MMSE Criterion Research Articles

Application of a joint and iterative MMSE-based estimation of SNR and frequency-selective channel for OFDM systems

This article presents an iterative minimum mean square error- (MMSE-) based method for the joint estimation of signal-to-noise ratio (SNR) and frequency-selective channel in an orthogonal frequency division multiplexing (OFDM) context. We estimate the SNR thanks to the MMSE criterion and the channel frequency response by means of the linear MMSE (LMMSE). As each estimation requires the other one to be performed, the proposed algorithm is iterative. In this article, a realistic case is considered; i.e., the channel covariance matrix used in LMMSE is supposed to be totally unknown at the receiver and must be estimated. We will theoretically prove that the algorithm converges for a relevantly chosen initialization value. Furthermore simulations show that the algorithm quickly converges to a solution that is close to the one in which the covariance matrix is perfectly known. Compared to existing SNR estimation methods, the algorithm improves the trade-off between the number of required pilots and the SNR estimation quality.

Nearly optimal linear transceiver design for amplify‐and‐forward MIMO multiple‐relay systems under MMSE criterion

SUMMARYIn this paper, we consider amplify‐and‐forward multiple‐input multiple‐output multiple‐relay systems, where all the nodes have multiple antennas. For enhancing link reliability, we address the problem of designing optimal linear transceiver to minimize the mean squared error (MSE) of symbol estimations subject to the total relay transmit power constraint. This problem is highly complex and has not been solved in the literature. We first simplify this optimization problem to one that takes a singular value vector and a unitary matrix as optimization variables. Then based on the analyses for the simplified problem, we develop an iterative algorithm consisting of one boundary optimization and one unitary matrix constrained optimization. We show analytically that the proposed iterative algorithm always converges, and the MSE is monotonically decreasing from one iteration to the next. Finally, numerical results demonstrate the nearly optimal performance of the proposed scheme. Copyright © 2012 John Wiley & Sons, Ltd.

A Novel Data-Aided Channel Estimation With Reduced Complexity for TDS-OFDM Systems

In contrast to the classical cyclic prefix (CP)-OFDM, the time domain synchronous (TDS)-OFDM employs a known pseudo noise (PN) sequence as guard interval (GI). Conventional channel estimation methods for TDS-OFDM are based on the exploitation of the PN sequence and consequently suffer from intersymbol interference (ISI). This paper proposes a novel dataaided channel estimation method which combines the channel estimates obtained from the PN sequence and, most importantly, additional channel estimates extracted from OFDM data symbols. Data-aided channel estimation is carried out using the rebuilt OFDM data symbols as virtual training sequences. In contrast to the classical turbo channel estimation, interleaving and decoding functions are not included in the feedback loop when rebuilding OFDM data symbols thereby reducing the complexity. Several improved techniques are proposed to refine the data-aided channel estimates, namely one-dimensional (1-D)/two-dimensional (2-D) moving average and Wiener filtering. Finally, the MMSE criteria is used to obtain the best combination results and an iterative process is proposed to progressively refine the estimation. Both MSE and BER simulations using specifications of the DTMB system are carried out to prove the effectiveness of the proposed algorithm even in very harsh channel conditions such as in the single frequency network (SFN) case.

An Improved MMSE Pre-Coding Method for the Downlink Multi-User MIMO System

Recently many practical downlink multi-user MIMO linear pre-coding methods have been proposed, such as the channel inversion method and the block diagonalization method (BD). Considering the channel inversion method based on MMSE criterion (MMSE-CI) which is confined to a single receives antenna case, the BD has more advantages in multiple antennas cases, however, it has poor performance at the low and medium SNR regime on account of no consideration on the noise. In this paper, an improved MMSE pre-coding method is proposed with multi receive antennas of each user. Based on MMSE-CI, the cooperation of multiple antennas is adopted to further suppress the residual interference during designing the pre-coding matrix, which could increase the signal-to- interference-plus-noise ratio (SINR) at each user’s receiver. The proposed method obtains a better performance than the MMSE-CI and the BD algorithms, and its effectiveness is validated by both theoretical analyses and numerical simulations.

An Improved MMSE Pre-Coding Method for the Downlink Multi-User MIMO System

Recently many practical downlink multi-user MIMO linear pre-coding methods have been proposed, such as the channel inversion method and the block diagonalization method (BD). Considering the channel inversion method based on MMSE criterion (MMSE-CI) which is confined to a single receives antenna case, the BD has more advantages in multiple antennas cases, however, it has poor performance at the low and medium SNR regime on account of no consideration on the noise. In this paper, an improved MMSE pre-coding method is proposed with multi receive antennas of each user. Based on MMSE-CI, the cooperation of multiple antennas is adopted to further suppress the residual interference during designing the pre-coding matrix, which could increase the signal-to- interference-plus-noise ratio (SINR) at each user’s receiver. The proposed method obtains a better performance than the MMSE-CI and the BD algorithms, and its effectiveness is validated by both theoretical analyses and numerical simulations.

Complex Generalized Basis Reduction Assisted Successive Interference Cancellation Detection for SCBLAST Systems

Complex generalized basis reduction assisted successive interference cancellation is proposed for mitigating multi-stream interference of transmitted signals in single code Bell Laboratories layered space-time systems. Generalized basis reduction method is modified to better the complex channel matrix, which leads to the extended generalized reduction basis channel matrix with shorter and roughly orthogonal basis vectors in polynomial-time. This distinguished property guarantees the concatenated successive interference cancellation detector, based on the MMSE criterion, converges to the approximately global optimum estimation points. Emulation results have shown that the proposed detection scheme is superior to other suboptimum detection schemes considered in this paper in terms of two points. They are the mitigation of multi-stream interference and the diversity gain. Its performance is close to the sphere decoder but with a lower complexity.

Performance of MMSE Receiver based Multi Input Multi Output-Interleave Division Multiple-Access System with Multi-user Detection over Frequency Selective Wireless Communication Channel

Problem statement: This study presents the performance analysis of turbo assisted Interleave Division Multiple-Access (IDMA) system with Multi Input Multi Output (MIMO) support for multi user scenario over correlated frequency selective and uncorrelated frequency selective channel. Approach: The key principle of IDMA is that interleaver unique which distinguishes the users in contrast to spreading sequence in Code Division Multiple Access System (CDMA). Results: In this work, we assume that Interleavers are generated independently and randomly. At the receiver, we employed Ordered SIC (OSIC) technique using ZF and MMSE criterion to combat Inter Antenna Interference (IAI) and Multi User Interference (MUI) problem along with iterative decoding to improve the performance in terms of BER. The performance of system has been discussed for different channel conditions with realistic channel model using extensive simulation runs based on Monte Carlo simulation trials. We have exhibited the flexibility and robustness provided by MIMO-IDMA. Conclusion/Recommendations: It has been proved from the results that IDMA principle can be applied to realize many potential performance gains highlighted by information theory, including coding gain multiplexing gain and multiuser gain. Simulation results presented to demonstrate the benefits of IDMA with MUD and iterative decoding. It is discerned that IDMA performs better than CDMA in frequency selective channel for high load conditions which is assessed through computer simulation results.

MMSE-BLE Algorithm of Single-Carrier Multi-User Channel Capacity

A kind of minimum mean square error linear equalizer (MMSE-BLE) algorithm is presented for the solution on channel capacity of single-carrier code division multiple accesses (SC-CDMA) system, this algorithm received data symbol vector multiplied by covariance matrix by using Wiener estimator, and gets the decorrelation of multiple access interference (MAI), inter-symbol interference (ISI) and noise. MMSE-BLE algorithm calculates the channel capacity with MMSE criterion algorithm, so that it can analyze the multi-user uplink channel capacity of space-time coding SC-CDMA system under the multipath conditions effectively. The simulation results show that the number of user, path, transmitting and receiving antennas, multipath diversity gain, etc. All of them have an impact on the capacity of multi-user system, it seems that multiple antennas should be used for reception to get single-path diversity gain in frequency selective channels.

Lattice-reduction-aided MMSE equalization and the successive estimation of correlated data

Over the last years, novel low-complexity approaches to the equalization of MIMO channels have gained much attention. Thereby, methods based on lattice basis reduction are of special interest, as they achieve the optimum diversity order. In this paper, a tutorial overview on LRA equalization optimized according to the MMSE criterion is given. It is proven that applying the zero-forcing BLAST algorithm to a suitably augmented channel matrix – the inverse of the square root of the correlation matrix of the data symbols times the noise variance forms its lower part – results in the optimum solution. This fact is already widely used but lacks a formal proof. It turns out that it is more important to take the correlations of the data correctly into account than what type of lattice reduction actually is used.

Joint Tomlinson–Harashima Source and Linear Relay Precoder Design in Amplify-and-Forward MIMO Relay Systems via MMSE Criterion

Existing minimum-mean-square-error (MMSE) transceiver designs in amplify-and-forward (AF) multiple-input-multiple-output (MIMO) relay systems all assume a linear precoder at the source. Nonlinear precoders in such a system have yet to be considered. In this paper, we study a nonlinear transceiver in AF MIMO relay systems in which a Tomlinson-Harashima (TH) precoder is used at the source, a linear precoder is used at the relay, and an MMSE receiver is used at the destination. Since two precoders and three links are involved, the transceiver design, which is formulated as an optimization problem, is difficult to solve. We first propose an iterative method to overcome the problem. In the method, the two precoders are separately optimized in an iterative step. To further improve the performance, we then propose a non-iterative method that can yield closed-form solutions for the precoders. This method uses the primal decomposition technique in which the original optimization can first be decomposed into a master and a subproblem optimization. In the subproblem, the optimum source precoder is solved as a function of the relay precoder. In the master problem, the optimization is then transferred to a relay-precoder-only problem. However, the optimization is not convex, and the primal decomposition cannot be directly applied. We then propose cascading a unitary precoder after the TH precoder so that the optimization in the subproblem and the master problem can be conducted. Furthermore, using a relay precoder structure, we can transfer the master problem to a convex optimization problem and obtain a closed-form solution by the Karuch-Kuhn-Tucker (KKT) conditions. Simulations show that the proposed transceivers can significantly outperform existing linear transceivers.

A Near-Optimum Multiuser Receiver for STBC MC-CDMA Systems Based on Minimum Conditional BER Criterion and Genetic Algorithm-Assisted Channel Estimation

The implementation of efficient baseband receivers characterized by affordable computational load is a crucial point in the development of transmission systems exploiting diversity in different domains. This would be a crucial point in the future development of 4G systems, where space, time, and frequency diversity will be combined together in order to increase system throughput. In this framework, a linear multiuser detector for MC-CDMA systems with Alamouti's Space-Time Block Coding (STBC), which is inspired by the concept of Minimum Conditional Bit Error Rate (MCBER), is proposed. The MCBER combiner has been implemented in adaptive way by using Least-Mean-Square (LMS) optimization. The estimation of Channel State Information (CSI), necessary to make practically feasible the MCBER detection, is aided by a Genetic Algorithm (GA). The obtained receiver scheme is near-optimal, as both LMS-based MCBER and GA-assisted channel estimation perform closely to optimum in fulfilling their respective tasks. Simulation results evidenced that the proposed receiver always outperforms state-of-the-art receiver schemes based on EGC and MMSE criterion exploiting the same degree of channel knowledge.

Who will be eligible? An investigation of the dementia population eligible for cholinesterase treatment following the change in NICE guidance

Investigate the impact of the changes in eligibility within England and Wales (E&W) for prescription within the UK National Health Service for treatment of Alzheimer's disease (AD). A population-based study in England and Wales with 13,004 individuals measured with MMSE at baseline was used to examine the distributions of individuals within eligibility criteria. Information obtained from informants enabled classification of the study defined dementia cases to ICD10 diagnosis of subtype (AD, dementia with vascular risk, both or other). Fifty six per cent of dementia patients (representing 323,000 individuals in E&W) fall into the new MMSE criteria band. A further 120,000, 20% of dementia patients, are estimated to have disease that is considered too mild for treatment. Further examination of type of dementia showed that those with mixed AD and vascular dementia had similar proportions of dementia cases within the treatable MMSE group as the subgroup with AD alone, though with mixed disease individuals more often score below the lower threshold. There is substantial instability in the eligibility groupings over a short time period. The population impact of new NICE criteria of excluding high MMSE scores is to exclude one in five individuals with AD and a further one in ten of those with a mixed disease. Changing the guidance has almost balanced the loss of treatment for the high MMSE group (13%) with the introduction of treatment for those scoring 10/11 (11%).

An Estimation Method for InSAR Interferometric Phase Based on MMSE Criterion

In this paper, we propose a method based on minimum mean squared error (mmse) criterion to estimate synthetic aperture radar interferometry (InSAR) interferometric phase. In this method, the cross-correlation coefficient vector with large coregistration error is given first, and then, the cost function under the mmse criterion is used to estimate the InSAR interferometric phase. The method can auto-coregister the SAR images and reduce the interferometric phase noise simultaneously. Theoretical analysis and computer simulation results show that the method can provide an accurate estimate of the terrain interferometric phase (interferogram) even when the coregistration error reaches 1 pixel.

Joint source/relay precoder design in nonregenerative cooperative systems using an MMSE criterion

This paper considers transmitter precoding in an amplify-and-forward cooperative system where multiple antennas are equipped at the source, the relay, and the destination. Existing methods for the problem only consider the design of the relay precoder. To further improve the performance, we include the source precoder into the design. Using a minimum-meansquare- error (MMSE) criterion, we propose a joint source/relay precoder design method, taking both the direct and relay links into account. It is shown that the MMSE is a highly nonlinear function of the precoding matrices, and a direct minimization is not feasible. To facilitate analysis, we propose to design the precoders toward first diagonalizing the MSE matrix of the relay link. This imposes certain structural constraints on both precoders that allow us to derive an analytically tractable MSE upper bound. By conducting minimization with respect to this bound, the solution can be obtained by an iterative water-filling technique.

Optimal and robust waveform design for MIMO radars in the presence of clutter

Waveform design for target identification and classification in MIMO radar systems has been studied in several recent works. While the previous works assumed that the noise was independent of the transmission signals, here we extend the results to the signal dependent noise (clutter). We consider two scenarios. In the first scenario it is assumed that different transmit antennas see uncorrelated aspects of the target. In the second scenario, we consider the correlated target. As clutter is dependent to signal, target estimation error cannot vanish only by increasing the transmission power. It can be shown that in the second scenario, MIMO radar receiver can nullify the clutter subspace. Thus, in the second scenario, target estimation error tends to zero if the transmission power tends to infinity. We consider waveform design problem for these scenarios based on MMSE and MI criteria. Like previous works, we find that these criteria lead to the same solution. Our problems lead to the convex optimization problems, which can be efficiently solved through tractable numerical methods. Closed-form solutions are also developed for this SDP problem in two cases. In the first case, target and clutter covariance matrices are jointly diagonalizable and in the second, signal to noise ratio (SNR) is assumed to be sufficiently high. We also present two suboptimal formulations which require less knowledge of the statistical model of the target. In the first one the robust waveforms are computed by minimizing the estimation error of the worst-case target realization and in the second, target estimation error of the scaled least square (SLS) estimator is minimized.

Iterative Channel Estimation in MIMO Antenna Selection Systems for Correlated Gauss-Markov Channel

We address the issue of MIMO channel estimation with the aid of a priori temporal correlation statistics of the channel as well as the spatial correlation. The temporal correlations are incorporated to the estimation scheme by assuming the Gauss-Markov channel model. Under the MMSE criteria, the Kalman filter performs an iterative optimal estimation. To take advantage of the enhanced estimation capability, we focus on the problem of channel estimation from a partial channel measurement in the MIMO antenna selection system. We discuss the optimal training sequence design, and also the optimal antenna subset selection for channel measurement based on the statistics. In a highly correlated channel, the estimation works even when the measurements from some antenna elements are omitted at each fading block.

Cooperation over frequency-selective fading relay channels

We study information-rate calculations and coded cooperation strategies for relay channels with frequency-selective (FS) fading. We develop suitable channel trellises for the multiaccess and broadcast parts of the relay channel, and employ simulation-based techniques to calculate (approximate) ergodic information-rate bounds with FS Rayleigh fading. Our results show that frequency selectivity provides higher information rates than flat fading when the fading coefficients are known at the receiver, however, the improvement becomes marginal with increasing number of channel taps (when the overall signal to noise ratio is kept constant). Furthermore, we develop a distributed turbo-coding strategy and several decode-and-forward type detection/decoding schemes to ensure successful cooperative communication where the source and the relay may transmit simultaneously. We show that with suitable coding and iterative decoding, one can approach the approximate information-rate limits closely, and that detection schemes based on MMSE criterion provide a good performance/complexity trade-off.

ADAPTIVE TURBO-EQUALIZER DESIGN FOR MULTI-USER MOBILE COMMUNICATION CHANNEL

Broadband single carrier modulated signals experience severe multipath distortion scrambling & ISI when propagating through physical medium. Correcting the distortion with channel equalization is the foremost task of the detector. Prior information about the transmitted signals in the form of channel decoder feedback can significantly enhance equalization accuracy. An algorithm that iteratively performs channel decoding and equalization with prior information is generally denoted turbo-equalizer. Turbo-Equalizer uses prior information & the principle of interference cancellation by MMSE criterion. Here we have tested Adaptive Turbo Equalization with least Mean Square Algorithm (LMS) & modified normalized LMS algorithm & Turbo-Decoding with a Log-Map. Consequently the Mean Square Error analysis, Stability analysis and convergence analysis are provided and its shown if the system is sparse, then the system will converge faster for a given total asymptotic MSE, though the choice of initialization is important. Here all the Implementation concepts have been verified in MATLAB platform and evaluation of the proposal is presented. The measurement for the performance is displayed as bit error rates (BER) in comparison to SNR of the Channel.

A two-stage MMSE multiuser decision feedback detector using successive/parallel interference cancellation

In this paper, we present a novel two-stage minimum-mean-squared-error (MMSE) multiuser decision feedback detector (DFD) for code division multiple access systems working in the frequency-selective multipath fading environment. The first stage of the proposed cascaded structure is the noise-predictive successive DFD (NP-S-DFD), in which the active users are detected successively using the conventional bell labs layered space-time (BLAST) ordering criterion. The second stage includes an adaptive successive/parallel DFD (SP-DFD), which uses the tentative decisions obtained at the first stage for multiuser interference cancellation and data detection. Therefore, the proposed two-stage DFD may be called noise-predictive successive SP-DFD (NP-S-SP-DFD). Simulation results are presented to demonstrate the substantial improvement in the bit error rate performance of NP-S-SP-DFD over the conventional single-stage and cascaded DFDs. It may be inferred that the proposed DFD provides additional performance gain, when the order in which the users are detected is optimized according to the BLAST ordering based on MMSE criterion.

New concatenated coding and space–time modulation scheme for MIMO wireless communications

Zheng and Tse have demonstrated that there exists an optimal trade-off between diversity gain and multiplexing gain. To realise the predicted optimal trade-off, we propose a new multiple-input multiple-output transmission scheme for a concatenated coding and space–time (ST) modulation system aimed at applications that require flexible trade-off between performance and data rate. The proposed scheme is multi-layered with linear ST modulation to allow various multiplexing gain. Through a judicious design of the inner ST modulation, the optimisation of spatial multiplexing is made simple. Moreover, a joint iterative receiver based on MMSE criterion with a priori information is developed to reduce computational complexity. Simulation results are provided to demonstrate the merits of the new design.