On the performance of space-time codes over spatially correlated Rayleigh fading channels

We derive the exact pairwise error probability (PEP) for space-time coding over quasi-static Rayleigh fading channels in the presence of spatial fading correlation. We show that receive correlation always degrades the PEP for all signal-to-noise ratios (SNRs). We quantify the effect of receive correlation by employing the notion of "majorization". We show that the stronger the receive correlation, the worse the PEP for all SNRs. We show that at low SNR, depending on the codes, transmit correlation can either improve or degrade the PEP performance. We show that to guarantee robust performance for arbitrary transmit correlation, the minimum eigenvalue of the codeword pair difference matrix should be maximized among all codeword pairs.     

AWGN和Rayleigh信道下的自适应多级编码系统设计

基于信道容量规则和分组分割,构造自适应于AWGN和Rayleigh两种信道的多级编码系统,为移动信道编码调制系统的设计度量提供参考。提出利用信道状态信息的软判决支路度量计算公式,分析分组分割方案的自适应特性,比较软、硬判决译码对系统性能的影响,结果表明本文提出的自适应系统比未编码系统获得可观的编码增益。     

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。     

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.     

Bandwidth efficient block codes for Rayleigh fading channels

It is shown that the effective code length (ECL) of a short ECL block modulation code (BCM) is the dominant factor in its performance over a Rayleigh fading channel. To demonstrate this, three new BCM codes are presented as examples. Their performances are evaluated and compared on both Gaussian and fading channels.<>     

Concatenated codes for fading channels based on recursive space-time trellis codes

We propose a class of codes which combine the principles of turbo coding and space-time trellis codes. It is first shown that several classes of space-time codes have an equivalent recursive realization. This fact is then exploited to design serial concatenated coding schemes with an outer code, interleaver, and an inner recursive space-time encoder. Two solutions are proposed in this paper - the use of convolutional outer codes aimed mainly to improve the power efficiency and the use of very high-rate outer codes to obtain significant improvement in power efficiency with a marginal decrease in spectral efficiency. We show that single parity check based turbo product codes are a good candidate for very high-rate outer codes. Finally, we propose an automatic repeat request scheme based on recursive realizations of space-time codes and show that the proposed scheme provides significant reduction in frame error rate.     

Improved space-time convolutional codes for quasi-static slow fading channels

Space-time convolutional codes, that provide maximum diversity and coding gain, are produced for cases with PSK modulation and various numbers of states and antennas. The codes are found using a new approach introduced previously in a companion paper. The new approach provides an efficient method that allows a search for optimum codes for many practical problems. The new approach also provides a simple method for augmenting the criteria of maximum diversity and coding gain with a new measure which is shown to be extremely useful for evaluating code performance without extensive simulations. To validate the approach, an extensive set of simulation results are presented comparing the codes designed here to many other previously proposed space-time convolutional codes. The comparisons, given in terms of frame error rate (FER), indicate that our new method provides codes which yield excellent performance. The approach is especially useful for finding a handful of good codes. Selection among these codes can be made with a limited number of simulations for FER.     

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.     

On performance bounds for space-time codes on fading channels

We evaluate truncated union bounds on the frame-error rate (FER) performance of space-time (ST) codes operating over the quasi-static fading channel and compare them with computer simulation results. We consider both ST trellis and block codes. We make the following contributions. For the case of ST trellis codes, we develop a general method, which we denote as measure spectrum analysis, that characterizes ST codeword differences and accommodates the combined influences of the ST code and channel scenario. We propose a numerical bounding method that converges in the measure spectrum to within a very small fraction of a decibel to the simulated FER over the full range of signal-to-noise ratio. In addition, we demonstrate the existence of dominant quasi-static fading error events and detail a method for predicting them. Using only this set of dominant measure spectrum elements, very rapid and tight numerical estimation of FER performance is attained.     

Performance analysis of orthogonal space-time block codes in spatially correlated MIMO Nakagami fading channels

Orthogonal space-time block coding (STBC) is an open-loop transmit diversity scheme that decouples the multiple-input multiple-output (MIMO) channel, thereby reducing the space-time decoding into a scalar detection process. This characteristic of STBC makes it a powerful tool, achieving full diversity over MIMO fading channels, and requiring little computational cost for both the encoding and decoding processes. In this paper, we exploit the single-input single-output equivalency of STBC in order to analyze its performance over nonselective Nakagami fading channels in the presence of spatial fading correlation. More specifically, we derive exact closed-form expressions for the outage probability and ergodic capacity of STBC, when the latter is employed over spatially correlated MIMO Nakagami fading channels. Moreover, we derive the exact symbol error probability of coherent M-PSK and M-QAM, when these modulation schemes are used along with STBC over such fading channels. The derived formulae are then used to assess the robustness of STBC to spatial correlation by considering general MIMO correlation models and analyzing their effects on the outage probability, ergodic capacity, and symbol error probability achieved by STBC.     

Iterative diversity detection for correlated continuous-time Rayleigh fading channels

An antenna array is proposed as a means of achieving a space-diversity effect that partly overcomes the severity of continuous-time Rayleigh fading channels. The investigated channel is assumed to be frequency-nonselective with correlated diversity links, where the correlation is related to the array geometry and the spatial and Doppler dispersions. Further, the error performance is improved by bit interleaving and channel coding, where the encoders/channel is viewed as a serially concatenated system: a convolutional code constitutes the outer code, whereas a differential encoder and the fading channel (having truncated memory) form a joint inner code. In order to obtain a practical detector structure it is desirable to perform iterative decoding by applying some a posteriori probability (APP) algorithms. For this purpose, we propose a novel generalization of the well-known Bahl-Cocke-Jelinek-Raviv (1974) algorithm that calculates the APPs over channels having memory. Numerical results indicate that iterative decoding becomes more powerful when the exploited channel memory depth is extended. Also, the error performance is significantly improved by introducing multiple antennas. The interleaver gain is, however, seen to be quite moderate, in contrast to additive white Gaussian noise channels.     

Decoding of space-time codes for Rayleigh flat fading with arrivaltime differences

Space-time coded systems for Rayleigh flat fading environments are considered, in which the signal arrivals from each transmit antenna to a receive antenna are different. For this situation, a maximum likelihood (ML) decoding algorithm for space-time codes which considers the arrival differences is proposed. The simulation results show that the proposed algorithm considerably outperforms the conventional one     

Generalized principal ratio combining for space-time codes inslowly fading channels

We present a generalized version of principal ratio combining (PRC), which is a near-optimum detection scheme for space-time codes in quasistatic flat fading environments. In Tarokh and Lo (1998), the performance penalty increases as the number of receive antennas increases. In the proposed scheme, receive antennas are optimally grouped by K, and the PRC detection method is applied to each group. This shows a flexible tradeoff between performance and decoding complexity by choosing the appropriate K     

Differential space-time modulation with eigen-beamforming for correlated MIMO fading channels

In this paper, joint differential space-time modulation (DSTM) and eigen-beamforming for correlated multiple-input multiple-output (MIMO) fading channels. While DSTM does not require knowledge of each channel realization, the channel's spatial correlation can be easily estimated without training at the receiver and exploited by the transmitter to enhance the error probability performance. A transmission scheme is developed here that combines beamforming with differential multiantenna modulation based on orthogonal space-time block coding. Error probability is analyzed for both spatially correlated and independent Rayleigh fading channels. Based on the error probability analysis, power loading coefficients are derived to improve performance. The analytical and simulation results presented here corroborate that the proposed scheme can achieve considerable performance gain in correlated channels relative to DSTM without beamforming.     

On CDMA with space-time codes over multipath fading channels

We explore code-division multiple-access systems with multiple transmitter and receiver antennas combined with algebraic constellations over a quasi-static multipath fading channel. We first propose a technique to obtain transmit diversity for a single user over quasi-static fading channels by combining algebraic constellations with full spatial diversity and spreading sequences with good cross-correlation properties. The proposed scheme is then generalized to a multiuser system using the same algebraic constellation and different spreading sequences. We also propose a linear multiuser detector based on the combination of linear decorrelation with respect to all users, and the application of the sphere decoder to decode each user separately. Finally, we consider the generalization to multipath fading channels where the additional diversity advantage due to multipath is exploited by the sphere decoder, and a method of blind channel estimation based on subspace decomposition is examined.     

Pilot-symbol-assisted LDPC coded BICM over correlated Rayleigh fading channels

Pilot-symbol-assisted low-density parity-check (LDPC)-coded bit-interleaved coded modulation (BICM) is analyzed using the density evolution (DE) and the extrinsic information-transfer (EXIT) chart for correlated Rayleigh fading channels. The key parameter (the power correlation coefficient) is identified, and the threshold degradation is quantified. The optimal tradeoff of energy allocation between pilots and coded symbols is found to be sensitive to the normalized Doppler spread of the channel, the interpolation filter, the modulation scheme, and the pilot selection. In addition, a simple upper bound on the performance of any receiver that performs joint iterative decoding and channel estimation is derived. Extension to irregular code design is also discussed.     

Diversity analysis of space-time coding in cascaded Rayleigh fading channels

Cascaded Rayleigh distribution is used to model multipath fading in mobile-to-mobile communication scenarios and provides a better fit to experimental data in such scenarios compared to the conventional Rayleigh channel model. In this letter, we derive an exact expression for the pairwise error probability (PEP) of space-time trellis codes over the cascaded Rayleigh fading channel, which is in the form of a simple single finite-range integral. Through the derived PEP expression, we present the maximum diversity order achievable over such channels and demonstrate the performance degradation in comparison to conventional Rayleigh channels. Monte-Carlo simulations are further demonstrated to confirm the analytical results.     

A trellis-coded DS-CDMA system in correlated Rayleigh fading channels

We present the trellis-coded code-division multiple-access (TC-CDMA) system based on a multisequence signaling, called orthogonal plane sequence modulation (OPSM), in correlated Rayleigh fading channels and derive its pairwise error probability with different degrees of channel state information. Numerical results show that the OPSM-based TC-CDMA system outperforms conventional convolutionally coded CDMA or TC-CDMA systems.