Regularized Channel Inversion Precoding Research Articles

Low-complexity Kaczmarz precoding in DL massive MIMO with partial CSI and correlation

The capacity achieved by three low-complexity precoders is compared considering a single-cell massive MIMO (M-MIMO) broadcast channel; these linear precoders include the conventional zero-forcing (ZF) beamforming, regularized channel inversion (RCI) precoding, and a precoding version based on the iterative randomized Kaczmarz algorithm (rKA). The capacity vs complexity tradeoff is analyzed in the downlink (DL) with a base-station (BS) deploying massive uniform linear array (ULA) antennas, while mobile terminals (MT) are equipped with single-antenna. Based on the precoding matrix associated with each scheme, we first derive the interference matrix and, consequently, the capacity achieved by each analyzed precoder. Numerical results demonstrate that the rKA’s performance-complexity tradeoff is superior compared to conventional ZF and RCI precoding when operating in M-MIMO scenario, since it holds a relative robustness against system loading increasing, appears to be equally efficient under a simple equal power assignment (EPA) policy and implies in a considerably reduced number of complex operations.

Improving Secrecy via Extension to Regularized Channel Inversion Precoding

This letter extends the regularized channel inversion (RCI) precoding to include more regularization parameters. Compared with the RCI precoding, more practical user channels are considered and the information obtained from the eigen-decomposition of the channel covariance matrix is exploited. The weighted sum-rate problem with different confidentiality requirements of the users is discussed, and the simple gradient descent method is used to solve the problem and determine the regularization parameters. The numerical results show that the proposed precoder outperform the RCI precoder in terms of the weighted sum-rate.

Transmit-Power Efficient Linear Precoding Utilizing Known Interference for the Multiantenna Downlink

It has been shown that the knowledge of both channel and data information at the base station prior to downlink transmission can help increase the received signal-to-noise ratio (SNR) of each user without the need to increase the transmitted power. Achievability is based on the idea of phase alignment (PA) precoding, where instead of nulling out the destructive interference, it judiciously rotates the phases of the transmitted symbols. In this way, they add up coherently at the intended user and yield higher received SNRs. In addition, it is well known that regularized channel inversion (RCI) precoding improves the performance of channel inversion (CI) in multiantenna downlink communications. In line with this and similar to the RCI precoding, in this paper, we propose the idea of regularized PA (RPA), which is shown to improve the performance of original PA precoding. To do this, we first rectify the original PA precoding, deriving a closed-form expression to evaluate the amount of transmit-power reduction achieved for the same average output SNR compared with CI precoding. We then use this new analysis to select the appropriate regularization factor for our proposed RPA scheme. It is shown by means of theoretical analysis and simulations that the proposed RPA precoding outperforms CI, RCI, and PA precoders from both symbol error rate (SER) and throughput perspectives and provides a more power-efficient alternative. This is particularly pronounced as the number of transmit antennas becomes larger, where up to a 50-times reduction in the transmit power is achieved by RPA (PA) compared with RCI (CI) precoding for a given performance.

Physical Layer Security in Downlink Multi-Antenna Cellular Networks

In this paper, we study physical layer security for the downlink of cellular networks, where the confidential messages transmitted to each mobile user can be eavesdropped by both (i) the other users in the same cell and (ii) the users in the other cells. The locations of base stations and mobile users are modeled as two independent two-dimensional Poisson point processes. Using the proposed model, we analyze the secrecy rates achievable by regularized channel inversion (RCI) precoding by performing a large-system analysis that combines tools from stochastic geometry and random matrix theory. We obtain approximations for the probability of secrecy outage and the mean secrecy rate, and characterize regimes where RCI precoding achieves a nonzero secrecy rate. We find that unlike isolated cells, the secrecy rate in a cellular network does not grow monotonically with the transmit power, and the network tends to be in secrecy outage if the transmit power grows unbounded. Furthermore, we show that there is an optimal value for the base station deployment density that maximizes the secrecy rate, and this value is a decreasing function of the signal-to-noise ratio.

Large System Analysis of Linear Precoding in MISO Broadcast Channels with Confidential Messages

In this paper, we study the performance of regularized channel inversion (RCI) precoding in large MISO broadcast channels with confidential messages (BCC). We obtain a deterministic approximation for the achievable secrecy sum-rate which is almost surely exact as the number of transmit antennas M and the number of users K grow to infinity in a fixed ratio β=K/M. We derive the optimal regularization parameter ξ and the optimal network load β that maximize the per-antenna secrecy sum-rate. We then propose a linear precoder based on RCI and power reduction (RCI-PR) that significantly increases the high-SNR secrecy sum-rate for 1<;β<;2. Our proposed precoder achieves a per-user secrecy rate which has the same high-SNR scaling factor as both the following upper bounds: (i) the rate of the optimum RCI precoder without secrecy requirements, and (ii) the secrecy capacity of a single-user system without interference. Furthermore, we obtain a deterministic approximation for the secrecy sum-rate achievable by RCI precoding in the presence of channel state information (CSI) error. We also analyze the performance of our proposed RCI-PR precoder with CSI error, and we determine how the error must scale with the SNR in order to maintain a given rate gap to the case with perfect CSI.

Secrecy Sum-Rates for Multi-User MIMO Regularized Channel Inversion Precoding

In this paper, we propose a linear precoder for the downlink of a multi-user MIMO system with multiple users that potentially act as eavesdroppers. The proposed precoder is based on regularized channel inversion (RCI) with a regularization parameter α and power allocation vector chosen in such a way that the achievable secrecy sum-rate is maximized. We consider the worst-case scenario for the multi-user MIMO system, where the transmitter assumes users cooperate to eavesdrop on other users. We derive the achievable secrecy sum-rate and obtain the closed-form expression for the optimal regularization parameter α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LS</sub> of the precoder using large-system analysis. We show that the RCI precoder with α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LS</sub> outperforms several other linear precoding schemes, and it achieves a secrecy sum-rate that has same scaling factor as the sum-rate achieved by the optimum RCI precoder without secrecy requirements. We propose a power allocation algorithm to maximize the secrecy sum-rate for fixed α. We then extend our algorithm to maximize the secrecy sum-rate by jointly optimizing α and the power allocation vector. The jointly optimized precoder outperforms RCI with α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LS</sub> and equal power allocation by up to 20 percent at practical values of the signal-to-noise ratio and for 4 users and 4 transmit antennas.