Hybrid Precoding Design for MIMO System With One-Bit ADC Receivers

When wireless transmission is performed over the bandwidth in the order of a gigahertz, high-resolution analog-to-digital converters (ADCs), and the large number of radio frequency chains significantly increase the power consumption. To address this issue, one promising technique is to use low-resolution, even one-bit ADCs. Another promising technique is to apply a hybrid precoding architecture to reduce the number of RF chains. In this paper, we propose to combine those techniques to reduce the hardware costs in multi-input multi-output system. Our objective is to optimize the hybrid precoder with the aim of increasing the achievable rate. To this end, we first derive an expression for the achievable rate in flat fading channels based on the Bussgang theorem, which is able to reformulate the nonlinear quantitative process as a linear function with identical first- and second-order statistics. To solve the non-convex hybrid precoding design problem, we treat the hybrid precoding design as a matrix factorization problem, which can be solved with an efficient alternating minimization algorithm. That is, we solve the digital precoder and the analog precoder in an alternative way in two separate subproblems. To find the optimal precoder in the first subproblem, we first prove the optimal structure of the digital precoding matrix. With it, we transfer the digital precoding design to a power allocation problem, the closed-form solution of which is then optimally found by using Karush-Kuhn-Tucker conditions. In the second subproblem, due to the non-convex modulus-norm constraint, it is challenging to directly solve the analog precoder. To resolve this problem, we propose to optimize the phases in the analog precoding matrix and adopt the subgradient algorithm to find the local optimal solution. Our simulation results show that the proposed hybrid precoding design effectively improves the achievable rates.