Joint linear transceiver design in amplify-and-forward mimo relay system using an MMSE criterion

In this paper, we use the minimum mean square error (MMSE) criterion to design the scaled and offset belief propagation (BP)-based decoding algorithms for short low-density parity-check (LDPC) codes on the fast Rayleigh fading channel. Based on the MMSE criterion, the theoretical formulas and numerical calculations on the optimum factors for these two improved BP-based algorithms are provided. The simulation results for several short (Chen et al., 2005 and Gallager, 1962) regular LDPC codes on the fast Rayleigh fading channel demonstrate that the scaled and offset BP-based algorithms with our proposed factors can achieve the performance better than that of the BP algorithm.

In recent years, a lot of attention has been drawn to the use of multiple antennas at both the transmitter and receiver sides. Such techniques are named here as space-time transmission and noted as STT. By their use of the available space dimension, STT techniques can achieve very high spectral efficiencies in Rayleigh fading channels with rich scattering. The use of STT techniques for indoor wireless systems with a huge number of antennas is considered. As a low complexity detection algorithm, ordered successive detection based schemes are considered. A scheme known as V-BLAST (vertical Bell Labs layered space-time) is proposed in the zero forcing (ZF) criterion (see Wolniansky, P.W. et al., Proc. ISSSE'98, 1998). In a previous work, it has been shown how this scheme can be much improved by the use of a backward iterative detection algorithm (see Benjebbour, A. et al., Proc. WPMC, p.819-24, 2000; Proc. VTC2001 Spring, 2001). An extension of the conventional V-BLAST algorithm to the minimum mean square error (MMSE) criterion is now proposed. For the proposed receiver, an ordering metric is defined. Then, the effect of ordering on both receivers is discussed. And finally, it is shown how the ordering metric in the MMSE criterion can be simplified.

The problem of iterative multiuser detection in single-carrier broadband multiple-input multiple-output (MIMO) system is studied in this paper. Two minimum mean squared error (MMSE) multiuser receivers are proposed for space-time trellis coded systems in frequency selective channels. The first receiver uses the MMSE criterion both for multiuser detection and equalization. The second one uses the MMSE criterion only for multiuser detection, while the equalization part is an optimal maximum a posteriori (MAP) equalizer. The second receiver significantly outperforms the first one both in the presence and in the absence of the unknown co-channel interference, at the expense of increased complexity.

To address the nonlinear state estimation problem, the generalized conversion filter (GCF) is proposed using a general conversion of the measurement under minimum mean square error (MMSE) criterion. However, the performance of the GCF significantly deteriorates in the presence of complex non-Gaussian noise as the symmetry of the MMSE is compromised, leading to performance degradation. To address this issue, this paper proposes a new GCF, named generalized loss-based GCF (GLGCF) by utilizing the generalized loss (GL) as the loss function instead of the MMSE criterion. In contrast to other robust loss functions, the GL adjusts the shape of the function through the shape parameter, allowing it to adapt to various complex noise environments. Meanwhile, a linear regression model is developed to obtain residual vectors, and the negative log-likelihood of GL is introduced to avoid the problem of manually selecting the shape parameter. The proposed GLGCF not only retains the advantage of GCF in handling strong measurement nonlinearity, but also exhibits robust performance against non-Gaussian noises. Finally, simulations on the target-tracking problem validate the strong robustness and high filtering accuracy of the proposed nonlinear state estimation algorithm in the presence of non-Gaussian noise.

To suppress the effects of ultra-wideband receiver caused by non-Gaussian noise and difference of channel profile, an adjustable observation window length equalisation receiver based on H∞ criterion is proposed. In contrast to the existing fixed observation window length (FOWL) equalisation receivers based on the minimum mean square error (MMSE) criterion, the proposed receiver is found on H∞ criterion and can adaptively adjust the observation window length according to the specific channel profile. The proposed receiver so designed is shown to outperform the FOWL equalisation receivers based on the conventional MMSE criterion in a non-Gaussian noise environment.

In this paper, a pilot-assisted minimum mean square error (MMSE) multiuser channel estimation algorithm is proposed for quasi-synchronous code-division multiple-access (CDMA) systems that undergo frequency-selective channel fading. The frequency-selective multiuser fading channel is represented as a symbol-wise time-varying chip-spaced tapped delay line filter with correlated filter taps. The multiuser channel tap coefficients at pilot symbol positions are estimated under the MMSE criterion with the help of the channel intertap correlation matrix, which is determined by the combined effects of the physical fading channel, transmit filter, and receive filter. In the development of the estimation algorithm, the channel intertap correlation matrix is deemed as an essential factor, and a novel iterative method is proposed for the joint estimation of the channel intertap correlation and filter tap timing based on the received pilot samples. Simulations show that the information of the channel intertap correlation is critical to the performance of the channel estimation, and the channel taps at different delays cannot be assumed uncorrelated for CDMA systems experiencing frequency-selective fading.

To date, most linear and nonlinear Kalman filters (KFs) have been developed under the Gaussian assumption and the well-known minimum mean square error (MMSE) criterion. In order to improve the robustness with respect to impulsive (or heavy-tailed) non-Gaussian noises, the maximum correntropy criterion (MCC) has recently been used to replace the MMSE criterion in developing several robust Kalman-type filters. To deal with more complicated non-Gaussian noises such as noises from multimodal distributions, in this article, we develop a new Kalman-type filter, called minimum error entropy KF (MEE-KF), by using the minimum error entropy (MEE) criterion instead of the MMSE or MCC. Similar to the MCC-based KFs, the proposed filter is also an online algorithm with the recursive process, in which the propagation equations are used to give prior estimates of the state and covariance matrix, and a fixed-point algorithm is used to update the posterior estimates. In addition, the MEE extended KF (MEE-EKF) is also developed for performance improvement in the nonlinear situations. The high accuracy and strong robustness of MEE-KF and MEE-EKF are confirmed by experimental results.

In this paper, we investigate channel estimation and robust detection for uplink massive multi-input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) systems with in-phase and quadrature-phase imbalances (IQI). We represent the received signal with a real-valued model, where the combination of the IQI and the wireless channel is treated as the effective channel. Based on the real-valued model, we then perform the minimum mean square error (MMSE) criterion based estimation for the effective channel. We use adjustable phase shift pilots (APSPs) to reduce the pilot overhead and verify that the MSE of the effective channel estimation can be minimized by scheduling the pilot phase shifts properly. We propose a pilot phase shift scheduling algorithm based on the covariance matrices of the effective channels. Since the channel estimation performance might be degraded due to using APSPs, we develop an MMSE criterion based data detection scheme which is robust to the channel estimation error. Using operator-valued free probability theory, we derive an asymptotic deterministic equivalent for the ergodic achievable sum rate of the proposed detection scheme. The performance of the channel estimation with APSPs and the robust data detection is demonstrated via extensive numerical results.

Information theory, and particularly the mutual information (MI), has provided fundamental guidance for communications research. In Bell's 1993 paper, the MI was first applied to radar waveform design. Similar to its communications counterpart, the solution comes in a water-filling form. However, the practical meaning of MI in the sensing context remains unclear to date. Recently, Yang and Blum's 2007 paper shows that under the white noise assumption, the optimum water-filling scheme simultaneously maximizes the MI and minimizes the estimation minimum mean square error (MMSE). Such an equivalence, however, does not hold when the target parameter statistics are not perfectly known as shown in Yang and Blum's subsequent work. To further the understanding of the practical meaning of MI and to establish a connection between the MI and commonly adopted MSE measures for sensing, this paper takes a fresh look at the target estimation problem. We consider the general colored noise, incorporate the normalized MSE (NMSE), and develop joint robust designs for both the transmitter (waveforms) and the receiver (estimator) under various target and noise uncertainty models. Our results show that i) the optimum waveform designs resulted from the MI, MMSE and NMSE criteria are all different and ii) compared to MMSE, the NMSE-based designs share more similarities with the MI-based ones, especially when the target and noise statistics are not perfectly known.

In this paper, we propose a family of distributed space-frequency codes (SFCs) for frequency asynchronous cooperative relay networks with multiple carrier frequency offsets (CFOs) and flat fading channels. The codes have the special structures that the columns of each code matrix can be divided into several orthogonal groups and each group is stacked by several sub-blocks with Toeplitz structure. These codes possess two interesting properties: a) Even under the frequency-asynchronous scenario, the codes can , namely, if R relay nodes participate the cooperation adopting the proposed SFCs, then at the destination node, the achievable diversity order is R; b) Only , such as zero-forcing (ZF) and minimum mean square error (MMSE) receivers, are required to collect the full cooperative diversity, instead of the maximum likelihood (ML) detector as utilized in most existing STC (SFC) schemes. The codes in this family have different symbol rates, orthogonality and performances for different numbers of relay nodes, which can be adjusted by choosing different design parameters. It is shown that frequency-reversal SFC (FR-SFC), and frequency-shift SFC (FS-SFC) proposed in previous papers are only two special members of the code family, and new SFCs outperforming both of them are proposed.

Adaptive channel equalisation is a signal processing technique to mitigate inter-symbol interference (ISI) in a time dispersive channel. To this end, the use of least mean squares (LMS) algorithm and its variants is widespread since they minimise the minimum mean squared error (MMSE) criteria by online stochastic gradient algorithms and they asymptotically tend to the optimal Weiner solution for linearly separable channels. The kernel least mean squares (KLMS) algorithm and its variants are based on the MMSE based algorithms for non-linear channels. However, as has been pointed out in the literature, the minimum bit/symbol error rate (MBER/MSER) criterion is a better choice for adapting an equaliser as compared to the traditional approaches based on MMSE criterion. In this paper, we propose a novel equaliser that is inspired from the recently proposed MSER adaptation by Gong et al. using the kernel trick for non-linear channel equalisation.

In much theoretical work, the minimum mean-square error (MMSE) criterion is used as a basis of design for receivers of dispersed digital signals in the presence of noise. A variant of this criteria that is also frequently used is the MMSE with the constraint of zero intersymbol interference (OISI). In this discussion we compare the probability of error P(e) of receivers designed with the MMSE and MMSE-OISI criterion with a receiver designed by computer minimization of P(e) by variation of pole locations of a fixed order filter. The performance of these receivers is then compared with the isolated pulse lower bound and the probability of error of the maximum likelihood receiver. These Comparisons are made for a channel that is an approximation to 6000 ft of twisted pair paper insulated cable with a transmission rate of 1.5 Mb.

An adaptive distributed space-time coding (DSTC) scheme is proposed for two-hop cooperative MIMO networks. Linear minimum mean square error (MMSE) receive filters and adjustable code matrices are considered subject to a power constraint with an amplify-and-forward (AF) cooperation strategy. In the proposed adaptive DSTC scheme, an adjustable code matrix obtained by a feedback channel is employed to transform the space-time coded matrix at the relay node. The effects of the limited feedback and the feedback errors are assessed. Linear MMSE expressions are devised to compute the parameters of the adjustable code matrix and the linear receive filters. Stochastic gradient (SG) and least-squares (LS) algorithms are also developed with reduced computational complexity. An upper bound on the pairwise error probability analysis is derived and indicates the advantage of employing the adjustable code matrices at the relay nodes. An alternative optimization algorithm for the adaptive DSTC scheme is also derived in order to eliminate the need for the feedback. The algorithm provides a fully distributed scheme for the adaptive DSTC at the relay node based on the minimization of the error probability. Simulation results show that the proposed algorithms obtain significant performance gains as compared to existing DSTC schemes.

In cooperative communications, due to the distributed nature, multiple different carrier frequency offsets (CFOs) may occur and make the channel time-varying. It is hard for the receiver to compensate multiple CFOs from multiple relay nodes simultaneously. Thus, the conventional space-time codes to collect cooperative diversity for co-located multi-input multi-output (MIMO) systems may not be applied directly. In this paper, we consider the cooperative transmission with multiple CFOs when the channels from relay nodes to destination node are flat (frequency-non-selective) fading. We approximate a flat fading channel with CFO as a block time-invariant intersymbol-interference (ISI) channel in the frequency domain. We then propose two distributed space-frequency codes (SFC) for such ISI channels in the frequency domain to achieve the cooperative full spatial diversity, where the space-frequency coding concept is different from the one in the literature and also has a different role. One is called frequency-reversal SFC and the other is called frequency-domain linear convolutive SFC. Furthermore, we show that, with only linear receivers, such as zero-forcing (ZF) and minimum mean square error (MMSE) receivers, our codes achieve the full cooperative diversity.

This paper addresses the joint transceiver design for uplink multiuser non-regenerative MIMO relay systems, where spatial multiplexing (SM) is applied at all users and linear processing is performed at the relay station (RS) and base station (BS). Based on the minimum mean square error (MMSE) criterion, subject to maximum power constraint at the RS, an iterative algorithm is proposed to jointly optimize the RS processing matrix and the BS decoding matrix. Simulation results show that the proposed scheme outperforms several existing schemes in terms of BER and robustness.