基于有限反馈的MIMO系统鲁棒性均匀信道分解

 在MIMO系统中,当假设发送端和接收端已知完美信道状态信息的情况下,均匀信道分解(UCD)被证明在误码率性能上是最优的且是容量无损的.然而在实际系统中,接收端或发送端获得的信道信息通常存在着一定的估计误差.本文提出一种基于有限反馈的鲁棒性均匀信道分解方案,在设计方案中充分考虑了信道估计误差的影响,并利用香农率失真定理和广义Lloyd矢量量化算法(GLA)得到了信道估计误差的近似值,使得本文提出的方案有很好的实用性.仿真结果表明与传统均匀信道分解方案相比,本文提出的鲁棒性均匀信道分解方案有效地降低了系统的误码平层,提高了系统容量.     

Practical robust uniform channel decomposition scheme for CSI mismatch in limited feedback MIMO systems

Uniform channel decomposition (UCD) has been proven to be optimal in bit error rate (BER) performance and strictly capacity lossless when perfect channel state information (CSI) is assumed to be available at both the transmitter and receiver side. In practice, CSI can be obtained by channel estimation at receiver and conveyed to transmitter via a limited-rate feedback channel. In such case, the implementation of traditional UCD by treating the imperfect CSI as perfect CSI cause significant performance degradation due to inevitable channel estimation error and vector quantization error. To overcome this problem, a practical robust UCD scheme was proposed in this paper, which includes two steps, firstly, a matching architecture was proposed to eliminate the mismatch between CSI at receiver (CSIR) and CSI at transmitter (CSIT), secondly, an MMSE based robust UCD scheme considering channel estimation error and vector quantization error as an integral part of the design was derived. Simulation results show that the proposed practical robust UCD scheme is capable of improving the BER performance greatly in the context of channel estimation error and vector quantization error compared with the traditional UCD scheme.     

Uniform channel decomposition for MIMO communications

Assuming the availability of the channel state information at the transmitter (CSIT) and receiver (CSIR), we consider the joint optimal transceiver design for multi-input multi-output (MIMO) communication systems. Using the geometric mean decomposition (GMD), we propose a transceiver design that can decompose, in a strictly capacity lossless manner, a MIMO channel into multiple subchannels with identical capacities. This uniform channel decomposition (UCD) scheme has two implementation forms. One is the combination of a linear precoder and a minimum mean-squared-error VBLAST (MMSE-VBLAST) detector, which is referred to as UCD-VBLAST, and the other includes a dirty paper (DP) precoder and a linear equalizer followed by a DP decoder, which we refer to as UCD-DP. The UCD scheme can provide much convenience for the modulation/demodulation and coding/decoding procedures due to obviating the need for bit allocation. We also show that UCD can achieve the maximal diversity gain. The simulation results show that the UCD scheme exhibits excellent performance, even without the use of any error correcting codes.     

Robust hybrid beamforming design for millimeter-wave massive MIMO systems

Hybrid analog-digital beamforming is recognized as a promising solution for a practical implementation of massive multiple-input multiple-output(MIMO) systems based on millimeter-wave(mmWave) technology. In view of the overwhelming hardware cost and excessive power consumption and the imperfection of the channel state information(CSI), a robust hybrid beamforming design is proposed for the mmWave massive MIMO systems, where the robustness is defined with respect to imperfect knowledge or error of the CSI at the transmitter due to limited feedback and/or imperfect channel estimation. Assuming the errors of the CSI are bounded, the optimal hybrid beamforming design with robustness is formulated to a mean squared error(MSE) minimization problem. An iterative semidefinite programming(SDP) based algorithm is proposed to obtain the beamforming matrices. Simulation results show that the proposed robust design can provide more than 4 dB performance gain compared to that of non-robust design.     

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.     

Exact BER analysis for M-QAM modulation with transmit beamforming under channel prediction errors

Significant throughput improvements can be obtained in multiple-inputmultiple-output (MIMO) fading channels by merging beamforming at the transmitter and maximal ratio combining (MRC) at the receiver. In general, accurate channel state information (CSI) is required to achieve these performance gains. In this paper, we analyze the impact of channel prediction error on the bit error rate (BER) of combined beamforming and MRC in slow Rayleigh fading channels. Exact closed-form BER expressions are obtained in terms of elementary functions. Numerical results show that imperfect CSI causes little BER degradation using channel prediction of moderate complexity.     

On the Performance of the MIMO Zero-Forcing Receiver in the Presence of Channel Estimation Error

By employing spatial multiplexing, multiple-input multiple-output (MIMO) wireless antenna systems provide increases in capacity without the need for additional spectrum or power. Zero-forcing (ZF) detection is a simple and effective technique for retrieving multiple transmitted data streams at the receiver. However the detection requires knowledge of the channel state information (CSI) and in practice accurate CSI may not be available. In this letter, we investigate the effect of channel estimation error on the performance of MIMO ZF receivers in uncorrelated Rayleigh flat fading channels. By modeling the estimation error as independent complex Gaussian random variables, tight approximations for both the post-processing SNR distribution and bit error rate (BER) for MIMO ZF receivers with M-QAM and M-PSK modulated signals are derived in closed-form. Numerical results demonstrate the tightness of our analysis     

Tomlinson-Harashima precoding with partial channel knowledge

We consider minimum mean-square error Tomlinson-Harashima (MMSE-TH) precoding for time-varying frequency-selective channels. We assume that the receiver estimates the channel and sends the channel state information (CSI) estimate to the transmitter through a lossless feedback channel that introduces a certain delay. Thus, the CSI mismatch at the receiver is due to estimation errors, while the CSI mismatch at the transmitter is due to both estimation errors and channel time variations. We exploit a priori statistical channel knowledge, and we derive an optimal TH precoder, adopting a Bayesian approach. We use simulations to compare the performance of the so-derived TH precoder with that of the same-complexity MMSE decision-feedback equalizer (DFE). We observe that for low signal-to-noise ratios (SNRs) and sufficiently slow channel time variations, the optimal TH precoder outperforms the DFE, while at high SNR, the opposite happens.     

Capacity and performance of lattice reduction aided linear processing with lattice encoding and decoding in limited feedback systems

Linear processing for multi-input multi-output (MIMO) antenna systems is preferred to non-linear ones for computational efficiency. Using channel state information (CSI) at the receiver, channel matrix can be decomposed via singular value decomposition (SVD), and if the transmitter can be fed back with the right-unitary-matrix of the SVD from the receiver, the maximum channel-capacity can be achieved with linear processing in point-to-point wireless MIMO communications. However, if the transmitter receives no-feedback, the optimal linear detector at the receiver is the minimum-mean-squareerror- estimator, of which capacity is far below the channelcapacity. In practice, reducing the amount of feedback information to achieve a "reasonably close channel-capacity" is an important issue in point-to-point wireless communications. In this paper, we propose a limited feedback system employing linear processing, which achieves near-channel-capacity. The feedback information is only an integer matrix, which is much less than that of the right-unitary-matrix of the SVD. Key ideas of the proposed scheme are the lattice reduction and modulo operation. Moreover, the amount of feedback information can be further reduced to a binary matrix using multi-level/multi-stage encode and decode. Under the turbo channel code the proposed scheme shows excellent performance at high data rates. We compare our simulation results with Shannon capacity limits for ergodic MIMO channels.     

Joint pre-processing co-channel interference cancellation for single user MIMO

In general, multiplexing and diversity gains of single user MIMO systems are restricted by min(M,N) where M, N denote the number of antenna elements at a transmitter and receiver, respectively. In order to increase the multiplexing/diversity gains and improve the performance of single user MIMO systems, a joint pre-processing co-channel interference cancellation (JPCIC) method is proposed. The JPCIC is analyzed in both the perfect and the imperfect channel state information. The dependence of channel capacity on the number of antenna elements in every subset, the number of subsets, transmit powers and channel estimation errors is discussed. As theoretical calculation result, the channel capacity increases when the multiplexing/diversity gains and/or the transmit power increase in a certain channel model whether the channel estimation error is absent or present. Compared to the conventional zero-forcing method, the channel capacity of JPCIC is considerably higher because of higher multiplexing/diversity gains, however, it is less robust and decreased more rapidly due to incomplete cancellation of interference terms when the channel estimation error increases. There is a trade-off between the channel capacity and the complexity of system, however, according to quick development in circuit techniques and miniaturization of devices, the JPCIC is expected to be an attractive technology for MIMO system.     

基于容量的MIMO信道发射天线选择算法

当前的MIMO系统是在假设接收端已知信道信息(CSI)而发射端未知CSI的情况下进行研究的.本文提出的发射天线选择算法是用极小的信息反馈量,即反馈一组最优的发射天线子集,就可使信道容量得到很大的增加,较传统的注水算法而言,反馈量大大减少,而容量只略微减少,从而大大降低了反馈信道的带宽.     

Capacity Improvement for TDD-MIMO Systems via AR Modeling Based Linear Prediction

The quality of channel state information (CSI) affects the performance of multiple input multiple output (MIMO) systems which employ multi-elements antenna arrays at both the transmitter and the receiver. In a time division duplex (TDD) systems, the CSI for downlink can be obtained from uplink channel using reciprocity principal. However, the performance of a MIMO system can be degraded due to channel impairments especially in fast fading scenarios when the CSI obtained from uplink is used for downlink transmission. In this paper, we study performance of autoregressive (AR) modeling based MIMO channel prediction under varying channel propagation conditions (mobile speed, multipath number and angle spread) and prediction filter order. Our simulation results show that using the predicted CSI for downlink provides capacity improvement compared to conventional method.     

Optimal minimum distance-based precoder for MIMO spatial multiplexing systems

We describe a new precoder based on optimization of the minimum Euclidean distance d/sub min/ between signal points at the receiver side and for use in multiple-input multiple-output (MIMO) spatial multiplexing systems. Assuming that channel state information (CSI) can be made available at the transmitter, the three steps ( noise whitening, channel diagonalization and dimension reduction), which are currently used in investigations on MIMO systems, are performed. Thanks to this representation, an optimal d/sub min/ precoder is derived in the case of two different transmitted data streams. For quadrature phase-shift keying (QPSK) modulation, a numerical approach shows that the precoder design depends on the channel characteristics. Comparisons with maximum signal-to-noise ratio (SNR) strategy and other precoders based on criteria, such as water-filling (WF), minimum mean square error (MMSE), and maximization of the minimum singular value of the global channel matrix, are performed to illustrate the significant bit-error-rate (BER) improvement of the proposed precoder.     

An iterative singular vectors estimation scheme for beamforming transmission and detection in MIMO systems

A novel iterative singular vector estimation scheme has been proposed for a beamforming transmission and detection in wireless multiple input multiple output (MIMO) systems. Two singular channel matrix vectors, which correspond to the largest singular value, are iteratively obtained at the transmitter and the receiver without estimating the channel coefficients. The proposed singular vectors estimation strategy has advantages over the conventional MIMO channel estimation schemes in terms of both frame-error-rate performance, bandwidth efficiency and computation complexity.     

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.     

Power allocation for multi-antenna systems with space-time block coding in the presence of estimation error and delayed feedback

Based on imperfect channel state information with channel estimation error at the receiver and delayed feedback at the transmitter, a suboptimal power allocation (PA) scheme to minimize bit error rate (BER) under a power constraint is developed for beamforming multi-antenna systems with space-time block coding. The proposed scheme is based on a so-called compressed signal-to-noise ratio criterion, where a single compressed factor is utilized, and it can be used to generalize some existing schemes by setting the compressed factor to different forms. A closed-form compressed factor is derived to minimize the BER, and the resultant close-form expression of power allocation is attained. This closed-form expression is computational efficient and can obtain the BER performance close to the existing optimal approach which requires numerical search. Simulation results show that the proposed scheme can provide BER lower than the equal power allocation scheme. However, due to the impact of both estimation error and delayed feedback, it has performance degradation when compared to the PA scheme with estimation error or delayed feedback only.     

OFDMA uplink frequency offset estimation via cooperative relaying

Frequency offset estimation for an orthogonal frequency-division multiple access (OFDMA) uplink for amplify-and-forward (AF) relays and a new type of relay (R) called decode-and-compensate-and-forward (DcF) relays are studied. Multiple relays are considered, and the relay with the best S rarr R channel is chosen to perform re-transmission, where S and R represent the source and relay nodes, respectively. Frequency offsets due to the mismatches between the transmitter and receiver oscillators are considered, and without considering the effect of Doppler shift, both S rarr D and S rarr R rarr D links have the same frequency offset, where D represents the destination. Thus, by using these two transmissions, D generates two frequency offset estimates, which are combined to minimize the mean square error (MSE). Power allocation between S and R can be adaptively adjusted to optimize the cooperative scheme in terms of frequency offset error variance. When channel state information (CSI) is available at each mobile node, a scheme where the relays adaptively switch between the cooperative and conventional (no relaying) transmissions is proposed to optimize the frequency offset estimation. Although the frequency offset estimation accuracy in the DcF mode is somewhat worse than the AF mode, both modes outperform the conventional transmission. However, DcF (or decode-and-forward (DF)) relays outperform AF relays in terms of channel capacity and bit error rate (BER).     

MIMO-HARQ系统中低反馈量序贯功率分配的传输方法

混合自动重传请求(HARQ)是一种保证可靠通信的差错控制方式。通过采用空分复用MIMO技术和HARQ机制,可以进行高速可靠的通信。该文提出了一种MIMO-HARQ系统中以低反馈量进行序贯功率分配的传输方法,接收机根据当前的信道信息,搜索下次HARQ重传使用的最优天线间功率分配矢量,并将其序号反馈给发射机,序贯地实现码流间的功率分配。这种方法不仅需要的反馈量少,而且对反馈延迟的要求也很低。仿真分析表明,该方法可以显著提高系统在空间相关信道下的误码性能。     

Transparent Inband Feedback for Training-Based MIMO Systems

Recently, Echo-MIMO, a delay-free feedback scheme has been proposed for Closed-Loop MIMO systems, where the receiver echoes the received signal on the fly to the transmitter without any processing. While this reduced feedback latency allows for more use of the channel’s coherence time for data transmission, it comes at high power-and-bandwidth costs, as two MIMO transmissions are required in the feedback phase. In this paper, we present a feedback scheme that preserves the advantages of Echo-MIMO while requiring only one feedback transmission. The echoed signals are judiciously combined with the receiver’s signals such that their separation at the transmitter be lossless, and that no extra transmit power nor bandwidth be required. In addition, we highlight the estimation accuracy degradation in Echo-MIMO owing to the echoed noise, and analytically confirm the intuition that removing the noise prior to echoing the received signal provides better estimation than echoing the noisy received signal as is and later account for the noise effect upon echo reception. Simulation results show that the proposed scheme outperforms Echo-MIMO in terms of channel estimation accuracy and achievable capacity.     

Multiuser receivers for CDMA systems in Rayleigh fading channels

Multiuser demodulation in relatively fast fading channels is analyzed. The optimal maximum likelihood sequence detection (MLSD) receiver is derived and a general suboptimal receiver to approximate the MLSD is proposed. The performance of the parallel interference cancellation (PIC) and decorrelating receivers is compared. The PIC receiver is demonstrated to achieve better performance in known channels than the decorrelating receiver, but it is observed to be more sensitive to the channel coefficient estimation errors than the decorrelator. At high channel loads the PIC receiver suffers from bit error rate (BER) saturation, whereas the decorrelating receiver does not. The performance of data-aided (DA) and decision-directed (DD) multiuser channel estimation is also compared. DA channel estimation is shown to be more robust than DD channel estimation, which may suffer from BER saturation caused by hangups at high signal-to-noise ratios (SNRs). The impact of channel estimation filter impulse response on the BER is studied by comparing optimal and suboptimal channel estimation filters. The implementation complexity of the decorrelating and PIC receivers is compared in terms of required floating point operations and clock cycles in a practical communication scenario. It is observed that the PIC receiver is only moderately more complex to implement than the conventional matched filter bank receiver, whereas the decorrelating receiver is significantly more complex