Linear Precoding for MIMO Channels with QAM Constellations and Reduced Complexity

In this paper, the problem of designing a linear precoder for Multiple-Input Multiple-Output (MIMO) systems in conjunction with Quadrature Amplitude Modulation (QAM) is addressed. First, a novel and efficient methodology to evaluate the input-output mutual information for a general Multiple-Input Multiple-Output (MIMO) system as well as its corresponding gradients is presented, based on the Gauss-Hermite quadrature rule. Then, the method is exploited in a block coordinate gradient ascent optimization process to determine the globally optimal linear precoder with respect to the MIMO input-output mutual information for QAM systems with relatively moderate MIMO channel sizes. The proposed methodology is next applied in conjunction with the complexity-reducing per-group processing (PGP) technique, which is semi-optimal, to both perfect channel state information at the transmitter (CSIT) as well as statistical channel state information (SCSI) scenarios, with high transmitting and receiving antenna size, and for constellation size up to $M=64$. We show by numerical results that the precoders developed offer significantly better performance than the configuration with no precoder, and the maximum diversity precoder for QAM with constellation sizes $M=16,~32$, and $~64$ and for MIMO channel size $100\times100$

Downlink Precoding for Massive MIMO Systems Exploiting Virtual Channel Model Sparsity

In this paper, the problem of designing a forward link linear precoder for Massive Multiple-Input Multiple-Output (MIMO) systems in conjunction with Quadrature Amplitude Modulation (QAM) is addressed. First, we employ a novel and efficient methodology that allows for a sparse representation of multiple users and groups in a fashion similar to Joint Spatial Division and Multiplexing. Then, the method is generalized to include Orthogonal Frequency Division Multiplexing (OFDM) for frequency selective channels, resulting in Combined Frequency and Spatial Division and Multiplexing, a configuration that offers high flexibility in Massive MIMO systems. A challenge in such system design is to consider finite alphabet inputs, especially with larger constellation sizes such as $M\geq 16$. The proposed methodology is next applied jointly with the complexity-reducing Per-Group Processing (PGP) technique, on a per user group basis, in conjunction with QAM modulation and in simulations, for constellation size up to $M=64$. We show by numerical results that the precoders developed offer significantly better performance than the configuration with no precoder or the plain beamformer and with $M\geq 16$

Joint Precoder and Artificial Noise Design for MIMO Wiretap Channels with Finite-Alphabet Inputs Based on the Cut-Off Rate

We consider precoder and artificial noise (AN) design for multi-antenna wiretap channels under the finite-alphabet input assumption. We assume that the transmitter has access to the channel coefficients of the legitimate receiver and knows the statistics of the eavesdropper's channel. Accordingly, we propose a secrecy rate maximization algorithm using a gradient descent-based optimization of the precoder matrix and an exhaustive search over the power levels allocated to the AN. We also propose algorithms to reduce the complexities of direct ergodic secrecy rate maximization by: 1) maximizing a cut-off rate-based approximation for the ergodic secrecy rate, simplifying the mutual information expression, which lacks a closed-form and 2) diagonalizing the channels toward the legitimate receiver and the eavesdropper, which allows for employing a per-group precoding-based technique. Our numerical results reveal that jointly optimizing the precoder and the AN outperforms the existing solutions in the literature, which rely on the precoder optimization only. We also demonstrate that the proposed low complexity alternatives result in a small loss in performance while offering a significant reduction in computational complexity. © 2002-2012 IEEE

Analysis of SVD-Based Hybrid Schemes for Massive MIMO with Phase Noise and Imperfect Channel Estimation

In hybrid analog-digital schemes, proposed to reduce the number of RF chains especially at millimeter waves, the precoding at the transmitter and the combining at the receiver are split into digital and analog parts. We analyze the sensitivity of hybrid schemes to phase noise and channel estimation errors and we compare them to a full-digital approach. The scheme adopted for the analog part employs fixed phase shifters, then the digital part is optimized by a singular-value decomposition. We derive analytical expressions for the interference and the SNR degradation arising from the imperfect decomposition due to phase noise and the channel estimation error, for typical millimter-wave massive MIMO channels. In particular we show that when the channel estimation is made in the beam-space, this hybrid scheme is more robust to the phase noise and to the channel estimation errors than a full-digital approach

Low-complexity MIMO precoding with discrete signals and statistical CSI

In this paper, we investigate the design of multiple-input multiple-output single-user precoders for finite-alphabet signals under the premise of statistical channel-state information at the transmitter. Based on an asymptotic expression for the mutual information of channels exhibiting antenna correlations, we propose a low-complexity iterative algorithm that radically reduces the computational load of existing approaches by orders of magnitude with only minimal losses in performance. The complexity savings increase with the number of transmit antennas and with the cardinality of the signal alphabet, making it possible to support values thereof that were unwieldy in existing solutions.The work of Y. Wu and R. Schober was supported by the Alexander von/nHumboldt Foundation. The work of C.-K. Wen was supported in part by the/nthe Ministry of Science and Technology, Taiwan, under Grant MOST103-/n2221-E-110-029-MY3

Low-complexity MIMO precoding with discrete signals and statistical CSI

In this paper, we investigate the design of multiple-input multiple-output single-user precoders for finite-alphabet signals under the premise of statistical channel-state information at the transmitter. Based on an asymptotic expression for the mutual information of channels exhibiting antenna correlations, we propose a low-complexity iterative algorithm that radically reduces the computational load of existing approaches by orders of magnitude with only minimal losses in performance. The complexity savings increase with the number of transmit antennas and with the cardinality of the signal alphabet, making it possible to support values thereof that were unwieldy in existing solutions.The work of Y. Wu and R. Schober was supported by the Alexander von/nHumboldt Foundation. The work of C.-K. Wen was supported in part by the/nthe Ministry of Science and Technology, Taiwan, under Grant MOST103-/n2221-E-110-029-MY3