Partial sampling MMSE interference suppression in asynchronousmulticarrier CDMA system

Linear minimum mean square error (LMMSE) receivers for asynchronous multicarrier code division multiple access (MC-CDMA) system under frequency-selective Rayleigh fading channel is studied. The performance of this LMMSE receiver is evaluated and shown to be superior to that of the other two schemes, equal-gain combining (EQC) and maximum-ratio combining (MRC). However, a perfect timing estimation of the desired user is needed for these receivers, as a misaligned sampling interval of these receivers results in severely self intersymbol interference (ISI) and intercarrier interference (ICI) for the desired signal at the output. In order to remove the timing acquisition requirement of a receiver for an asynchronous MC-CDMA system, we proposed a novel partial sampling MMSE (PS-MMSE) receiver. Numerical result shows that the PS-MMSE receiver without timing knowledge provides significantly stronger interference suppression capability than the LMMSE receiver with known timing. Moreover, a so-called reduced complexity partial sampling MMSE (RPS-MMSE) receiver is proposed to make the number of the receiver's taps independent of the number of subcarriers. Results show that with a proper grouping parameter, a much less complicated RPS-MMSE receiver achieves almost the same performance as the PS-MMSE receiver. Thus, one is able to implement an MMSE receiver without a prior timing requirement to perform multiuser detection for the MC-CDMA system in an asynchronous scenario at the expense of a slight complexity increase     

An Adaptive MMOE-PIC Detector for Asynchronous DS-CDMA Communications

We propose a modified linear parallel interference cancelation (PIC) structure using the adaptive minimum mean output-energy (MMOE) algorithm for direct-sequence code-division multiple-access (DS-CDMA) systems. The complexity of the proposed receiver structure is shown to be linear in the number of users and hence, lower complexity than the centralized minimum mean-squared error (MMSE) multiuser detector. It is demonstrated that the proposed receiver structure can significantly reduce the long training period required by the standard adaptive MMOE receiver in near-far environments. Both numerical and theoretical results show that the proposed receiver performs close to the optimum MMSE receiver whereas the conventional adaptive MMOE detector suffers from high BER’s due to the imperfect filter coefficients. Also our results show a three fold increase in the number of users when the MMOE-PIC is used relative to the conventional MMOE receiver. Furthermore, the transient behavior of the proposed MMOE-PIC receiver due to abrupt changes in the interference level is examined. It is shown that the proposed adaptive receiver offers much faster self recovery, with less signal-to-interference ratio (SIR) degradation, than the standard MMOE in sever near-far scenarios.     

Rank constrained temporal-spatial matrix filters for CDMA systems

Efficient interference suppression techniques are needed to maximally utilize the potential gains of code-division multiple-access systems. In this letter, a receiver structure which combines multiuser detection (temporal filtering) and receiver beamforming (spatial filtering) in a multipath environment is considered. Following previous work, we model the receiver as a linear matrix filter and use the minimum mean-squared error (MMSE) as the performance criterion. Motivated by the high complexity of the optimum receiver, we propose rank constrained temporal-spatial filters which are simpler and near-optimum. The MSE is minimized subject to a structural constraint, using an iterative algorithm based on alternating minimization. The constraint on the receiver matrix filter narrows down the solution space, which helps to solve the optimization problem more efficiently. The constraint can be set appropriately by the system designer to achieve the desired tradeoff between performance and complexity. Numerical results indicate that a performance close to that of the optimum filter can be achieved with a simple iterative structure, even in highly loaded systems. Adaptive implementation of the rank constrained filters is derived. A new adaptive scheme is proposed which is a combination of the alternating minimization and the least mean squares methods. The convergence properties are investigated along with the effect of the number paths.     

An asynchronous multiuser CDMA detector based on the Kalman filter

We introduce a multiuser receiver based on the Kalman filter, which can be used for joint symbol detection and channel estimation. The proposed algorithm has the advantage of working even when the spreading codes used have a period larger than one symbol interval (“long codes”), unlike adaptive equalizer-type detectors. Simulation results which demonstrate the performance advantage of the proposed receiver over the conventional detector, the minimum mean squared error (MMSE) detector and a recursive least squares (RLS) multiuser detector are presented. A thorough comparison of the MMSE detector and the proposed detector is attempted because the Kalman filter also solves the MMSE parameter estimation problem, and it is concluded that, because the state space model assumed by the Kalman filter fits the code division multiple access (CDMA) system exactly, a multiuser detector based on the Kalman filter must necessarily perform better than a nonrecursive, finite-length MMSE detector. The computational complexity of the detector and its use in channel estimation are also studied     

A constrained MMSE receiver for DS/CDMA systems in fading channels

The convergence problem of minimum mean square-error (MMSE) receivers is discussed, and to overcome the problem, a constrained MMSE receiver is proposed. In addition, we propose the orthogonal decomposition-based least mean square algorithm to implement the constrained MMSE receiver adaptively. Through computer simulations, it is shown that the proposed receiver provides significant performance improvement in the bit-error rate over the conventional matched filter receiver and currently available MMSE receivers.     

Adaptive MMSE receiver with beamforming for DS/CDMA systems

The minimum mean-squared error (MMSE) receiver is a linear filter which can suppress multiple access interference (MAI) effectively in direct-sequence code-division multiple-access (CDMA) communications. An antenna array is also an efficient scheme for suppressing MAI and improving the system performance. In this letter, we consider an adaptive MMSE receiver in conjunction with beamforming in CDMA systems employing an antenna array. The proposed structure is featured as a low complexity receiver, which adapts the MMSE filter coefficients and the beamforming weights simultaneously. However, it does require the channel state information and the direction of arrival (DOA) of the desired user signal. As a result, we propose two adaptation methods to perform joint channel estimation and signal detection without any training sequence. It is demonstrated that the two proposed methods achieve similar bit-error-rate performance. More importantly, their performance degradation compared with the case with perfect channel information is small.     

Design of linear equalizers optimized for the structural similarity index.

We propose an algorithm for designing linear equalizers that maximize the structural similarity (SSIM) index between the reference and restored signals. The SSIM index has enjoyed considerable application in the evaluation of image processing algorithms. Algorithms, however, have not been designed yet to explicitly optimize for this measure. The design of such an algorithm is nontrivial due to the nonconvex nature of the distortion measure. In this paper, we reformulate the nonconvex problem as a quasi-convex optimization problem, which admits a tractable solution. We compute the optimal solution in near closed form, with complexity of the resulting algorithm comparable to complexity of the linear minimum mean squared error (MMSE) solution, independent of the number of filter taps. To demonstrate the usefulness of the proposed algorithm, it is applied to restore images that have been blurred and corrupted with additive white gaussian noise. As a special case, we consider blur-free image denoising. In each case, its performance is compared to a locally adaptive linear MSE-optimal filter. We show that the images denoised and restored using the SSIM-optimal filter have higher SSIM index, and superior perceptual quality than those restored using the MSE-optimal adaptive linear filter. Through these results, we demonstrate that a) designing image processing algorithms, and, in particular, denoising and restoration-type algorithms, can yield significant gains over existing (in particular, linear MMSE-based) algorithms by optimizing them for perceptual distortion measures, and b) these gains may be obtained without significant increase in the computational complexity of the algorithm.     

Soft input soft output Kalman equalizer for MIMO frequency selective fading channels

We consider the Kalman filter for equalization of a multiple-input multiple-output (MIMO), frequency selective, quasi-static fading channel. More specifically, we consider a coded system, where the incoming bit stream is convolutionally encoded, interleaved and then spatially multiplexed across the transmit antennas. Each substream is modulated into M-ary symbols before being transmitted over a frequency selective channel. At the receiver, we propose to use the Kalman filter as a low complexity MIMO equalizer, as opposed to the trellis based maximum a-posteriori (MAP) equalizer whose computational complexity grows exponentially with the channel memory, the number of transmit antennas and the spectral efficiency (bits/s/Hz) of the system. We modify the structure of the Kalman filter and enable it to process the a-priori (soft) information provided by the channel decoder, thereby allowing us to perform iterative (turbo) equalization on the received sequence. The iterative equalizer structure is designed for general M-ary constellations. We also propose a low complexity version of the above algorithm whose performance is comparable to its full complexity counterpart, but which achieves a significant complexity reduction. We demonstrate via simulations that for higher order constellations, when sufficient number of receive antennas are available (e.g. for a 2 transmitter, 3 receiver system, QPSK), the performance of the proposed algorithms after 4 iterations is within 1.5 dB of the non-iterative MAP algorithm with close to an order of magnitude complexity reduction. By objectively quantifying the complexity of all the considered algorithms we show that the complexity reduction for the proposed schemes becomes increasingly significant for practical systems with moderate to large constellation sizes and a large number of transmit antennas     

Efficient compressive sensing based sparse channel estimation for 5G massive MIMO systems

Massive MIMO (multiple-input-multiple-output) is one of the key technologies of 5G mobile cellular networks, which can form a huge antenna array by providing a large number of antennas at the cell base station. It will greatly improve the channel capacity and spectrum utilization and has become a hotspot in the field of wireless communications in recent years. Aiming at the high complexity of channel estimation algorithm for massive MIMO system, a sparse channel estimation algorithm with low complexity is proposed based on the inherent sparsity of wireless communication channel. The algorithm separates the channel taps from the noise space on the basis of the traditional discrete Fourier transform (DFT) channel estimation, so that the channel estimation only needs to calculate the part of the channel tap, so the computational complexity of the algorithm is greatly reduced. The simulation results show that the proposed algorithm can achieve near minimum mean square error (MMSE) performance while maintaining low complexity. Moreover, the Bit Error Rate and Inter-Cell Interference also indicates that the proposed improved algorithm shows better overall performance than the conventional algorithms which makes it suitable from practical perspective.     

A Low Complexity Near Optimal Signal Detection for Large Scale MIMO SC-FDMA Uplink System

This article proposes an improved Newton algorithm as a low complexity signal detection scheme for linear receiver in large scale multiple- input multiple- output (LS-MIMO) single carrier frequency division multiple access (SC-FDMA) uplink system, where a large number of antennas are set up at the base station and active users are with a single antenna system. Data detection for uplink SC-FDMA system is one of the specific challenges due to the significant rise in the dimension of antennas and number of subcarriers. Especially for symbol detection process, LS-MIMO SC-FDMA system with linear detector requires to perform a large matrix inverse computation. Even though linear detectors such as zero forcing (ZF) and minimum mean square error (MMSE) can achieve near-optimal detection performance, they still introduce high computational complexity and obliviously involve in the computation of matrix inversion. Therefore, a design of complexity reduction algorithm based near-optimal detector for LS-MIMO SC-FDMA system attains research interest. The improved Newton algorithm is employed to obtain linear detection solution which iteratively performs matrix free-inversion operation. The new algorithm performs matrix–matrix multiplication into matrix–vector multiplication, which substantially reduces receiver detection complexity. The efficacy of the proposed method is investigated at 16-QAM. Both ZF and MMSE criteria are proposed and compared through simulations. Simulation results illustrate that the proposed scheme outperforms the conventional detection schemes and exhibits near-optimal performance with a small number of iterations. Further, bit-error-rate performance is closer to classical linear detector with affordable computational complexity.

     

Adaptive DFE Multiuser Receiver for CDMA Systems using Two-Step LMS-Type Algorithm: An Equalization Approach

This paper presents an adaptive decision feedback equalizer (DFE) based multiuser receiver for code division multiple access (CDMA) systems over smoothly time-varying multipath fading channels using the two-step LMS-type algorithm. The frequency-selective fading channel is modeled as a tapped-delay-line filter with smoothly time-varying Rayleigh-distributed tap coefficients. The receiver uses an adaptive minimum mean square error (MMSE) multiuser channel estimator based on the reduced Kalman least mean square (RK-LMS) algorithm to predict these tap coefficients (Kohli and Mehra, Wireless Personal Communication 46:507–521, 2008). We propose the design of adaptive MMSE feedforward and feedback filters by using the estimated channel response. Unlike the previously available Kalman filtering algorithm based approach (Chen and Chen, IEEE Transactions on Signal Processing 49:1523–1532, 2001), the incorporation of RK-LMS algorithm reduces the computational complexity of multiuser receiver. The computer simulation results are presented to show the substantial improvement in its bit error rate performance over the conventional LMS algorithm based receiver. It can be inferred that the proposed multiuser receiver proves to be robust against the nonstationarity introduced due to channel variations, and it is also beneficial for the multiuser interference cancellation and data detection in CDMA systems.     

Structure adaptation of linear MMSE adaptive filters

The tap-length, or the number of the taps, is an important structural parameter of the linear MMSE adaptive filter. Although the optimum tap-length that balances performance and complexity varies with scenarios, most current adaptive filters fix the tap-length at some compromise value, making them inefficient to implement especially in time-varying scenarios. A novel gradient search based variable tap-length algorithm is proposed, using the concept of the pseudo-fractional tap-length, and it is shown that the new algorithm can converge to the optimum tap-length in the mean. Results of computer simulations are also provided to verify the analysis.     

Performance of coded DS‐CDMA system using reduced rank MMSE receiver in Rayleigh fading channels

This paper examines the performance of a reduced rank minimum mean square error (MMSE) receiver‐based direct sequence code division multiple access (DS‐CDMA) system. For such system, when a large processing gain is employed, substantial time is consumed in computing the filter tap weights. Many schemes for reducing the complexity of the MMSE have been proposed in recent years. In this paper, computational complexity reduction of the MMSE receiver is achieved by using the K‐mean classification algorithm. The performance of the uncoded and coded systems are investigated for the full rank MMSE receiver and reduced rank MMSE receiver and results are compared in terms of bit error rate at different loading levels in both AWGN and fading channels. A system with the matched filter (MF) receiver is also presented for the purpose of comparison and an analytical pair‐wise error bound for the coded system is derived. In the adaptive implementation of the receivers, results show that good performance is achieved for the reduced rank receiver when compared to the full rank receiver in both coded and uncoded systems, while in the optimum implementation of the tap weights, the reduced dimension receiver performance experiences degradation when compared to the full rank scheme. Over the band‐limited channels considered, results for the reduced rank receiver also reiterate the fact that higher code rates tend to yield lower BER than that of low rate codes. Copyright © 2006 John Wiley & Sons, Ltd.     

Equalization for discrete multitone transceivers to maximize bitrate

In a discrete multitone receiver, a time-domain equalizer (TEQ) reduces the intersymbol interference (ISI) by shortening the effective duration of the channel impulse response. Current TEQ design methods such as the minimum mean-squared error (MMSE), maximum shortening SNR (MSSNR), and maximum geometric SNR (MGSNR) do not directly maximize bit rate. We develop two TEQ design methods to maximize the bit rate. First, we partition an equalized multicarrier channel into its equivalent signal, noise, and ISI paths to develop a new subchannel SNR definition. Then, we derive a nonlinear function of TEQ taps that measures the bit rate, which the proposed maximum bit rate (MBR) method optimizes. We also propose a minimum-ISI method that generalizes the MSSNR method by weighting the ISI in the frequency domain to obtain higher performance. The minimum-ISI method is amenable to real-time implementation on a fixed-point digital signal processor. Based on simulations using eight different carrier-serving-area loop channels, (1) the proposed methods yield higher bit rates than MMSE, MGSNR, and MSSNR methods; (2) the proposed methods give three-tap TEQs with higher bit rates than 17-tap MMSE, MGSNR, and MSSNR TEQs; (3) the proposed MBR method achieves the channel capacity (as computed by the matched filter bound using the proposed subchannel SNR model) with a five-tap TEQ; and (4) the proposed minimum-ISI method achieves the bit rate of the optimal MBR method     

MMSE receivers for multirate DS-CDMA systems

Minimum-mean squared error (MMSE) receivers are designed and analyzed for multiple data rate direct-sequence code-division multiple-access (DS-CDMA) systems. The inherent cyclostationarity of the DS-CDMA signal is exploited to construct receivers for asynchronous multipath channels. Multiple- and single-bandwidth access are treated for both single and multicarrier scenarios. In general, the optimal receiver is periodically time-varying. When the period of the optimal receiver is large, suboptimal receivers are proposed to achieve a lower complexity implementation; the receivers are designed as a function of the cyclic statistics of the signals. In multiple chipping rate systems, the complexity of receivers for smaller bandwidth users can also be controlled by changing their front-end filter bandwidth. The effect of front-end filter bandwidth on receiver performance and system capacity is quantified for a variable chipping rate system. Analysis and simulation show that significant performance gains are realized by the periodically time-varying MMSE receivers over their time-invariant counterparts     

Group-Based Space-Time Multiuser Detection with User Sharing

To reduce the complexity of space-time multiuser detection, it has been proposed recently to exploit the spatial dimension by forming groups of users and apply the detection individually to each group. In this work we propose a new space-time receiver structure based on the group-optimal MMSE linear detector along with a new grouping algorithm that respects practical hardware limitations. Furthermore, an extension of the proposed structure which allows non-mutually exclusive grouping is presented. The simulation results show that the proposed reduced-complexity receiver structure provides a bit error rate (BER) performance close to the full linear MMSE multiuser detector.     

MMSE准则下近似最优MIMO分组并行检测算法

在采用多天线高阶QAM的MIMO通信系统中,现有基于信道分组并行检测算法虽然接近最优检测性能但以牺牲计算效率为代价.针对这一问题,本文提出一种MMSE准则下基于信道分组的并行检测算法,不但有效降低计算复杂度,而且仍保证检测性能.该算法采用MMSE准则下格归约算法改进分组后条件较好子信道矩阵特性,并在消除参考信号基础上利用改进的子信道矩阵对剩余信号以非线性方式进行检测.仿真结果表明:对4×4和6×6MIMO系统,该算法检测性能达到最优,对于8×8 MIMO系统,比最优算法所需信噪比提高约1dB.复杂度分析表明:相比现有信道分组检测算法,相同检测性能下该算法在6×6 MIMO系统中复杂度降低90%以上,在8×8 MIMO系统中复杂度降低98%以上.     

基于负熵准则的FastICA盲多用户检测的研究

该文给出了一种基于负熵准则的FastICA盲多用户检测方法。修改了FastICA算法中的非2次函数,引入4次幂函数,把基于负熵的非高斯性测度转化为信号峰度的形式,这样降低了计算量。同时,算法充分考虑了各个用户信号的统计独立性,在下行链路干扰用户的扩频码未知情况下,把目标用户的扩频码作为训练序列,并用于初始化FastICA算法的分离向量,使用随机梯度法进行优化计算,能够获得优异的符号估计性能。对算法的计算复杂度的分析可以看出,计算量随着接收数据长度和用户数的增加而增加。通过与传统匹配滤波器,MMSE检测算法比较,表明在同步CDMA信道中,MAI较低时算法检测性能与MMSE检测器的性能接近,随着MAI增加,算法的性能明显优于MMSE算法。     

Multistage MMSE PIC Space–Time Receiver With Non-Mutually Exclusive Grouping

The arrival of new data services for wireless mobile communications requires an efficient use of the available bandwidth. Interference-limited cellular systems based on code-division multiple access (CDMA) can benefit from multiuser detection (MUD) and beamforming with antenna array to reduce multiple-access interference. Group-based techniques have been proposed to reduce the complexity of space-time MUD and have been shown to provide a performance-complexity tradeoff between matched filtering and full MUD. In this paper, the intergroup interference, which is a limiting factor in group-based systems, is reduced using multistage parallel interference cancellation after group-based minimum mean square error (MMSE) linear filtering. In addition, the extra resources that are available at the receiver are exploited by sharing users among groups. The proposed receiver is shown to converge, as the number of stages increases, to the full space-time MMSE linear MUD filter. The results show that the new approach provides bit error rate (BER) performance close to the full MUD receiver at a fraction of the complexity.     

MMSE interference suppression for direct-sequence spread-spectrumCDMA

We consider interference suppression for direct-sequence spread-spectrum code-division multiple-access (CDMA) systems using the minimum mean squared error (MMSE) performance criterion. The conventional matched filter receiver suffers from the near-far problem, and requires strict power control (typically involving feedback from receiver to transmitter) for acceptable performance. Multiuser detection schemes previously proposed mitigate the near-far problem, but are complex and require explicit knowledge or estimates of the interference parameters. In this paper, we present and analyze several new MMSE interference suppression schemes, which have the advantage of being near-far resistant (to varying degrees, depending on their complexity), and can be implemented adaptively when interference parameters are unknown and/or time-varying, Numerical results are provided that show that these schemes offer significant performance gains relative to the matched filter receiver. We conclude that MMSE detectors can alleviate the need for stringent power control. In CDMA systems, and may be a practical alternative to the matched filter receiver