Minimum Mean Square Error Scheme Research Articles

Resource efficiency and pilot decontamination in XL‐MIMO double‐scattering correlated channels

AbstractIn extra‐large scale massive MIMO (XL‐MIMO) systems, due to the large antenna array physical dimensions, the received signal at the base‐station (BS) results in spatial non‐stationarities and visibility regions (VRs), limited regions of the array which are visible to the users equipments (UEs). In crowded XL‐MIMO scenarios, the reuse of pilot sequences is a path to provide massive connectivity, principally when the radio resources are scarce. However, such reuse increases the intra‐cell interference, since UEs sharing the same pilot sequences may have overlapped VRs. Thus, despite the minimum mean‐squared error (MMSE) combiner having a high computational complexity, its capability in mitigating the pilot contamination, and even in eliminating such effect in asymptotic antenna regime, justify its use to provide massive connectivity with high spectral efficiency (SE). In this work, we evaluate the performance of the MMSE combiner in XL‐MIMO systems in terms of the SE, energy efficiency (EE), resource efficiency (RE), and capability of eliminating the intra‐cell pilot contamination. The MMSE channel estimator is deployed to estimate the channel vectors. Indeed, the performance of the zero‐forcing combiner and the randomized Kaczmarz regularized zero‐forcing combiner is evaluated and compared with the MMSE scheme. For modeling the XL‐MIMO propagation channel, we use the double‐scattering channel model, which considers clusters of scatterers on both the BS‐side and the UE‐side to model the spatial channel correlation. In parallel, we develop the analysis considering the single‐scattering channel model, a useful simplification of the double‐scattering channel model. The numerical results reveal that, at the cost of a high computational complexity, the MMSE combiner achieves remarkable SE and EE results. However, such superior performance is limited by the number of antennas, being recommended for cases where the size of the VR (number of active antennas) is reduced.

MMSE channel estimation for two-port demodulation reference signals in new radio

Two-port demodulation reference signals (DMRS) have been employed in new radio (NR) recently. In this paper, we firstly propose a minimum mean square error (MMSE) scheme with full priori knowledge (F-MMSE) to achieve the channel estimation of two-port DMRS in NR. When the two ports are assigned to different users, the full priori knowledge of two ports is not easy to be obtained for one user. Then, we present a MMSE scheme with partial priori knowledge (P-MMSE). Finally, numerical results show that the proposed schemes achieve satisfactory channel estimation performance. Moreover, for both mean square error and bit error ratio metrics, the proposed schemes can achieve better performance compared with the classical discrete Fourier transform based channel estimation. Particularly, P-MMSE scheme delivers almost the same performance compared with F-MMSE scheme by a small amount of prior knowledge.

Fountain Codes and Linear Filtring to Mitigate Pilot Contamination Issue in Massive MiMo

The fifth generation of cellular mobile (5G) is a future technology to meet growing capacity of users. For this prupose 5G will use advanced technologies. Very large multi- input multi- output or massive MiMo (m-MiMo) is considered as one of the promising technology. Nevertheless, the performance of m-MiMo is limited by pilot contamination issue. In fact, to mitigate pilot contamination issues in massive multi-input multi-output (m-MiMo), we proposed in previous work a new scheme where Raptor decoded symbols are used to estimate channel with Minimum Mean Square Error (MMSE) technique. The main benefit of this method is that the receiver does not need a transmitted pilot symbols to evaluate the channel, which allows saving power at transmission. The results showed that the MMSE scheme achieved the ideal case of the perfect channel. In this precedent paper, the MMSE detector and raptor code are used for their robustness among other schemes of linear detectors, and corrector codes, nevertheless, in case of m-MiMO, it was shown that all linear detectors work optimally. For this purpose, we include in this present article an additional linear filter to enhance the prior study, in which two supplementary detectors are considered, namely Zero Forcing (ZF) and Maximum Ratio Compression (MRC). The objective of this paper is to determine the ideal filtering technique and the robustness fountain code to address pilot contamination problem. In fact, the simulation results show that the ZF can attain the same ideal performance as the MMSE with raptor decoded symbols while MRC achieved lower performance compared to the other two shemes. 

Joint MMSE transceiver design for downlink heterogeneous network

In this paper, we propose a minimum mean square error (MMSE) based transceiver design scheme for a downlink multiple-input multiple-output (MIMO) two-tier heterogeneous network with general linear equality per-cell power constraints. Three practical channel models with both perfect and imperfect channel state information are used in simulations. In each channel model, we consider two system configurations, two data transmission schemes and two cellular cooperation scenarios. Our study shows that the proposed MMSE scheme is more flexible than interference alignment (IA) based scheme. For the cases where the IA-type scheme is applicable, the proposed scheme generally outperforms IA-type scheme in terms of average sum rate and bit error rate (BER), but is computationally more complex than the IA-type scheme.

Design, Simulation & Concept Verification of 4 × 4, 8 × 8 MIMO With ZF, MMSE and BF Detection Schemes

AbstractA conventional MIMO system is designed consisting of 4 antenna elements at both the receiver and transmitter ends. Different kinds of signal detection techniques, namely, zero forcing (ZF), minimum mean square error (MMSE) and beamforming (BF), are used at the receiver end for signal detection. The performance of the system is analyzed by calculating BER vs SNR for each of the above techniques separately. The present work has been thoroughly analyzed and implemented using MATLAB. On the basis of the results obtained, it is summarized that as the values of SNR increase, BER decreases for ZF and MMSE and it almost vanishes to zero even for low SNR values if BF is used. Although ZF and MMSE are suitable for designing a conventional MIMO system with 4 antenna elements, it becomes too difficult for a large number of antenna elements due to its complexity of calculating the inverse of a (N×N) matrix. Based on the results analyzed so far, it is concluded that beamforming (BF) is a suitable technique for designing a system that has a large number of antenna elements at the base station. A further improved system with enhanced performance regarding lower BER for even smaller values of SNR is designed in the present study, consisting of 8 antennas at the base station. The results obtained are enthusiasm-provoking and encouraging for further studies to develop a concept for next-generation wireless communication systems with an optimum design.

On the Diversity of Linear Transceivers in MIMO AF Relaying Systems

In this paper, we provide a comprehensive survey on designs and analyses of various relay-destination transceiving schemes, such as zero-forcing (ZF), minimum mean squared error (MMSE), and maximum information rate (MIR) criteria, in multiple-input multiple-output (MIMO) amplify-and-forward (AF) relaying systems. In the first part of the paper, we suggest a new framework for the transceiver designs utilizing a decomposable property of the error covariance matrix to give a general insight on the system and make the analysis more tractable. Then, in the second part of the paper, we provide an in-depth analysis on their diversity performance. Our analysis embraces two different scenarios, namely, the diversity-multiplexing tradeoff (DMT) and the diversity-rate tradeoff (DRT). First, we derive compact closed-form expressions for the DMT through tight upper and lower bounds. Then, we observe that while our DMT analysis accurately predicts performance of the ZF and MIR schemes, the MMSE-based designs exhibit a complicated rate-dependent behavior and, thus, are very unpredictable via DMT for finite rate cases. Thus, second, we highlight this interesting observation and characterize the diversity of the MMSE schemes at all finite rates. This leads to closed-form expressions for the DRT which reveals relationship between diversity, spectral efficiency, and the number of antennas at each node. The DRT analysis compliments our work on DMT, and thus, the paper provides a complete understanding on the diversity of MIMO AF relaying systems.

Minimizing performance loss of MMSE algorithm for CDMA-based O-MIMO-OFDM

This paper presents an algorithm to minimize the performance loss (PL) of minimum mean square error (MMSE) in code division multiple access (CDMA) based optical multiple input multiple output orthogonal frequency division multiplexing (O-MIMO-OFDM) systems over 1200km of standard single mode fiber (SSMF). The performance of the system using proposed algorithm scheme is compared to MMSE scheme by simulation results. It shows the superior performance of proposed algorithm.

Performance analysis of D-BLAST aided Turbo Encoded SC-FDMA wireless communication system

In this paper, an effort has been to assess critically the performance of a punctured Turbo channel coded SC-FDMA wireless communication system under consideration of Diagonal Bell Laboratories Layered Space Time (D-BLAST) architecture. The proposed system under investigation adopts MIMO technique with 4 × 4 antenna configuration. Various channel equalization schemes such as Minimum mean square error (MMSE), Zero-Forcing (ZF), ZF-SIC, MMSE-SIC, Lattice Reduction-Based ZF and Lattice Reduction-Based MMSE Scheme have been used. From MATLAB based simulated study on synthetically generated binary data transmission, it is found that the system shows its improved and robust performance in perspective of QAM digital modulation and Lattice Reduction-Based MMSE Scheme.

Belief propagation-based joint iterative algorithm for detection and decoding in asynchronous CDMA satellite systems

As the geostationary orbit (GEO) is congested in the commercial Ku band, the adjacent satellites will receive the interference from small aperture terminals which have a wide field of view. To reduce the interference toward the adjacent satellites, code division multiple access (CDMA) with spread spectrum needs to be adopted in the satellite communications on-the-move system. However, the mutual interference between CDMA users leads to the performance loss, which is not acceptable for the power-sensitive small aperture terminals, and the computation complexity is still an intractable problem when the conventional iterative minimum mean square error (MMSE) scheme is employed to suppress the multiple access interference (MAI) in satellite systems especially that is coded by low-density parity-check (LDPC) code. Moreover, the long transmission delays of different users caused by the long transmission distance require the robustness of the interference suppression for the asynchronous case. In this paper, a joint chip-level algorithm for CDMA multiuser detection and LDPC decoding with a new and simple iterative structure based on belief propagation (BP) for satellite systems is developed, which integrates the iterations of multiuser detection and the iterations of LDPC decoding with factor graphs. Through analysis and simulations, it is verified that the proposed algorithm is robust to the asynchronous CDMA satellite system, and with the similar iterative complexity, the performance of the proposed algorithm outperforms that of the conventional iterative MMSE scheme in the asynchronous CDMA satellite system.

Wireless MIMO switching: network‐coded MMSE relaying and user group selection

ABSTRACTA wireless relay that forms a one‐to‐one mapping from the inputs (uplinks) to the outputs (downlinks) is called a multiple‐input multiple‐output (MIMO) switch. The MIMO switch carries out precode‐and‐forward, where all users send their signals in the uplink, and then, the MIMO switch precodes the received vector signal for broadcasting in the downlink. Ideally, each user employs a receive filter to recover its desired signal from one other user with no or little interference from other users. We first propose a joint design of the precoder and the receive filters to achieve the minimum‐mean‐ square‐error (MMSE), where network coding technique is incorporated, assuming that full channel state information is available at the relay. When the number of relay antennas is smaller than the number of source users, that is, the users that need to transmit signals, we investigate user group selection algorithms for the proposed MMSE relaying schemes. Our results indicate that the proposed MMSE relaying scheme outperforms the existing zero‐forcing/MMSE schemes. In addition, the results validate the efficiency of the proposed user group selection algorithms. Copyright © 2012 John Wiley & Sons, Ltd.

Equalization and Carrier Frequency Offsets Compensation for the SC-FDMA System

Recently, the Single-Carrier Frequency Division Multiple Access (SC-FDMA) system has attracted the attention as an efficient alternative to the Orthogonal Division Multiple Access (OFDMA) system in the uplink communications. In this system, the Carrier Frequency Offsets (CFOs) disrupt the orthogonality between subcarriers, and give rise to Inter-Carrier Interference (ICI), and Multiple Access Interference (MAI) among users. In this paper, the impact of the CFOs on the performance of the Discrete Fourier Transform SC-FDMA (DFT-SC-FDMA) and the Discrete Cosine Transform SC-FDMA (DCT-SC-FDMA) systems is investigated. Based on the Minimum Mean Square Error (MMSE) criterion, a new low-complexity joint equalization and CFOs compensation scheme is proposed. It is refered to as the MMSE scheme. The MMSE weights of the proposed scheme are derived taking into account the MAI and the noise. Furthermore, a hybrid scheme comprising the proposed MMSE scheme and a Parallel Interference Cancellation (PIC) stage is also suggested and investigated to further enhance the performance of interleaved subcarriers mapping systems. From the obtained simulation results, it is clear that CFOs disrupt the orthogonality between the subcarriers in SC-FDMA systems and degrade the Bit Error Rate (BER) performance. The proposed compensation schemes are able to enhance the system performance, even in the presence of the estimation errors.

Performance of Interference Cancellation Scheme for Multihop Military Communication Systems

In this paper, we analyze co-channel interference cancellation performance to be generated in multi-hop military communication system. First, remove interference using zero-forcing (ZF) and minimum mean square error (MMSE) scheme as interference cancellation methods, and then obtain additional diversity gain and improve interference cancellation performance by applying successive interference cancellation (SIC). We consider Rayleigh fading channel and system performance is analyzed as respect of bit error probability. From simulation results, we confirm MMSE improves significantly BER performance than ZF in multi-hop wireless network environment. It is also confirmed ZF and MMSE schemes applying SIC algorithm have better performance comparing to the existing schemes. Therefore, MMSE-SIC method can provide more reliable signal transmission in the multi-hop military communication system.

MMSE Based Transceiver Designs in Closed-Loop Non-Regenerative MIMO Relaying Systems

In this paper, we propose a new design strategy based on the minimum mean-squared error (MMSE) in closed-loop non-regenerative multiple-input multiple-output relaying systems. Instead of conventional singular value decomposition based methods, we address the problem for joint MMSE design in a different approach using the Wiener filter solution which leads to simple derivations of the optimal MMSE designs. First, allowing the channel state information (CSI) at the source, we provide a new closed form solution for a source-relay-destination joint MMSE design by extending existing relay-destination joint MMSE designs. Second, for the limited feedback scenario, we address a codebook design criteria for the multiple streams preceding design with respect to the MMSE criterion. From our design strategy, we observe that compared to conventional non-regenerative relaying systems, the source or the destination only needs to know the CSI corresponding to its own link such as the source-to-relay or the relay-to-destination in view of the MMSE. Simulation results show that the proposed design gives about 7.5 dB gains at a bit error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> over existing relay-destination joint MMSE schemes and we can get close to the optimal unquantized schemes with only a few feedback bits.

Hybrid detectors for wireless orthogonal frequency division multiplexing with code division multiplexing systems based on reliability information

Orthogonal frequency division multiplexing with code division multiplexing (OFDM-CDM) is attractive for the next generation high-speed wireless systems due to the fact that the performance of OFDM-CDM systems can be considerably improved by employing a joint detection scheme such as the maximum likelihood (ML) detector. However, the complexity of the ML detector increases rapidly as the number of orthogonal spreading codes and/or the number of bits per modulation symbol increase. In this study, the authors introduce a unified detection model and propose two hybrid detectors, which combine zero forcing (ZF) with successive interference cancellation (SIC) and sphere detection (SD) algorithms, respectively. After obtaining the initial solution from the front-end ZF receiver, the proposed back-end algorithms are adopted to extend the potential solution list and search for the final result. The objective is to utilise the combination of a simplified linear equaliser and a comprehensive detection scheme to achieve enhanced performance and offer alternatives to the more complex and channel-estimation-sensitive minimum mean squared error (MMSE) scheme. The results show that the proposed hybrid detectors are able to achieve superior performance compared to the MMSE scheme and provides a significant performance improvement compared to the conventional OFDM counterpart.

Intercarrier Interference Suppression for OFDMA Uplink in Time- and Frequency-Selective Fading Channels

This paper investigates intercarrier interference (ICI) suppression and channel estimation for the uplink of an orthogonal frequency-division multiple-access (OFDMA) system in a time- and frequency-selective fading channel. In such a doubly selective channel, channel variations within each OFDMA block disrupt the orthogonality among subcarriers and leads to ICI. We develop an appropriate signal model for the OFDMA uplink in a doubly selective fading channel and propose a minimum mean square error (MMSE) scheme and an MMSE successive detection (MMSE-SD) scheme to suppress ICI. It is shown that the MMSE scheme is the optimal linear scheme in terms of maximizing achievable data rate and that the MMSE-SD scheme is able to further remove ICI and exploit the Doppler diversity embedded in time-varying channels. As an essential component in ICI suppression, channel estimation is also considered. A basis expansion model (BEM) is formulated for the OFDMA uplink channel, and a pilot-aided channel-estimation algorithm is developed to track users' channels in the time domain. Simulation results are presented to illustrate the overall performance improvements that can be obtained from using the proposed ICI suppression and channel-estimation schemes.

주파수 선택적 시변 채널 OFDM 시스템에서의 파일럿 심볼을 이용한 채널 예측 및 등화

본 논문에서는 주파수 선택적 시변 채널 OFDM 시스템에서 파일럿 심볼을 이용하는 채널 예측 및 등화 방식의 성능을 분석하고 문제점 및 개선 방안을 제시한다. 주파수 영역 채널 행렬의 대역폭을 제한하기 위하여 시간 영역 윈도우를 도입하며, 채널 예측에 LS(Least Square) 및 선형 MMSE(Minimum Mean Square Error) 예측 방식을 이용한다. 채널 등화에는 채널 예측에 이용되는 파일럿 심볼의 존재가 고려된 선형 MMSE 및 결정 귀환 등화 방식을 이용한다. 계산량을 감소시키기 위하여 채널 등화 알고리즘에 요구되는 선형 연립 방정식의 풀이에 band LU 행렬 분해 알고리즘을 도입하며, 컴퓨터 시뮬레이션을 통하여 기존 방식과의 성능을 비교한다. 결정 귀환 등화 방식에 시간 영역 윈도우를 적용하는 경우, 결정 귀환 관련 행렬의 대역폭이 제한되지 않아 성능이 저하되는 문제점을 분석하였다. In this paper, we analyze the performance of pilot symbol assisted channel estimation and equalization schemes for OFDM systems over frequency-selective time-varying channels and propose methods to improve the system performance. In the least square(LS) and linear minimum mean square error(MMSE) channel estimation, time domain windowing is introduced for banding the frequency domain channel matrix. The linear MMSE and decision feedback equalization schemes are employed with the pilot symbols for channel estimation taken into account in the equalization process. To reduce computational complexity, the band LU matrix factorization algorithm is introduced in solving the linear systems involved in the equalization, and the performances are compared with the known previous results by computer simulations. When time domain windowing is employed in the decision feedback equalization, the matrix related with the decision feedback process is shown to be unhanded and the resultant performance degradation is analyzed.

Downlink MMSE Transceiver Optimization for Multiuser MIMO Systems: Duality and Sum-MSE Minimization

We address the problem of minimum mean square error (MMSE) transceiver design for point-to-multipoint transmission in multiuser multiple-input-multiple-output (MIMO) systems. We focus on the problem of minimizing the downlink sum-MSE under a sum power constraint. It is shown that this problem can be solved efficiently by exploiting a duality between the downlink and uplink MSE feasible regions. We propose two different optimization frameworks for downlink MMSE transceiver design. The first one solves an equivalent uplink problem, then the result is transferred to the original downlink problem. Duality ensures that any uplink MMSE scheme, e.g., linear MMSE reception or MMSE-decision feedback equalization (DFE), has a downlink counterpart. We propose two globally optimum algorithms based on convex optimization. The basic idea of the second framework is to perform optimization in an alternating manner by switching between the virtual uplink and downlink channels. This strategy exploits that the same MSE can be achieved in both links for a given choice of transmit and receive filters. This iteration is proven to be convergent.

Combined ML and MMSE Multiuser Detection for STBC-OFDM Systems

Performance of the minimum mean square error (MMSE) detection is far below that of the maximum likelihood (ML) detection in a multiuser environment and decreases significantly as the number of co-channel users increases. In this paper, we propose a combined MMSE and ML multiuser detection scheme for space-time block coded (STBC) orthogonal frequency division multiplexing (STBC-OFDM) which has improved performance but with low complexity. In particular, we propose a reduced complexity ML post-detection (ML-PDP) scheme which can correct erroneously estimated bits from the outputs of MMSE multiuser detection. The proposed ML-PDP scheme performs sequential search to detect a predefined number of bits with higher probability of error and then uses ML detection to correct them. Upon controlling the number of corrected bits it is possible to balance the system performance with complexity associated with the ML-PDP. We show that significant improvement can be achieved at the cost of only small additional complexity compared with the MMSE multiuser detection.

On the Efficiency and Robustness of Discrete Proportional-Integral Control Schemes

Feedback control schemes have been widely used in process industries for many years. They are also increasingly being used in the discrete-parts manufacturing industry in recent years. Proportionalintegral (PI) schemes are especially popular, primarily because of their simple structure and ease of implementation. This article studies the efficiency and robustness properties of discrete PI schemes under some commonly encountered situations. For process disturbance, we consider the stationary ARMA (1, 1) model and the nonstationary ARIMA (1, 1, 1) model. Process dynamics is studied under a first-order dynamic model, including the special case of pure gain. The efficiency of PI schemes is compared with that of minimum mean squared error (MMSE) schemes under these models. The PI schemes are seen to be quite efficient over a broad range of the parameter space. Furthermore, the PI schemes are much more robust than MMSE schemes to model misspecihcations, especially the presence of first-order nonstationarity. The results here provide additional justification for the use of discrete PI schemes.

On the Efficiency and Robustness of Discrete Proportional-Integral Control Schemes

Feedback control schemes have been widely used in process industries for many years. They are also increasingly being used in the discrete-parts manufacturing industry in recent years. Proportionalintegral (PI) schemes are especially popular, primarily because of their simple structure and ease of implementation. This article studies the efficiency and robustness properties of discrete PI schemes under some commonly encountered situations. For process disturbance, we consider the stationary ARMA (1, 1) model and the nonstationary ARIMA (1, 1, 1) model. Process dynamics is studied under a first-order dynamic model, including the special case of pure gain. The efficiency of PI schemes is compared with that of minimum mean squared error (MMSE) schemes under these models. The PI schemes are seen to be quite efficient over a broad range of the parameter space. Furthermore, the PI schemes are much more robust than MMSE schemes to model misspecihcations, especially the presence of first-order nonstationarity. The results here provide additional justification for the use of discrete PI schemes.