Abstract
In this paper, we propose practical yet effective statistically-aided codebook-based hybrid precoding schemes for massive multiple-input multiple-output systems in millimeter wave bands. Particularly, we develop novel low-overhead hybrid precoding algorithms for selecting the baseband digital and radio frequency analog precoders from statistically skewed DFT-based codebooks. The proposed algorithms aim at maximizing the spectral efficiency based on minimizing the chordal distance between the optimal unconstrained precoder and the hybrid beamformer and maximizing the signal to the interference noise ratio for the single-user and multi-user cases, respectively. We investigate the performance of the proposed algorithms by considering the mutual information of the analog beamforming procedure (the common stage among the proposed algorithms) as a performance evaluation metric. We derive lower and upper bounds on the mutual information of the channel given the proposed algorithms. Moreover, we show that the performance gap between the lower and upper bounds depends heavily on how many DFT columns are aligned to the largest eigenvectors of the transmit antenna array response of the millimeter wave channel or equivalently the transmit channel covariance matrix when only statistical channel knowledge is available at the transmitter. Then, we show that the proposed algorithms are asymptotically optimal as the number of transmit antennas M goes to infinity and the millimeter wave channel has a limited number of paths P, i.e., P <; M. Further, we verify the performance of the proposed algorithms numerically where results illustrate that the spectral efficiency of the proposed algorithms can approach that of the optimal precoder in certain scenarios. Furthermore, these results show that the proposed hybrid precoding schemes have superior spectral efficiency performance while requiring lower (or at most comparable) channel feedback overhead in comparison with the prior art.
Highlights
Hybrid beamforming is the low-cost and energy-saving solution to achieve high spectral efficiency performance for most massive multiple-input multiple-output (MIMO) systems operating in millimeter wave bands [1]
SIMULATION RESULTS we evaluate the performance of the proposed algorithms, Algorithm 1 and Algorithm 2, and their variants. All these hybrid beamforming schemes are compared with the prominent prior works, mentioned in Section I, in terms of spectral efficiency over millimeter wave (mmWave) bands
Utilizing the spatial correlation and sparsity the channel of recent wireless communication systems such as massive MIMO systems working in millimeter wave bands, we developed practical and simple codebook-based hybrid precoding strategies assuming limited feedback channel or partial channel knowledge while exploiting the statistical information of these channels
Summary
Hybrid (analog/digital) beamforming is the low-cost and energy-saving solution to achieve high spectral efficiency performance for most massive multiple-input multiple-output (MIMO) systems operating in millimeter wave (mmWave) bands [1]. Existing research works in this approach invoke computational intensive beamforming algorithms that either perform exhaustive search [2] or require complex iterative processing such as coordinate descent algorithm [12], Tabu search [10] and cross-entropy optimization method [11], and utilize inefficient codebooks such as Hadamard codebooks [13] and fixed parts of DFT matrices [15] To address these shortcomings, we propose a novel approach to design the hybrid precoder based on leveraging second-order statistics and propagation properties of the mmWave channel aiming mainly at decreasing the feedback overhead in FDD systems.
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