Robust Non-linear Precoder for Multiuser MISO Systems Based on Delay and Channel Quantization

In multiuser multiple-input single-output (MISO) systems, non-linear precoder is able to achieve the theoretical sum capacity of downlink channel with perfect channel state information (CSI). However, the perfect CSI is not available at the transmitter in practical system, especially in frequency division duplex (FDD) system where the imperfect CSI is the delayed, quantized channel direction information relayed back from the receiver through a dedicated feedback channel. So the performance of conventional non-linear precoder degrades significantly. In this paper, a robust non-linear Tomlinson–Harashima precoding (THP) based on sum mean squared error (SMSE) minimization for the downlink of multiuser MISO FDD systems is proposed. The proposed precoder is robust to the channel uncertainties arising from channel delay and quantization error. Furthermore, an improved non-linear THP with channel magnitude information (CMI) consideration is introduced to compensate the instantaneous CMI shortage at the transmitter. Additionally, the computational complexity of both proposed precoders can be reduced remarkably by Cholesky factorization with symmetric permutation. Simulation results demonstrate the improvement in bit error ratio performance and illustrate the SMSE performance of the proposed algorithms compared with conventional THP with perfect CSI in the literature.     

On the ergodic capacity as a function of the correlation properties in systems with multiple transmit antennas without CSI at the transmitter

In this letter, the impact of correlation of the transmit antennas of a multiple-input single-output (MISO) system, with no channel state information (CSI) at the transmitter and perfect CSI at the receiver is analyzed. We show that the ergodic capacity for the single-user MISO system is Schur-concave with respect to the vector with eigenvalues of the channel covariance matrix, i.e., the more correlation that exists between the transmit antennas, the less is the achievable capacity. Furthermore, the capacity loss for fully correlated transmit antennas in comparison with the uncorrelated case is derived. The results for the ergodic capacity are compared with the impact of correlation on the outage probability. The relationship between correlation properties and outage probability is more complicated than the relationship between the correlation properties and the ergodic capacity. It is shown that the outage probability is Schur-convex in the high signal-to-noise ratio (SNR) regime, and Schur-concave in the low SNR regime.     

Optimal transmission strategies and impact of correlation in multiantenna systems with different types of channel state information

We study the optimal transmission strategy of a multiple-input single-output (MISO) wireless communication link. The receiver has perfect channel state information (CSI), while the transmitter has different types of CSI, i.e., either perfect CSI, or no CSI, or long-term knowledge of the channel covariance matrix. For the case in which the transmitter knows the channel covariance matrix, it was recently shown that the optimal eigenvectors of the transmit covariance matrix correspond with the eigenvectors of the channel covariance matrix. However, the optimal eigenvalues are difficult to compute. We derive a characterization of the optimum power allocation. Furthermore, we apply this result to provide an efficient algorithm which computes the optimum power allocation. In addition to this, we analyze the impact of correlation on the ergodic capacity of the MISO system with different CSI schemes. At first, we justify the belief that equal power allocation is optimal if the transmitter is uninformed and the transmit antennas are correlated. Next, we show that the ergodic capacity with perfect CSI and without CSI at the transmitter is Schur-concave, i.e., the more correlated the transmit antennas are, the less capacity is achievable. In addition, we show that the ergodic capacity with covariance knowledge at the transmitter is Schur-convex with respect to the correlation properties. These results completely characterize the impact of correlation on the ergodic capacity in MISO systems. Furthermore, the capacity loss or gain due to correlation is quantified. For no CSI and perfect CSI at the transmitter, the capacity loss due to correlation is bounded by some small constant, whereas the capacity gain due to correlation grows unbounded with the number of transmit antennas in the case in which transmitter knows the channel covariance matrix. Finally, we illustrate all theoretical results by numerical simulations.     

Variable rate and variable power MQAM system based on bayesian bit error rate and channel estimation techniques

The impact of inaccurate channel state information at the transmitter for a variable rate variable power multilevel quadrature amplitude modulation (VRVP-MQAM) system over a Rayleigh flat-fading channel is investigated. A system model is proposed with rate and power adaptation based on the estimates of instantaneous signal-to-noise ratio (SNR) and bit error rate (BER). A pilot symbol assisted modulation scheme is used for SNR estimation. The BER estimator is derived using a maximum a posteriori approach and a simplified closed-form solution is obtained as a function of only the second order statistical characterization of the channel state imperfection. Based on the proposed system model, rate and power adaptation is derived for the optimization of spectral efficiency subject to an average power constraint and an instantaneous BER requirement. The performance of the VRVP-MQAM system under imperfect channel state information (CSI) is evaluated. We show that the proposed VRVP-MQAM system that employs optimal solutions based on the statistical characterization of CSI imperfection achieves a higher spectral efficiency as compared to an ideal CSI assumption based method.     

Throughput-Optimal Precoding and Rate Allocation for MISO Systems With Noisy Feedback Channels

A throughput metric is considered for a multiple-input single-output (MISO) system with noisy feedback of channel state information (CSI). The goal is to optimize a precoding matrix with a medium-access control layer metric. The problem is a nonlinear multidimensional optimization. Results show that the optimal precoding turns into beamforming when the signal-to-noise ratio (SNR) of CSI feedback is sufficiently large. A necessary condition for the optimality of beamforming under the throughput metric is determined, and the necessary and sufficient condition is numerically found based on the Gauss-Chebyshev Quadrature method. Next, the rate allocation for beamforming and spatial diversity is analyzed. Then, a two-mode transmission scheme is proposed such that the transmitter is engaged in either the beamforming mode or the spatial diversity mode depending on the SNR of the CSI feedback. It is shown that at a fairly high SNR of CSI feedback, the rate allocation needs to be reduced, while at a low SNR of CSI feedback, the allocated rate should be increased. It is shown that when the SNR of CSI feedback is lower than a threshold, there always exists an SNR of the transmitted signal such that the CSI feedback can be viewed as the real CSI solely for the purpose of rate allocation. The result also shows that the throughput of two-mode transmission is almost the same as the throughput of the optimal precoding scheme, even with a low SNR and large feedback delay.     

Novel transmit antenna selection strategy for massive MIMO downlink channel

In this paper, we deal with the problem of acquiring the channel state information (CSI) at the transmitter in large-scale multiple input multiple output (MIMO) systems, so-called massive MIMO systems. Clearly, obtaining CSI plays a central role to provide high system performance. Even though, in frequency-division duplexed systems, acquiring this information requires a prohibitive amount of feedback, since it increases with the number of transmit antenna. In this work, we design an efficient transmit antenna selection strategy aware of the amount of required CSI for a point-to-multipoint transmission in massive MIMO systems. The proposed strategy provides high sum-rate with limited CSI feedback and limited computational complexity. Innovatively, the antenna selection in our strategy is performed in a decentralized fashion successively at the receiving users. Two schemes are proposed in this work to perform the antenna selection at each user. Next, taking into consideration that the large-scale MIMO transmitter suffers from imperfect knowledge of CSI, we design a new performance criterion. Computer simulations validate that, when the CSI is perfectly known, the proposed strategy is able to achieve high performance in terms of system sum-rate while a significant reduction in both CSI feedback overhead and computational complexity is observed. Moreover, assuming imperfect CSI, the new proposed criterion achieves higher performance when the estimation accuracy is low and at high SNR regime.     

Chaos-Coded Modulations Over Rician and Rayleigh Flat Fading Channels

In this brief, we analyze a kind of chaos-coded modulations over both Rician and Rayleigh frequency non-selective uncorrelated fading in the presence of additive white Gaussian noise. We provide bounds both for the case when perfect channel-state information (CSI) is available at the decoder and when there is no CSI. We show that the bounds proposed can be tight enough to give reason of the behavior of these systems in a flat fading channel. We compare the results with a related trellis-coded modulation and show that the degradation in performance can be at least as low as with conventional coded modulation systems.     

多用户MISO干扰信道中的安全协同波束成形

针对多用户多输入单输出(MISO, multiple-input single-output)干扰信道中保密信息泄露问题,提出了理想信道状态信息(CSI, channel state information)下的安全协同波束成形(SCB, secure coordinated beamforming)方案和非理想CSI下的顽健安全协同波束成形(RSCB, robust secure coordinated beamforming)方案。对于理想CSI情况,联合设计最优的协同波束成形向量,最大化最小安全速率。采用半定松弛(SDR, semidefinite relaxation)技术和连续的凸估计(SCA, successive convex approximation)算法得到原始非凸问题的局部最优解。进一步,将该框架扩展到信道向量和信道协方差矩阵存在确定误差的情况,提出的RSCB方案能够最大化最差情况的安全速率。仿真结果验证了所提方案的有效性和顽健性。     

"Turbo DPSK" using soft multiple-symbol differential sphere decoding

Coded interleaved differential M-ary phase-shift keying (M-DPSK) with iterative decoding, the so-called "Turbo DPSK," is known as a power-efficient transmission format. Due to the rotational invariance of DPSK, it particularly enables detection without channel state information (CSI). However, the soft-input soft-output (SISO) component decoder for DPSK is the computational bottleneck if performance close to the ideal case of perfect CSI is desired. In this paper, we take a fresh look at SISO decoding without CSI and apply sphere decoding (SD) to reduce complexity. In particular, we devise a maximum a posteriori probability (MAP) multiple-symbol differential sphere decoder (MSDSD) which efficiently solves the high-dimensional search problem inherent to detection without CSI. Together with a soft-output generation device the MAP-MSDSD algorithm forms a new SISO-MSDSD module for iterative decoding. We analyze the extrinsic information transfer (EXIT) characteristic of the novel module, by means of which we are able to design powerful encoder and decoder structures. For, respectively, the additive white Gaussian noise (AWGN) and the continuously time-varying Rayleigh-fading channel without CSI these designs operate within 1.7-1.9 and 2.3-2.5 dB of channel capacity assuming perfect CSI. These figures compare favorably with results available in the literature, especially for reasonably high data rates of 1-2 bit/channel use. Simulation studies of the average and the maximum complexity required by SISO-MSDSD demonstrate the advantageous performance versus complexity tradeoff of our approach.     

Joint optimization of relay-precoders and decoders with partial channel side information in cooperative networks

We jointly optimize the relay-precoders and decoders with full or partial channel side information (CSI) in a cooperative network. Specifically, three different CSI assumptions are considered: 1) full CSI at the destination terminal and the relay terminals; 2) full CSI at the destination terminal and partial CSI at the relay terminals; 3) partial CSI at the destination terminal and the relay terminals. We show that, under the assumption of full CSI at the destination terminal and the relay terminals, the optimum relay-precoder is the cooperative transmission beamforming and the optimum decoder is a maximum ratio combiner. Under the two partial CSI assumptions, the optimum relay-precoders and decoders work in a fashion of channel selection. It is demonstrated that the proposed optimum relay-precoders and decoders improve the performance considerably     

Analysis of Multiple Antenna Systems With Finite-Rate Channel Information Feedback Over Spatially Correlated Fading Channels

This paper employs a high resolution quantization framework to study the effects of finite-rate quantization of the channel state information (CSI) on the performance of MISO systems over correlated fading channels. The contributions of this paper are twofold. First, as an application of the general distortion analysis, tight lower bounds on the capacity loss of correlated MISO systems due to the finite-rate channel quantization are provided. Closed-form expressions for the capacity loss in high-signal-to-noise ratio (SNR) and low-SNR regimes are also provided, and their analysis reveals that the capacity loss of correlated MISO channels is related to that of i.i.d. fading channels by a simple multiplicative factor which is given by the ratio of the geometric mean to the arithmetic mean of the eigenvalues of the channel covariance matrix. Second, this paper extends the general asymptotic distortion analysis to the important practical problem of suboptimal quantizers resulting from mismatches in the distortion functions, source statistics, and quantization criteria. As a specific application, two types of mismatched MISO CSI quantizers are investigated: quantizers whose codebooks are designed with minimum mean square error (MMSE) criterion but the distortion measure is the ergodic capacity loss (i.e., mismatched design criterion), and quantizers with codebook designed with a mismatched channel covariance matrix (i.e., mismatched statistics). Bounds on the channel capacity loss of the mismatched codebooks are provided and compared to that of the optimal quantizers. Finally, numerical and simulation results are presented and they confirm the tightness of theoretical distortion bounds.     

On the Pairwise Error Probability of Linear Programming Decoding on Independent Rayleigh Flat-Fading Channels

In this paper, we consider the pairwise error probability (PEP) of a linear programming (LP) decoder for a general binary linear code as formulated by Feldman et al. (IEEE Trans. Inf. Theory, Mar. 2005) on an independent (or memoryless) Rayleigh flat-fading channel with coherent detection and perfect channel state information (CSI) at the receiver. Let H be a parity-check matrix of a binary linear code and consider LP decoding based on H. The output of the LP decoder is always a pseudocode-word. We will show that the PEP of decoding to a pseudocodeword w when the all-zero codeword is transmitted on the above-mentioned channel, behaves asymptotically as K(omega) ldr (E_s/N₀)^{-|chi(omega)|}, where chi(omega) is the support set of omega, i.e., the set of nonzero coordinates, E_s/N₀ is the average signal-to-noise ratio (SNR), and K(omega) is a constant independent of the SNR. Note that the support set chi(omega) of omega is a stopping set. Thus, the asymptotic decay rate of the error probability with the average SNR is determined by the size of the smallest nonempty stopping set in the Tanner graph of H. As an example, we analyze the well-known (155,64) Tanner code and present performance curves on the independent Rayleigh flat-fading channel.     

Multiple antenna MMSE based downlink precoding with quantized feedback or channel mismatch

In this paper, we consider the downlink of a multiuser wireless communication system with multiple antennas at the base station and users each with a single receive antenna. It is known that when channel state information (CSI) is available at the transmitter a large performance gain can be achieved. In a system employing time-division duplexing (TDD), CSI can be obtained at the base station if there is reciprocity between the forward and reverse channels. CSI can also be conveyed from the users to the base station via a limited-rate feedback channel in a frequency-division duplexing (FDD) system. In any case, channel estimation errors are inevitable due to the presence of background noise in the estimated signal and due to the finite number of feedback bits used in a limited-rate feedback system model. In this paper, we first consider the general case when partial CSI is available at the transmitter. We derive an MMSE based precoding technique that considers channel estimation errors as an integral part of the system design. Using rate-distortion theory and the generalized Lloyd vector quantization algorithm, we then specialize our results for the more practical limited-rate feedback system model. Compared to previously proposed precoding techniques such as channel inversion and regularized channel inversion, it is shown that the proposed precoding technique significantly improves the average bit error rate (BER) in the system. Furthermore, the performance of the proposed technique is investigated in the high signal-tonoise ratio (SNR) regime, and similar to [1], [2], it is shown that the proposed technique suffers from a ceiling effect that asymptotically limits the system performance.     

On joint source-channel coding for the Wyner-Ziv source and the Gel'fand-Pinsker channel

We consider the problem of lossy joint source-channel coding in a communication system where the encoder has access to channel state information (CSI) and the decoder has access to side information that is correlated to the source. This configuration combines the Wyner-Ziv (1976) model of pure lossy source coding with side information at the decoder and the Shannon/Gel'fand-Pinsker (1958, 1980) model of pure channel coding with CSI at the encoder. We prove a separation theorem for this communication system, which asserts that there is no loss in asymptotic optimality in applying, first, an optimal Wyner-Ziv source code and, then, an optimal Gel'fand-Pinsker channel code. We then derive conditions for the optimality of a symbol-by-symbol (scalar) source-channel code, and demonstrate situations where these conditions are met. Finally, we discuss a few practical applications, including overlaid communication where the model under discussion is useful.     

基于MMSE 信道估计的VRVP-MQAM 方法性能研究

信道估计对于VRVP-MQAM系统的整体性能至关重要,论述了VRVP-MQAM方法在实际应用中遇到的问题,针对假定CSI已知的传统研究方法,该文通过采用MMSE算法进行信道估计,研究了MMSE估计误差对VRVP-MQAM方法的ASE性能影响,并在Rayleigh衰落信道下进行了仿真,仿真结果表明:与信道状态已知(=1)相比,MMSE估计误差(=0.9时)会产生1~3 dB左右的ASE性能差距;当平均SNR为20 dB时,MMSE算法下信道状态的平均频谱效率为0.3 bps/Hz,比理想信道状态的平均频谱效率低。因此,VRVP-MQAM方法的应用将会越来越广泛。     

Design of Optimal Linear Precoder and Decoder for MIMO Channels with Per Antenna Power Constraint and Imperfect CSI

This paper addresses the problem of designing joint optimum precoder and decoder for multiple-input multiple-output communication system. Conventionally, most of the joint precoder and decoder designs are based on the sum power constraint (SPC) at the transmitter and perfect channel state information (CSI). However, in practice, per-antenna power constraint is more realistic as the power at each transmit antenna is limited individually by the linearity of the power amplifier. Further, the estimate of CSI cannot be obtained perfectly by any methods. Under imperfect CSI, the aim is to design jointly optimum precoder and decoder subject to a power constraint that jointly meets both per-antenna and SPCs. The objective function is formulated into an optimization problem that minimizes the mean square error in estimating the transmitted signal. The simulation results show that the proposed scheme has a near-optimum performance under practical constraints.     

Turbo codes for image transmission-a joint channel and sourcedecoding approach

This paper studies an application of turbo codes to compressed image/video transmission and presents an approach to improving error control performance through joint channel and source decoding (JCSD). The proposed approach to JCSD includes error-free source information feedback, error-detected source information feedback, and the use of channel soft values (CSV) for source signal postprocessing. These feedback schemes are based on a modification of the extrinsic information passed between the constituent maximum a posteriori probability (MAP) decoders in a turbo decoder. The modification is made according to the source information obtained from the source signal processor. The CSVs are considered as reliability information on the hard decisions and are further used for error recovery in the reconstructed signals. Applications of this joint decoding technique to different visual source coding schemes, such as spatial vector quantization, JPEG coding, and MPEG coding, are examined. Experimental results show that up to 0.6 dB of channel SNR reduction can be achieved by the joint decoder without increasing computational cost for various channel coding rates     

SNR mismatch and online estimation in turbo decoding

Iterative decoding of turbo codes, as well as other concatenated coding schemes of similar nature, requires knowledge of the signal-to-noise ratio (SNR) of the channel so that proper blending of the a posteriori information of the separate decoders is achieved. We study the sensitivity of decoder performance to misestimation of the SNR, and propose a simple online scheme that estimates the unknown SNR from each code block, prior to decoding. We show that this scheme is sufficiently adequate in accuracy to not appreciably degrade the performance     

Multiple-Antenna Signaling Over Fading Channels With Estimated Channel State Information: Performance Analysis

Multiple-antenna concepts for wireless communication systems promise high spectral efficiency and low error rates by proper exploitation of the randomness in multipath propagation. In this paper, we investigate the impact of channel uncertainty caused by channel estimation errors on the error rate performance. We consider a training-based multiple-antenna system that reserves a portion of time to sound the channel. Training symbols are used to estimate the channel by means of an arbitrary linear filter at the receiver. No channel state information (CSI) is assumed at the transmitter. We present a new framework to analyze training-based multiple-antenna systems by introducing an equivalent system model that specifies the channel by the estimated (and hence, known) channel coefficients and an uncorrelated, data-dependent, multiplicative noise. We derive the maximum-likelihood (ML) detector and highlight its behavior in the limiting cases of perfect CSI and no CSI, and its relation to several mismatched detectors. We deduce new exact expressions and Chernoff bounds of the pairwise error probability (PEP) used to assess word-error and bit-error rate bounds for ML and mismatched detection. Finally, we review the code design guidelines in terms of the deleterious effect of channel uncertainty for coherent and noncoherent signaling schemes, and present numerical results.     

Multiuser adaptive transmission technique for time-varying frequency-selective fading channels

This paper proposes an efficient multiuser adaptive modulation and coding (AMC) scheme that considers inevitable feedback delay by employing short-term and long-term channel state information (CSI) in time-varying frequency-selective fading channels. By taking the statistic of the true signal-to-noise ratio (SNR) at a given predicted SNR value into account, the required transmit power to meet the target packet-error-rate (PER) can be obtained and used for user selection, power allocation, and modulation and coding set (MCS) selection. In addition, a simple and useful approximation method of obtaining the required transmit power is proposed. The performance of the proposed scheme is shown to be much better than that of conventional schemes without considering the feedback delay or the prediction error. The proposed scheme can also reduce the feedback resource while maintaining the system throughput by allocating different feedback resources to different users according to their prediction error variances.