Real-valued maximum likelihood decoder for quasi-orthogonal space-time block codes

In this letter, we propose a low complexity Maximum Likelihood (ML) decoding algorithm for quasi-orthogonal space-time block codes (QOSTBCs) based on the real-valued lattice representation and QR decomposition. We show that for a system with rate r = n_s/T, where n_s is the number of transmitted symbols per T time slots; the proposed algorithm decomposes the original complex-valued system into a parallel system with n_s 2 × 2 real-valued components, thus allowing for a simple joint decoding of two real symbols. For a square QAM constellation with L points (L-QAM), this algorithm achieves full diversity by properly incorporating two-dimensional rotation using the optimal rotation angle and the same rotating matrix for any number of transmit antennas (N ⩾4). We show that the complexity gain becomes greater when N or L becomes larger. The complexity of the proposed algorithm is shown to be linear with the number of transmitted symbols n_s.     

Universally optimum block codes and convolutional codes with maximum likelihood decoding

A new proof is presented for the existence of block codes whose error probability under maximum likelihood decoding is bounded asymptotically by the random coding bound universally over all discrete memoryless channels. On the basis of this result, the existence of convolutional codes with universally optimum performance is shown. Furthermore the existence of block codes which attain the expurgated bound universally over all discrete memoryless channels is proved under the use of maximum likelihood decoding.     

BEM-based SISO detection of orthogonal space-time block codes over frequency flat-fading channels

The expectation-maximization algorithm for maximum a posteriori (MAP) estimation of a random vector is applied to the problem of detection of orthogonal space-time block codes over time-selective Rayleigh fading channels. This results in a soft-in soft-out detection algorithm suitable for iterative detection/decoding schemes. Simulation results show that the error performance of the proposed detection algorithm is very close to that of a MAP detector endowed with an ideal knowledge of the channel state if the fading rate is not too fast.     

Critical point for maximum likelihood decoding of linear block codes

In this letter, the SNR value at which the error performance curve of a soft decision maximum likelihood decoder reaches the slope corresponding to the code minimum distance is determined for a random code. Based on this value, referred to as the critical point, new insight about soft bounded distance decoding of random-like codes (and particularly Reed-Solomon codes) is provided.     

Successive interference cancelation for space-time block codes over time-selective channels

In this letter, we propose a very simple successive interference cancelation (SIC) based signal detector for space-time block codes (STBC) to combat time-selective fading. The main idea is to treat un-detected symbols as noise using a Gaussian approximation. Simulation results show that our scheme can provide performance very close to ML decoding with extremely low computational complexity     

频率选择信道下的空时分组码盲识别

在单接收天线下,针对频率选择性衰落信道下空时分组码( STBC)的盲识别问题,提出了一种基于Kolmogorov-Smirnov( K-S)检测的有效算法。该算法以经验累积分布函数作为特征函数,通过K-S检测经验累积分布函数之间的距离,达到识别空时分组码的目的。在不同调制方式、采样因子和置信区间的条件下分别对算法进行仿真并讨论其性能,结果表明,该算法性能较好,在信噪比大于6 dB时可达到90%以上的正确识别概率,在非合作通信方面具有一定的实用价值。     

空时网格码的正交构造法

空时编码是实现宽带无线数据通信的一种极有潜力的技术。然而，随着发射天线数目的增加，空时码的构造变得十分困难。本文提出了空时网格码的一种构造方法－正交构造法：这种方法可以根据已知的适用于M根发射天线的空时码来构造适用于KM（K≥2）根天线的空时码。仿真结果表明，对于相同的码率和和相近的译码复杂度，用正交构造法得到的空时码的差错性能甚至优于通过计算机搜索得到的空时卷积码。     

基于空时分组编码的差分检测方法

利用正交设计原理提出了通用的差分空时分组码(GDSTBC，general differential space-time block code)。与已有的差分调制方法相比，GDSTBC对信号星图无任何限制，因而可利用幅度和相位同时携带信息提高频谱效率。基于最大似然准则，给出了平坦。Rayleigh衰落信道下的非相干译码器。我们将证明：在高信噪比下，GDSTBC能够以线性复杂度和满天线分集恢复数据符号；在PSK调制方式下，没有信道估计时性能下降3dB；Ganesan基于PSK星图的差分空时分组码、Xia基于APSK星图的差分空时调制技术都可看成GDSTBC的特例。     

Bit-error probability for orthogonal space-time block codes with differential detection

Explicit closed-form expressions of the bit-error probabilities are obtained for space-time block codes based on generalized orthogonal designs with differential encoding and differential detection using 2/sup b/-ary phase-shift keying mapping. The frequency-nonselective, block-wise constant Rayleigh fading channel is considered here. The results are applicable to any number of transmit and receive antennas, where the number of transmit antennas is dictated by the available coding schemes.     

衰落信道空间相关对空时编码性能的影响

在各收发天线间的信道相互独立时,空时编码技术可获得最大分集增益。而在实际环境中,信道之间是彼此相关的,这将在一定程度上影响通信系统的性能。结合差分空时编码方案研究该问题,并以2个发射天线,1个接收天线为例详细推导了空间相关衰落信道条件下,差分检测方案误码率上界的解析表示式。计算机仿真验证了该表示式的有效性。     

Improved approximate maximum-likelihood receiver for differential space-time block codes over Rayleigh-fading channels

In this paper, an approximate maximum-likelihood (ML) receiver for differential space-time block codes is investigated. The receiver is derived from the ML criterion and is shown to mitigate error floor occurring in a conventional differential receiver very well. Because the receiver employs knowledges of signal-to-noise ratio (SNR) and fading rate, we study mismatched cases when these parameters are not accurate. It is shown that the receiver is more sensitive to the mismatched parameters when the fading rate is high. Then, a union bound on the bit error probability is derived. The bounds show good agreement with the simulation results at high fading rate and at high SNR. Finally, a modified receiver, denoted as multistage receiver, is proposed to compensate the so-called intrablock interference caused by the time-varying characteristic of the channel within a transmission block. The multistage receiver offers further reduction of error floor of about half order of magnitude as compared with an approximate ML receiver.     

Robust non-orthogonal space-time block codes over highly correlated channels: a generalisation

Little has so far been reported on the robustness of non-orthogonal space-time block codes (NO-STBCs) over highly correlated channels (HCC). Some of the existing NO-STBCs are indeed weak in robustness against HCC. With a view to overcoming such a limitation, a generalisation of the existing robust NO-STBCs based on a 'matrix Alamouti (MA)' structure is presented.     

Decision feedback detection with error compensation for hybrid space-time block codes

Spatial division multiplexing (SDM) techniques increase the total throughput by transmitting independent information streams through multiple transmit antennas whereas space time coding (STC) techniques utilize diversity gain. Hybrid space-time block code (STBC) schemes proposed combine the above two techniques to maximize the link performance. We propose a decision feedback detection method to improve the performance of the hybrid STBC scheme for orthogonal frequency division multiplexing (OFDM). In this scheme, we take the error propagation effect into account to enhance the detection performance. Simulation results show that the proposed method outperforms the conventional hybrid STBC detection algorithm by more than 3dB at 1% frame error rate for frequency selective fading channels.     

Efficient maximum likelihood decoding of linear block codes using a trellis

It is shown that soft decision maximum likelihood decoding of any(n,k)linear block code overGF(q)can be accomplished using the Viterbi algorithm applied to a trellis with no more thanq^{(n-k)}states. For cyclic codes, the trellis is periodic. When this technique is applied to the decoding of product codes, the number of states in the trellis can be much fewer thanq^{n-k}. For a binary(n,n - 1)single parity check code, the Viterbi algorithm is equivalent to the Wagner decoding algorithm.     

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.     

Multiple-symbol differential detection for MPSK space-time block codes: decision metric and performance analysis

Approximately 3 dB signal-to-noise ratio (SNR) loss is always paid with conventional differential space-time block codes (STBCs), compared with coherent STBCs. In this paper, a multiple-symbol differential detection (MSDD) technique is proposed for M-ary phase-shift keying (PSK) STBCs. The new scheme can greatly narrow the 3-dB performance gap by extending the observation interval for differential decoding. The technique uses maximum-likelihood sequence detection instead of traditional symbol-by-symbol detection, and is carried out on the slow, flat Rayleigh fading channel. A generalized decision metric is derived for an observation interval of arbitrary length. It is shown that for a moderate number of symbols, MSDD provides approximately 1.5 dB performance improvement over conventional differential detection. In addition, a closed-form pairwise error probability and approximate bit-error probability (BEP) are derived for multiple-symbol differential binary PSK STBC. Results show that the theoretical BEP matches simulation results well. The BEP is shown to converge asymptotically with the number of symbols in the observation interval to that of the differential scheme with coherent detection.     

Performance analysis of space-time block codes over keyhole Nakagami-m fading channels

In multiple-input-multiple-output (MIMO) fading environments, degenerate channel phenomena, called keyholes or pinholes, may exist under the realistic assumption that the spatial fading is uncorrelated at the transmitter and the receiver, but the channel has a rank-deficient transfer matrix. In this paper, we analyze the exact average symbol error rate (SER) of orthogonal space-time block codes (STBCs) with M-PSK and M-QAM constellations over Nakagami-m fading channels in the presence of the keyhole. We derive the moment generating function (MGF) of instantaneous signal-to-noise ratio (SNR) after space-time block decoding (signal combining) in such channels. Using a well-known MGF-based analysis approach, we express the average SER of the STBC in the form of single finite-range integrals whose integrand contains only the derived MGF. Numerical results show that the keyhole significantly degrades the SER performance of the STBC from idealistic behaviors in independent identically distributed MIMO channels.     

Double-differential orthogonal space-time block codes for arbitrarily correlated Rayleigh channels with carrier offsets

The presence of carrier offsets in the multiple-input multiple-output (MIMO) channels is an important practical and theoretical problem. Double-differential coding is a technique which allows the receiver to decode the data without any channel or carrier offset knowledge. We propose a double-differential (DD) coding scheme which is applicable to square orthogonal space-time block codes (OSTBC) using M-PSK constellation. The main advantages of our proposed DD coding scheme are: 1) The previously proposed DD codes are applicable only to the specific class of space-time block codes which follow the diagonal unitary group property, whereas our DD coding is applicable to any square OSTBC. 2) We propose a suboptimal decoder which preserves the linear decoding property of the OSTBC. 3) A theoretical analysis is performed to find a pairwise error probability (PEP) upper bound of the proposed doubledifferential orthogonal space-time block codes (DDOSTBC). 4) In order to improve the performance of DDOSTBC over the arbitrarily correlated Rayleigh channels we propose a precoder which minimizes an upper bound of the PEP. The proposed DDOSTBC are able to achieve higher coding gain than the similar rate existing DD coding scheme. In addition, the proposed precoded DDOSTBC achieves performance gain for correlated channels as compared to the unprecoded DDOSTBC.     

Properties of space-time codes for frequency-selective channels

Some important properties are derived for the diversity gain and the coding gain of space-time codes (STCs) for frequency-selective channels. It is proven that the diversity gain of a STC that provides maximum diversity gain for channels with a given number of taps is robust to a decrease in the number of taps. For coding gain analysis, we categorize the possible types of correlation matrices into several classes based on the type of power delay profile, spatial correlation, and tap correlation. It is proven that optimum STCs found for spatially independent and frequency-selective channels with uncorrelated taps and uniform power delay profile have coding gains that are robust against a mismatch in correlation structure if the number of taps is fixed. Thereafter, a systematic design procedure is applied to search for the best space-time trellis codes (STTCs) for frequency-selective channels. At a frame error rate (FER) of 0.01, our example 16-state binary phase-shift keying (BPSK) STTC outperforms the delay diversity code by 3.4 dB for a channel with three uncorrelated uniform taps. Further, the example STC designed for a channel with a given number of taps is shown to provide good performance for channels with fewer taps.     

BER analysis of MPSK space-time block codes with differential detection

Closed-form expressions of the bit error rate (BER) are derived for space-time block codes based on Alamouti's (1998) scheme and utilizing M-ary phase shift keying modulation with noncoherent differential encoding/decoding. The analysis is carried out for the flat block-fading Rayleigh channel, and the BER expression is an approximation for high signal to noise ratio. Theoretical results are validated by simulations for BPSK and QPSK modulations.