both in the transform (D-domain) formulation and when we impose finite block-length constraints (matrix formulation). The receiver is designed to utilize the algebraic structure of the codes in order to preserve the block quaternionic structure of the equivalent channel for each user. We also explore some algebraic properties of D-domain quaternionic matrices and of quaternionic circulant block matrices that arise in this study.     

在频率选择性相关信道中的空频分组编码技术

本文提出了频率选择性瑞利衰落信道中的对角空频分组码(DSF)，研究了码的性能。分析表明，在各天线对间的信道相互独立，系统有NT个发射天线，NR个接收天线和信道冲击响应长度是L时，DSF码可实现分集增益NRNTL。此外，相关的发射天线阵列会使DSF码分集增益下降，但是对码的性能影响不大，特别是在较长的多路径信道上。因此，DSF码对于相关的衰落信道显示出优越的鲁棒性能。最终仿真结果证实了本文的分析。     

Transmit antennae space-time block coding for generalized OFDM inthe presence of unknown multipath

Transmit antenna diversity has been exploited to develop high-performance space-time coders and simple maximum-likelihood decoders for transmissions over flat fading channels. Relying on block precoding, this paper develops generalized space-time coded multicarrier transceivers appropriate for wireless propagation over frequency-selective multipath channels. Multicarrier precoding maps the frequency-selective channel into a set of flat fading subchannels, whereas space-time encoding/decoding facilitates equalization and achieves performance gains by exploiting the diversity available with multiple transmit antennas. When channel state information is unknown at the receiver, it is acquired blindly based on a deterministic variant of the constant-modulus algorithm that exploits the structure of space-time block codes. To benchmark performance, the Cramer-Rao bound of the channel estimates is also derived. System performance is evaluated both analytically and with simulations     

Optimal constellation labeling for iteratively decoded bit-interleaved space-time coded Modulation

We consider the design of iteratively decoded bit-interleaved space-time coded modulation (BI-STCM) over fast Rayleigh-fading channels with N/sub t/ transmit and N/sub r/ receive antennas. We propose the design criterion to achieve the largest asymptotic coding gain inherited in the constellation labeling. In particular, for orthogonal space-time block codes, the labeling design criterion reduces to maximizing the (-N/sub t/N/sub r/)th power mean of the complete set of squared Euclidean distances associated with all "error-free feedback" events in the constellation. Based on this power mean criterion, we show that the labeling optimization problem falls into the category of quadratic assignment problems for constellations of any shape and with an arbitrary number of transmit and receive antennas. For a set of practical values of N/sub t/ and N/sub r/, we present optimal labeling maps for 8-PSK, 16-QAM, and 64-QAM constellations.     

On channel orthogonalization using space-time block coding with partial feedback

Orthogonal space-time block codes (OSTBCs) yield full diversity gain even while requiring only a linear receiver. Such full-rate (rate-one) orthogonal designs are available for complex symbol constellations only for N=2 transmit antennas. In this paper, we propose a new family of full-rate space-time block codes (STBCs) using a single parameter feedback for communication over Rayleigh fading channels for N=3,4 transmit antennas and M receive antennas. The proposed rate-one codes achieve full diversity, and the performance is similar to maximum receiver ratio combining. The decoding complexity of these codes are only linear even while performing maximum-likelihood decoding. The partial channel information is a real phase parameter that is a function of all the channel gains, and has a simple closed-form expression for N=3,4. This feedback information enables us to derive (channel) orthogonal designs starting from quasi-orthogonal STBCs. The feedback complexity is significantly lower than conventional closed-loop transmit beamforming. We compare the proposed codes with the open-loop OSTBCs and also with the closed-loop equal gain transmission (EGT) scheme which uses equal power loading on all antennas. Simulated error-rate performances indicate that the proposed channel orthogonalized STBCs significantly outperform the open-loop orthogonal designs, for the same spectral efficiency. Moreover, even with significantly lower feedback and computational complexity, the proposed scheme outperforms the EGT technique for M>N.     

Space-time block-coded multiple access through frequency-selectivefading channels

Mitigation of multipath fading effects and suppression of multiuser interference (MUI) constitute major challenges in the design of wide-band third-generation wireless mobile systems. Space-time (ST) coding offers an effective transmit-antenna diversity technique to combat fading, but most existing ST coding schemes assume flat fading channels that may not be valid for wide-band communications. Single-user ST coded orthogonal frequency-division multiplexing transmissions over frequency-selective channels suffer from finite-impulse response channel nulls (fades). Especially multiuser ST block-coded transmissions through (perhaps unknown) multipath present unique challenges in suppressing not only MUI but also intersymbol/chip interference. In this paper, we design ST multiuser transceivers suitable for coping with frequency-selective multipath channels (downlink or uplink). Relying on symbol blocking and a single-receive antenna, ST block codes are derived and MUI is eliminated without destroying the orthogonality of ST block codes. The system is shown capable of providing transmit diversity while guaranteeing symbol recovery in multiuser environments, regardless of unknown multipath. Unlike existing approaches, the mobile does not need to know the channel of other users. In addition to decoding simplicity, analytic evaluation and corroborating simulations reveal its flexibility and performance merits     

Space-time diversity systems based on linear constellation precoding

We present a unified approach to designing space-time (ST) block codes using linear constellation precoding (LCP). Our designs are based either on parameterizations of unitary matrices, or on algebraic number-theoretic constructions. With an arbitrary number of N/sub t/ transmit- and N/sub r/ receive-antennas, ST-LCP achieves rate 1 symbol/s/Hz and enjoys diversity gain as high as N/sub t/N/sub r/ over (possibly correlated) quasi-static and fast fading channels. As figures of merit, we use diversity and coding gains, as well as mutual information of the underlying multiple-input-multiple-output system. We show that over quadrature-amplitude modulation and pulse-amplitude modulation, our LCP achieves the upper bound on the coding gain of all linear precoders for certain values of N/sub t/ and comes close to this upper bound for other values of N/sub t/, in both correlated and independent fading channels. Compared with existing ST block codes adhering to an orthogonal design (ST-OD), ST-LCP offers not only better performance, but also higher mutual information for N/sub t/>2. For decoding ST-LCP, we adopt the near-optimum sphere-decoding algorithm, as well as reduced-complexity suboptimum alternatives. Although ST-OD codes afford simpler decoding, the tradeoff between performance and rate versus complexity favors the ST-LCP codes when N/sub t/, N/sub r/, or the spectral efficiency of the system increase. Simulations corroborate our theoretical findings.     

Performance analysis of concatenated space-time coding with two transmit antennas

In this paper, we show how Alamouti's simple but useful transmit diversity scheme for two antennas can be combined with a standard outer error-correcting code to achieve a stronger concatenated space-time coding scheme. By introducing a matrix formalism that allows us to interpret the transmission channel as a rotation in an Euclidean space, it can be easily shown that this scheme with two transmit (TX) and L/sub r/ receive (RX) antennas is equivalent to a simple RX antenna setup with 2L/sub r/ RX antennas. Analytical formulas for pair error probabilities will be derived for the time and/or frequency flat fading and for the ideally interleaved Rayleigh fading channel as well as for the correlated fading channel. As a practical example, we study how the performance of a Walsh-Hadamard coded multicarrier code-division multiple-access system depends on the correlation bandwidth of the channel and the number of RX and TX antennas.     

Turbo processing in transmit antenna diversity systems

We consider turbo-trellis-coded transmission over fading multiple-input-multiple-output (M1M0) channels with transmit diversity using space-time block codes. We give a new view on space-time block codes as a transformation of the fading MIMO channel towards a Gaussian single-input-single-output (siso) channel and provide analytical results on the BER of space-time block codes. Furthermore, we describe the concatenation of Turbo-TCM with a space-time block code and show that in addition to the transmit diversity substantial benefits can be obtained by turbo iterations as long as the channel is time-varying during transmission of a coded block or frequency hopping is applied. Finally, a double iterative scheme for turbo equalization and turbo decoding of the concatenation of Turbo-TCM and space-time block code in frequency-selective MIMO channels is described.     

Full-Diversity and Fast ML Decoding Properties of General Orthogonal Space-Time Block Codes for MIMO-OFDM Systems

In this letter we apply the general orthogonal space-time block codes (OSTBC) to MIMO-OFDM systems over frequency-selective fading channels and aim to exploit the potential multipath diversity. By replacing the scalar entry of an OSTBC matrix with the vector of repeated symbols, we obtain a new OSTBC which can achieve both spatial diversity and multipath diversity. Moreover, a fast maximum likelihood (ML) decoding is admitted. Simulation results show that the proposed OSTBC, for two transmit antennas, can obtain a higher diversity gain than the Alamouti code at the same ML decoding complexity     

Multiuser Interference Cancellation and Detection for Users with More Than Two Transmit Antennas

We consider J transmitter units each equipped with N transmit antennas over wireless Rayleigh fading channels. Previously in [1], it was proved that when each transmitter unit has TV transmit antennas, using (J - 1)N + r receive antennas for any r ges 1, the receiver can completely separate the signals of J users. The provided diversity to each user was shown to be Nr if the units employ space-time trellis codes even if the units transmit asynchronously. Here, we consider the case when all units are synchronized and employ quasi-orthogonal space-time block codes (N > 2). It is proved that in this case a receiver with J + r - 1 antennas with r ges 1 can separate the transmitted signals of all units and provide each unit with a diversity order of Nr. Based on our interference cancellation technique, we then offer an array processing scheme which provides trade-off between diversity and spatial multiplexing. It is shown via simulations that this array processing scheme performs better than well-known modulation schemes, e.g. space-time block codes and BLAST, for a moderate number of receive antennas.     

Some results on the sum-rate capacity of MIMO fading broadcast channels

We study the ergodic sum-rate capacity of the fading MIMO broadcast channel which is used to model the downlink of a cellular system with N/sub t/ transmit antennas at the,base and K mobile users each having N/sub r/ receive antennas. Assuming perfect channel state information (CSI) for all users is available at the transmitter and the receivers, we evaluate the sum-rate capacity numerically using the duality between uplink and downlink. Assuming Nt K, we also derive both upper and lower bounds on the sum-rate capacity to study its increase rate due to multi-user diversity. Finally, we compare three transmission schemes which use the single-user-MIMO scheme (SU-MIMO), ranked known interference (RKI) and zero-forcing beamforming (ZFB), respectively, to transmit to a selected set of users in order to approach the sum-rate capacity. We show that both ZFB and RKI outperform SU-MIMO in a cellular downlink scenario. when many mobile users are present.     

High-Rate Full-Diversity Space–Time–Frequency Codes for Broadband MIMO Block-Fading Channels

A systematic design of high-rate full-diversity space-time-frequency (STF) codes is proposed for multiple-input multiple-output frequency-selective block-fading channels. It is shown that the proposed STF codes can achieve rate M_t and full-diversity M_tM_rM_bL, i.e., the product of the number of transmit antennas M_t, receive antennas M_r, fading blocks M_b, and channel taps L. The proposed STF codes are constructed from a layered algebraic design, where each layer of algebraic coded symbols are parsed into different transmit antennas, orthogonal frequency-division multiplexing tones, and fading blocks without rate loss. Simulation results show that the proposed STF codes achieve higher diversity gain in block-fading channels than some typical space-frequency codes     

Diagonal block space-time code design for diversity and coding advantage over flat fading channels

The potential promised by multiple transmit antennas has raised considerable interest in space-time coding for wireless communications. In this paper, we propose a systematic approach for designing space-time trellis codes over flat fading channels with full antenna diversity and good coding advantage. It is suitable for an arbitrary number of transmit antennas with arbitrary signal constellations. The key to this approach is to separate the traditional space-time trellis code design into two parts. It first encodes the information symbols using a one-dimensional (M,1) nonbinary block code, with M being the number of transmit antennas, and then transmits the coded symbols diagonally across the space-time grid. We show that regardless of channel time-selectivity, this new class of space-time codes always achieves a transmit diversity of order M with a minimum number of trellis states and a coding advantage equal to the minimum product distance of the employed block code. Traditional delay diversity codes can be viewed as a special case of this coding scheme in which the repetition block code is employed. To maximize the coding advantage, we introduce an optimal construction of the nonbinary block code for a given modulation scheme. In particular, an efficient suboptimal solution for multilevel phase-shift-keying (PSK) modulation is proposed. Some code examples with 2-6 bits/s/Hz and two to six transmit antennas are provided, and they demonstrate excellent performance via computer simulations. Although it is proposed for flat fading channels, this coding scheme can be easily extended to frequency-selective fading channels.     

Space-time block coding for single-carrier block transmission DS-CDMA downlink

The combination of space-time block coding (STBC) and direct-sequence code-division multiple access (DS-CDMA) has the potential to increase the performance of multiple users in a cellular network. However, if not carefully designed, the resulting transmission scheme suffers from increased multiuser interference (MUI), which dramatically deteriorates the performance. To tackle this MUI problem in the downlink, we combine two specific DS-CDMA and STBC techniques, namely single-carrier block transmission (SCBT) DS-CDMA and time-reversal STBC. The resulting transmission scheme allows for deterministic maximum-likelihood (ML) user separation through low-complexity code-matched filtering, as well as deterministic ML transmit stream separation through linear processing. Moreover, it can achieve maximum diversity gains of N/sub T/N/sub R/(L+1) for every user in the system, irrespective of the system load, where N/sub T/ is the number of transmit antennas, N/sub R/ the number of receive antennas, and L the order of the underlying multipath channels. In addition, it turns out that a low-complexity linear receiver based on frequency-domain equalization comes close to extracting the full diversity in reduced, as well as full load settings. In this perspective, we also develop two (recursive) least squares methods for direct equalizer design. Simulation results demonstrate the outstanding performance of the proposed transceiver compared to competing alternatives.     

Space-time bit-interleaved coded modulation for OFDM systems

Space-time coding techniques significantly improve transmission efficiency in radio channels by using multiple transmit and/or receive antennas and coordination of the signaling over these antennas. Bit-interleaved coded modulation gives good diversity gains with higher order modulation schemes using well-known binary convolutional codes on a single transmit and receive antenna link. By using orthogonal frequency division multiplexing (OFDM), wideband transmission can be achieved over frequency-selective fading radio channels without adaptive equalizers. In this correspondence, we combine these three ideas into a family of flexible space-time coding methods. The pairwise error probability is analyzed based on the correlated fading assumption. Near-optimum iterative decoders are evaluated by means of simulations for slowly varying wireless channels. Theoretical evaluation of the achievable degree of diversity is also presented. Significant performance gains over the wireless local area network (LAN) 802.11a standard system are reported.     

Analysis of Differential Orthogonal Space–Time Block Codes Over Semi-Identical MIMO Fading Channels

We study the performance of differential orthogonal space-time block codes (OSTBC) over independent and semi-identically distributed block Rayleigh fading channels. In this semiidentical fading model, the channel gains from different transmit antennas to a common receive antenna are identically distributed, but the gains associated with different receive antennas are nonidentically distributed. Arbitrary fluctuation rates of the fading processes from one transmission block to another are considered. We first derive the optimal symbol-by-symbol differential detector, and show that the conventional differential detector is suboptimal. We then derive expressions of exact bit-error probabilities (BEPs) for both the optimal and suboptimal detectors. The results are applicable for any number of receive antennas, and any number of transmit antennas for which OSTBCs exist. For two transmit antennas, explicit and closed-form BEP expressions are obtained. For an arbitrary number of transmit antennas, a Chernoff bound on the BEP for the optimal detector is also derived. Our results show that the semi-identical channel statistics degrade the error performance of differential OSTBC, compared with the identical case. Also, the proposed optimal detector substantially outperforms the conventional detector when the channel fluctuates rapidly. But in near-static fading channels, the two detectors have similar performances     

Space-time block coding for wireless communications: performanceresults

We document the performance of space-time block codes, which provide a new paradigm for transmission over Rayleigh fading channels using multiple transmit antennas. Data is encoded using a space-time block code, and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise. Maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection. This uses the orthogonal structure of the space-time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver. We review the encoding and decoding algorithms for various codes and provide simulation results demonstrating their performance. It is shown that using multiple transmit antennas and space-time block coding provides remarkable performance at the expense of almost no extra processing     

The Minimum Decoding Delay of Maximum Rate Complex Orthogonal Space–Time Block Codes

The growing demand for efficient wireless transmissions over fading channels motivated the development of space-time block codes. Space-time block codes built from generalized complex orthogonal designs are particularly attractive because the orthogonality permits a simple decoupled maximum-likelihood decoding algorithm while achieving full transmit diversity. The two main research problems for these complex orthogonal space-time block codes (COSTBCs) have been to determine for any number of antennas the maximum rate and the minimum decoding delay for a maximum rate code. The maximum rate for COSTBCs was determined by Liang in 2003. This paper addresses the second fundamental problem by providing a tight lower bound on the decoding delay for maximum rate codes. It is shown that for a maximum rate COSTBC for 2m - 1 or 2m antennas, a tight lower bound on decoding delay is r = (_m-1 ^2m) . This lower bound on decoding delay is achievable when the number of antennas is congruent to 0, 1, or 3 modulo 4. This paper also derives a tight lower bound on the number of variables required to construct a maximum rate COSTBC for any given number of antennas. Furthermore, it is shown that if a maximum rate COSTBC has a decoding delay of r where r < r les 2r, then r=2r. This is used to provide evidence that when the number of antennas is congruent to 2 modulo 4, the best achievable decoding delay is 2(_m-1 ^2m_).