Robust MMSE transceiver designs for uplink MIMO systems subject to arbitrary linear equality power constraints

Interference alignment (IA) is a multi-user wireless communication strategy that enables several transmitters simultaneous communicate with their paired receivers without interfering each other. IA is a multiplexing gain optimal strategy at the expense of requiring the global channel state information (CSI) at the transmitters. Most previous works assume the availability of perfect CSI which is not possible in practice. The performance of IA algorithms based on perfect CSI drop dramatically in circumstance where CSI errors exist. In this paper we propose a robust minimum mean square error (MMSE) IA algorithm with imperfect CSI. Based on a Gaussian statistic channel error model, we give the mean square error objective function with per transmitter power constraint. The objective function is not joint convex in precoders and decoders, but convex in precoders with fixed decoders and vice versa. We convert the problem to two convex sub problems and iteratively find the solutions. Numerical results are presented to validate the effectiveness of proposed algorithm when CSI errors exist.

This paper considers the uplink of a single-cell large-scale multiuser multiple-input multiple-output (MU-MIMO) system. The transmitted data is detected by linear receivers at the base station (BS), that is, maximum ratio combining (MRC), zero-forcing (ZF) and minimum mean square error (MMSE). New non-asymptotic outage expressions that are valid for any number of BS antennas are derived. It is shown that the MMSE scheme always achieves the best outage performance, and the ZF scheme outperforms the MRC scheme in the high signal-to-noise-ratio (SNR) regime, while the opposite holds in the low SNR regime. We also demonstrate that when the number of BS antennas is very large and the number of users is fixed, the asymptotic outage probability tends to zero, providing that the channel state information (CSI) is perfect. However, if both the number of BS antennas and the number of users grow large, it would be a different matter. Extensive numerical results are presented to verify the theoretical analysis.

Multiple-input multiple-output (MIMO) systems can achieve high data-rate and high capacity transmission. In MIMO systems, the scheme that weight substreams based on minimum mean square error (MMSE) criterion at the transmitter using feedback channel state information (CSI) achieves good performance (denoted hereafter as MMSE precoder). However, if the optimum number of substreams is not selected based on CSI and methods for reducing the performance degradation due to feedback delay is not used, MMSE precoder cannot achieve the full performance possible. In this paper, we propose an MMSE precoder with mode selection for MIMO systems, which selects both the number of substreams and the modulation scheme for each substream to minimize the average BER at a fixed rate. We evaluate the BER of the proposed MMSE precoder with two methods for reducing performance degradation due to feedback delay, channel prediction and receive weight robust to feedback delay. We also evaluate the BER of the proposed MMSE precoder with the method that combines channel prediction with receive weight robust to feedback delay. Simulation results show that the BER of the proposed MMSE precoder is improved compared to that of the conventional MMSE precoder using the fixed number of substreams. We also show that the method that combines channel prediction with receive weight robust to feedback delay can achieve good BER even when the large feedback delay exists.

In systems employing pilot-symbol aided channel estimation, the pilot-to-data power ratio is known to have a large impact on performance. Therefore, previous works proposed methods setting the pilot power such that either the weighted sum of the mean squared error (MSE) of the estimated data symbols is minimized or the overall spectral efficiency (SE) is maximized. However, previous works did not take into account the impact of correlated antennas and channel state information (CSI) errors on the optimal pilot power setting. In this paper, we consider the uplink of a multiuser multiple-input multiple-output (MU MIMO) system employing a receiver that minimizes the MSE of the received data symbols in the presence of CSI errors and derive closed-form expressions for the MSE and the achievable SE. These expressions take into account the impact of antenna correlation and CSI errors, and are a function of pilot power and the number of receive antennas. The analytical and numerical results can help set the pilot power, minimizing the MSE in multiple antenna systems.

Multi-user multiple-input multiple-output (MU-MIMO) systems in the indoor visible light communication (VLC) have attracted significant attention due to the use of the lighting-emitting diodes (LEDs) for illumination and communication. However, they experience performance degradation due to interference from multiple users and low modulation bandwidth requiring the development of mitigation techniques. This work proposes a joint transceiver design using the minimum mean square error (MMSE) to minimize interference for the VLC systems. The mean square error (MSE) is minimised assuming perfect channel state information (CSI) to suppress the interference. The developed results show the proposed transceiver design providing fair data transmission and improving the bit error rate (BER) over the zero-forcing (ZF) scheme. Moreover, the proposed transceiver design shows better convergence than the ZF scheme.

In this paper, we design a zero-forcing (ZF) Tomlinson-Harashima precoding (THP) and a minimum mean square error (MMSE) THP for multiuser MIMO relay system with direct link. Based on these precoding structures, we propose the optimal combining weights of the ZF THP and the MMSE THP in half duplex relay system, and the sub-optimal weights of MMSE THP to reduce feedback channel state information (CSI). Through the Monte Carlo simulation, we verify that the optimal weights combining method outperforms the constant weights combining method. In addition, we confirm that the performance of the sub-optimal weights combining method is close to the optimal method, while reducing the feedback CSI simultaneously.

In this paper, we consider a new design problem of optimizing a linear transceiver for correlated multiple-input multiple-output (MIMO) interference channels in the presence of channel state information (CSI) errors, which is a more realistic and practical scenario than those considered in the previous studies on uncorrelated MIMO interference channels. By taking CSI errors into account, the optimization problem is initially formulated to minimize the average mean square error (MSE) under the general power constraints. Since the objective function is not jointly convex in precoders and receive filters, we split the original problem into two convex subproblems, and then linear precoders and receive filters are obtained by solving two subproblems iteratively. It is shown that the proposed algorithm is guaranteed to converge to a local minimum. The numerical results show that the proposed algorithm can significantly reduce the sensitivity to CSI errors compared with the existing robust schemes in the correlated MIMO interference channel.

Free space optical communication (FSO) is widely deployed to transmit high data rates for rapid communication traffic increase. Asymmetrically clipped optical orthogonal frequency division multiplexing (ACO-OFDM) modulation is a very efficient FSO communication technique in terms of transmitted optical power. However, its performance is limited by atmospheric turbulence. When the channel includes strong turbulence or is non-deterministic, the bit error rate (BER) increases. To reach optimal performance, the ACO-OFDM decoder needs to know accurate channel state information (CSI). We propose novel detection using different deep learning (DL) algorithms. Our DL models are compared with minimum mean square error (MMSE) detection methods in different turbulent channels and improve performance especially for non-stationary and non-deterministic channels. Our models yield performance very close to that of the MMSE estimator when the channel is characterized by weak or strong turbulence and is stationary. However, when the channel is non-stationary and variable, our DL model succeeds in improving the performance of the system and decreasing the signal to noise ratio (SNR) by more than 8 dB compared to that of the MMSE estimator, and it succeeds in recovering the received data without needing to know accurate CSI. Our DL decoders also show notable speed and energy efficiency improvement.

The time reversal (TR) technique combined with the ultra-wideband (UWB) system offers a new potential for decreasing the cost and complexity of the UWB receivers. In spite of TR–UWB's good performance in perfect channel state information (CSI), it is very sensitive to the channel estimation error. The effect of channel imperfection on the TR–UWB system is considered in this paper. At first, based on a minimum mean square error (MMSE) equalizer receiver, a prefilter is calculated in closed form to improve the performance of the TR–UWB system in an imperfect CSI scenario. Furthermore, for comparison purposes, a similar calculation for prefilter is carried out based on a simple matched filter (MF) receiver. Then, in order to improve the MF receiver performance, a two-stage iteration-based algorithm is developed. The initial value for this iteration-based improved algorithm is considered to be a prefilter which is calculated in the TR–UWB system with MMSE equalizer. This optimized algorithm causes the channel estimation error in the TR–UWB system to become zero in some steps. Finally, exhaustive simulations are done to demonstrate the performance advantage attained by the improved algorithm.

Multiple transmit antennas can be employed in a downlink channel to serve multiple users under the assumption of perfect channel state information (CSI) of all users at the base station. In practice, however, the channel knowledge available at the base station is not perfect. For instance, in case of a time division duplex (TDD) system, the transmit CSI is the estimated uplink channel. On the other hand, in a frequency division duplex (FDD) system, feedback from the users is required to obtain transmit CSI. In this case, we assume the transmit CSI consists of a quantized version of the normalized estimated channel vector and the statistics of the channel norm of each user. In this work we consider the transceiver design of the downlink of a multiuser MISO system based on the minimum mean square error (MMSE) criterion with imperfect CSI as discussed above.

Tomlinson Harashima Precoding (THP) for Multi-User Multiple Input Multiple Output (MU-MIMO) system has been proposed as an effective way to achieve near capacity to the theoretical limit in MU-MIMO channels. In order to achieve better performance, other THP methods such as minimum mean square error (MMSE) THP and lattice reduction aided (LRA) THP are proposed. Those methods outperform the conventional THP, however, the computational complexity also increases. In this paper, we propose a modified THP by new approach using square root with less increase of computational complexity. Computer simulation shows that proposed method can achieve better trade-off between bit error rate and computational complexity than MMSE THP and LRA THP.

In this letter, we study and present the performance of multi-user transmitter preprocessing (MUTP) assisted downlink (DL) communications, where the channel state information (CSI) required at the transmitter to carry out the MUTP is estimated at the receiver, and conveyed to the base station (BS) with the aid of a noisy feedback channel that undergoes fading as well. In particular, the CSI is estimated with a known channel estimation technique, and the phases and magnitudes of the CSI are vector quantized and fed back to the transmitter via a fading feedback channel. This vector quantized CSI which is also corrupted by noise is recovered with the aid of a minimum mean square error (MMSE) based hard detector. The recovered CSI is then exploited to formulate the preprocessing matrix which is based on creating an orthogonal subspace to the interfering subspace. Our simulations show that the impact of codebook size and quantization errors play a dominant role in determining the performance of the considered DL system in terms of the achievable symbol error rate (SER).

We address the problem of transmit beamforming under channel uncertainty for a multiuser (MU), single carrier frequency domain equalization multiple input multiple output (SC-FDE-MIMO) system. SC-FDE-MIMO scheme is effective solution with relative low complexity to combat inter -symbol interference (ISI) whilst exploiting multi antennas diversity gain. In our system, the signal to leakage ratio (SLR) criterion is used to design the transmit beamformer and the minimum mean square error (MMSE) criterion is employed for the receiver equalization and combining. Non-robust beamforming techniques require perfect channel state information (CSI) knowledge which is not available in practice. In this paper, we propose a robust transmit beamformer which can successfully tolerate CSI imperfection. Diagonal loading is employed to introduce robustness to channel state information errors. The novelty of this work, however, is the application of the robust beamforming in the context of downlink MU-SC transmission. Average bit error (BER) simulations are presented to verify the efficiency of the proposed method.

In this work, we propose a minimum mean squared error (MMSE) robust base station (BS) precoding strategy based on switched relaying (SR) processing and limited transmission of side information for interference suppression in the downlink of multiuser multiple-input multiple-output (MIMO) relay systems. The BS and the MIMO relay station (RS) are both equipped with a codebook of interleaving matrices. For a given channel state information (CSI) the selection function at the BS chooses the optimum interleaving matrix from the codebook based on two optimization criteria to design the robust precoder. Prior to the payload transmission the BS sends the index corresponding to the selected interleaving matrix to the RS, where the best interleaving matrix is selected to build the optimum relay processing matrix. The entries of the codebook are randomly generated unitary matrices. Simulation results show that the performance of the proposed techniques is significantly better than prior art in the case of imperfect CSI.

The IEEE802.11a standard for indoor wireless LAN systems was released commercially and is wide spread in the marketplace. To achieve higher throughput, IEEE802.11n was proposed and is now undergoing standardization. The MIMO-OFDM technique, which employs multiple antennas for transmission and reception, is the core technology for IEEE802.11n (Foshini and Gans, 1998). This technique requires estimation of channel state information (CSI) on the receiving side. Using the technique called adaptive MIMO-OFDM (Telatar, 1999) in which CSI is applied to both the transmitting and receiving sides, an even higher throughput is achieved. To achieve the maximum performance from adaptive MIMO-OFDM, we must accurately estimate the CSI for all the subcarriers; however, numerous calculations are needed to obtain this estimation. So, to actualize the adaptive MIMO-OFDM system, the calculation load must be decreased. This can be accomplished by applying one CSI to other subcarriers. However, channel error exists between the actual channel and the applied CSI. The channel error also plays a role in decreasing the communications quality (Medard, 2000). The communications quality when using the adaptive MIMO-OFDM technique that has CSI error was evaluated by simulation (Narula et al., 1998). However, there are few measurement evaluation reports on CSI error. This paper focuses on the ratio between the power of the eigenvalue and the interference power that suppresses the communication quality based on the measurement results. We propose an empirical formula for predicting the signal to interference ratio (SIR), which is the ratio between the power of the eigenvalue and the interference power. This SIR empirical formula helps to predict the communication quality and simplify the simulation.