Space–Time Block Codes Achieving Full Diversity With Linear Receivers

In most of the existing space–time code designs, achieving full diversity is based on maximum-likelihood (ML) decoding at the receiver that is usually computationally expensive and may not have soft outputs. Recently, Zhang–Liu–Wong introduced Toeplitz codes and showed that Toeplitz codes achieve full diversity when a linear receiver, zero-forcing (ZF) or minimum mean square error (MMSE) receiver, is used. Motivated from Zhang–Liu–Wong's results on Toeplitz codes, in this paper, we propose a design criterion for space–time block codes (STBC), in which information symbols and their complex conjugates are linearly embedded, to achieve full diversity when ZF or MMSE receiver is used. The (complex) orthogonal STBC (OSTBC) satisfy the criterion as one may expect. We also show that the symbol rates of STBC under this criterion are upper bounded by 1. Subsequently, we propose a novel family of STBC that satisfy the criterion and thus achieve full diversity with ZF or MMSE receiver. Our newly proposed STBC are constructed by overlapping the $2,times,2$ Alamouti code and hence named overlapped Alamouti codes in this paper. The new codes are close to orthogonal and their symbol rates can approach 1 for any number of transmit antennas. Simulation results show that overlapped Alamouti codes significantly outperform Toeplitz codes for all numbers of transmit antennas and also outperform OSTBC when the number of transmit antennas is above $4$.      

空时分组编码CDMA系统的性能分析

空时分组编码 ( STBC)可有效的应用于无线系统中 ,提高系统的容量。 STBC采用最大似然译码算法 ,译码过程中需要信道信息。本文利用导频辅助的方式获得信道信息 ,分析了Rayleigh信道下随着移动台速度的变化 STBC- CDMA系统的误码率性能     

Cyclic delay diversity with frequency domain turbo equalization for uplink fast fading channels

Cyclic delay diversity (CDD) is an attractive diversity technique due to its low complexity and compatibility to existing wireless communication systems. This letter proposes a CDD with frequency domain turbo equalization (FDTE) for single carrier (SC) transmission, in order to achieve the full spatial diversity of frequency-selective multi-antenna channels. The frequency diversity inherent in SC is picked up from the increased channel selectivity of CDD. The noise or intersymbol interference enhanced by equalization for highly selective channels is then mitigated through applying FDTE at the receiver. Simulation results show that the performance of proposed system approaches the corresponding orthogonal spacetime block coding (STBC) system in slowly fading channels without any data rate loss, and considerably outperforms the STBC system in fast fading channels.     

Array Processing for Multi-User Multi-Antenna Interference Channels Using Precoders

In this paper, we investigate how to send space-time codes with full diversity and low decoding complexity for interference channels using precoders. We assume that we have two transmitters and two receivers. Each transmitter sends codewords to respective receiver at the same time. We propose an orthogonal transmission scheme that combines space-time codes and array processing to achieve low-complexity decoding and full diversity for transmitted signals. To our best knowledge, this is the first scheme which can achieve low-complexity decoding and full diversity for any transmitted codeword in interference channel when all the users transmit at the same time. Simulation results validate our theoretical analysis.     

Noncoherent space-time coding: An algebraic perspective

The design of space-time signals for noncoherent block-fading channels where the channel state information is not known a priori at the transmitter and the receiver is considered. In particular, a new algebraic formulation for the diversity advantage design criterion is developed. The new criterion encompasses, as a special case, the well-known diversity advantage for unitary space-time signals and, more importantly, applies to arbitrary signaling schemes and arbitrary channel distributions. This criterion is used to establish the optimal diversity-versus-rate tradeoff for training based schemes in block-fading channels. Our results are then specialized to the class of affine space-time signals which allows for a low complexity decoder. Within this class, space-time constellations based on the threaded algebraic space-time (TAST) architecture are considered. These constellations achieve the optimal diversity-versus-rate tradeoff over noncoherent block-fading channels and outperform previously proposed codes in the considered scenarios as demonstrated by the numerical results. Using the analytical and numerical results developed in this paper, nonunitary space-time codes are argued to offer certain advantages in block-fading channels where the appropriate use of coherent space-time codes is shown to offer a very efficient solution to the noncoherent space-time communication paradigm.     

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.     

On the nonexistence of rate-one generalized complex orthogonal designs

Orthogonal space-time block coding proposed recently by Alamouti (1998) and Tarokh et al. (1999) is a promising scheme for information transmission over Rayleigh-fading channels using multiple transmit antennas due to its favorable characteristics of having full transmit diversity and a decoupled maximum-likelihood (ML) decoding algorithm. Tarokh et al. extended the theory of classical orthogonal designs to the theory of generalized, real, or complex, linear processing orthogonal designs and then applied the theory of generalized orthogonal designs to construct space-time block codes (STBC) with the maximum possible diversity order while having a simple decoding algorithm for any given number of transmit and receive antennas. It has been known that the STBC constructed in this way can achieve the maximum possible rate of one for every number of transmit antennas using any arbitrary real constellation and for two transmit antennas using any arbitrary complex constellation. Contrary to this, in this correspondence we prove that there does not exist rate-one STBC from generalized complex linear processing orthogonal designs for more than two transmit antennas using any arbitrary complex constellation.     

Adaptive Channel‐Matched Extended Alamouti Space‐Time Code Exploiting Partial Feedback

Since the publication of Alamouti's famous space‐time block code, various quasi‐orthogonal space‐time block codes (QSTBC) for multi‐input multi‐output (MIMO) fading channels for more than two transmit antennas have been proposed. It has been shown that these codes cannot achieve full diversity at full rate. In this paper, we present a simple feedback scheme for rich scattering (flat Rayleigh fading) MIMO channels that improves the coding gain and diversity of a QSTBC for 2ⁿ (n = 3, 4,…) transmit antennas. The relevant channel state information is sent back from the receiver to the transmitter quantized to one or two bits per code block. In this way, signal transmission with an improved coding gain and diversity near to the maximum diversity order is achieved. Such high diversity can be exploited with either a maximum‐likelihood receiver or low‐complexity zero‐forcing receiver.     

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.     

Analysis of Transmit Antenna Selection/Maximal-Ratio Combining in Rayleigh Fading Channels

In this paper, we investigate a multiple-input-multiple-output (MIMO) scheme combining transmit antenna selection and receiver maximal-ratio combining (the TAS/MRC scheme). In this scheme, a single transmit antenna, which maximizes the total received signal power at the receiver, is selected for uncoded transmission. The closed-form outage probability of the system with transmit antenna selection is presented. The bit error rate (BER) of the TAS/MRC scheme is derived for binary phase-shift keying (BPSK) in flat Rayleigh fading channels. The BER analysis demonstrates that the TAS/MRC scheme can achieve a full diversity order at high signal-to-noise ratios (SNRs), as if all the transmit antennas were used. The average SNR gain of the TAS/MRC is quantified and compared with those of uncoded receiver MRC and space-time block codes (STBCs). The analytical results are verified by simulation. It is shown that the TAS/MRC scheme outperforms some more complex space-time codes of the same spectral efficiency. The cost of the improved performance is a low-rate feedback channel. We also show that channel estimation errors based on pilot symbols have no impact on the diversity order over quasi-static fading channels.     

Performance Analysis of Space-Time Block Codes with Transmit Antenna Selection in Nakagami-m Fading Channels

In this paper, multiple-input multiple-output systems employing space-time block codes (STBCs) with transmit antenna selection (TAS) are examined for flat Nakagami-m fading channels. Exact symbol error rate (SER) expressions for M-ary modulation techniques are derived by using the moment generating function based analysis method. In the SER analysis, the receiver is assumed to use maximal ratio combining whereas a subset of transmit antennas that maximizes the instantaneous received signal-to-noise ratio (SNR) is selected for STBC transmission. The analytical SER results are validated by Monte Carlo simulations. By deriving upper and lower bounds for SER expressions, it is shown that TAS/STBC schemes achieve full diversity orders at high SNRs.     

Code and receiver design for the noncoherent fast-fading channel

This paper deals with the design of coding/modulation and demodulation/decoding schemes for single- or multiple-antenna systems with focus on fast-fading channels, where channel state information (CSI) is not available at the transmitter and the receiver. We explore two possible solutions for this channel with increasing degree of sophistication. The first one utilizes pilots at the transmitter and a simple and explicit noniterative channel estimation algorithm at the receiver. We show that this pilot-assisted system is exactly equivalent, in terms of performance analysis and design, to an appropriately "degraded" system having perfect CSI at the receiver. The second scheme utilizes pilots and a family of well-justified and simple suboptimal iterative detection/estimation algorithms. It is shown that when turbo-like codes are considered in conjunction with this pilot-assisted transmission scheme and the proposed receiver algorithm, the unitary constellations investigated in the literature are inferior to simple pilot-assisted constellations in both complexity and performance. Specific instances of the proposed systems (that use optimized irregular low-density parity-check outer codes) are designed. The design examples provided show that the proposed systems can achieve a good tradeoff between complexity and performance and can be used to bridge the gap between the high complexity/high-performance optimal scheme and low-complexity/mediocre performance noniterative estimation/coherent detection scheme.     

Interference mitigation in uplink STBC MC-CDMA system based on PIC receiver

Multi Carrier Code Division Multiple Access (MC-CDMA) is attractive technique for high speed data transmission in multipath fading channel. MC-CDMA system cannot handle the sudden time variations of the channel which cause the subcarriers to lose their orthogonality. The loss of orthogonality between the subcarriers of a user or unwanted correlation between the spreading codes of different user can lead to increase in Multiple Access Interference (MAI). Space Time Block Code (STBC) based MC-CDMA system is chosen to achieve full diversity and transmission rate without the knowledge of Channel State Information (CSI) at the transmitter. Thus, in the paper STBC is introduced at the transmitter to improve the quality of the receiver. Space Time Block Code-Parallel Interference Cancellation (STBC-PIC) receiver has been proposed for MC-CDMA system. In the proposed STBC-PIC receiver, at each interference cancellation stage, weighted signal of the other user is subtracted from signal of the desired user, thereby reducing the MAI and improving the BER performance. From the simulation results, it is observed that the proposed receiver outperforms STBC-Orthogonal Complete Complementary Code (STBC-OCCC), STBC-Minimum Mean Square Error (STBC-MMSE) and STBC-Zero Forcing (STBC-ZF) receivers for MAI reduction.     

New Combining Scheme in STBC Single Carrier Block Transmission System

A new diversity combining algorithm is presented in this paper with high performance in the STBC single carrier (SC) block transmission MISO system with two transmit antennas and one receive antenna. The decision on the transmitted signal is made by STBC-based SC frequency domain equalizer (STBC-SC-FDE), and then the line of sight (LOS) component under Rician fading channels or the component with highest power under Rayleigh fading channels in the received signal is obtained by cancelling the multipath signals reconstructed by the initial detecting solution and the channel impulse response (CIR) from the received signal. Then, the LOS or the strongest component is combined using STBC-like combining scheme. The new algorithm can achieve the performance advantages dramatically over STBC-SC-FDE which is verified by computer simulations carried out in the SUI-4 and TU wireless communication link.     

Trained Space-Time Block Decoding for Flat Fading Channels with Frequency Offsets

Space-time block coding (STBC) is a recent appealing solution to the problem of exploiting transmit diversity in multi-antenna systems for communications over flat fading channels. In a standard STBC scheme the receiver requires Channel State Information (CSI), which can be acquired via training at the expense of a reduced information rate. Alternatively, the requirement of CSI can be avoided altogether by using differential encoding. The existing trained or differential schemes for STBC assume that the channel is time-invariant during the transmission of at least two data blocks. However, wireless channels may often be time varying owing to frequency offsets induced by either Doppler shifts or carrier frequency mismatches. In this paper we present a simple trained STBC scheme for fading channels with frequency offsets. This revised version was published online in July 2006 with corrections to the Cover Date.     

Distributed differential space-time coding for wireless relay networks

Distributed space-time coding is a cooperative transmission scheme for wireless relay networks. With this scheme, antennas of the distributive relays work as transmit antennas of the sender and generate a space-time code at the receiver. It achieves the maximum diversity. Although the scheme needs no channel information at relays, it does require full channel information, both the channels from the transmitter to relays and the channels from relays to the receiver, at the receiver. In this paper, we propose a differential transmission scheme, which requires channel information at neither relays nor the receiver, for wireless relay networks. As distributed space-time coding can be seen as the counterpart of space-time coding in the network setting, this scheme is the counterpart of differential space-time coding. Compared to coherent distributed space-time coding, the differential scheme is 3dB worse. In addition, we show that Alamouti, square real orthogonal, and Sp(2) codes can be used differentially in networks with corresponding numbers of relays. We also propose distributed differential space-time codes that work for networks with any number of relays using circulant matrices.     

正交空时分组码在OFDM系统中的性能估计

在宽带OFDM系统中对正交空时分组码方案进行了研究,根据Almouti方案的译码原理给出了在正交空时分组码传输的频率选择性衰落信道条件下接收机输出瞬时信噪比的一般表达式,同时分两种情况进一步分析了其最小距离球界的符号差错性能。结果表明,在系统发送天线数、接收天线数及多径数目乘积较小的情形下,系统可以达到最大的分集增益。     

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 Trellis Codes Over Rapid Rayleigh Fading Channels With Channel Estimation---Part I: Receiver Design and Performance Analysis

The performance analysis of space-time trellis codes over rapid nonselective Rayleigh fading channels with imperfect channel state information is considered. A pilot-symbol-assisted-modulation scheme is used for channel estimation. The parameters used in this scheme, i.e., pilot spacing and Wiener filter length are chosen in a tradeoff between estimation accuracy, transmission rate/pilot overhead, and receiver complexity. A simple maximum likelihood receiver for M-ary phase shift keying modulation is derived. An exact closed-form pairwise error probability (PEP) expression and explicit PEP bounds are presented. It is shown that the performance loss caused by channel estimation errors increases mainly with the channel fade rate.     

Limited feedback unitary precoding for orthogonal space-time block codes

Orthogonal space-time block codes (OSTBCs) are a class of easily decoded space-time codes that achieve full diversity order in Rayleigh fading channels. OSTBCs exist only for certain numbers of transmit antennas and do not provide array gain like diversity techniques that exploit transmit channel information. When channel state information is available at the transmitter, though, precoding the space-time codeword can be used to support different numbers of transmit antennas and to improve array gain. Unfortunately, transmitters in many wireless systems have no knowledge about current channel conditions. This motivates limited feedback precoding methods such as channel quantization or antenna subset selection. This paper investigates a limited feedback approach that uses a codebook of precoding matrices known a priori to both the transmitter and receiver. The receiver chooses a matrix from the codebook based on current channel conditions and conveys the optimal codebook matrix to the transmitter over an error-free, zero-delay feedback channel. A criterion for choosing the optimal precoding matrix in the codebook is proposed that relates directly to minimizing the probability of symbol error of the precoded system. Low average distortion codebooks are derived based on the optimal codeword selection criterion. The resulting design is found to relate to the famous applied mathematics problem of subspace packing in the Grassmann manifold. Codebooks designed by this method are proven to provide full diversity order in Rayleigh fading channels. Monte Carlo simulations show that limited feedback precoding performs better than antenna subset selection.