Near-Optimal Pilot Signal Design for FDD Massive MIMO System: An Energy-Efficient Perspective

This paper investigates the pilot signal design for a massive multiple-input multiple-out (MIMO) frequency division duplexing downlink system by taking the channel spatial correlation into account. Our objective is to optimize the pilot pattern, including the pilot power and structure, from the perspective of energy-efficient communication, which can evaluate the channel estimation accuracy, spectral efficiency, and power consumption simultaneously. The original problem is established based on maximizing the energy efficiency (EE) with a predefined quality-of-service requirement and the total power budget, where the involved cost function is in a nonanalytic form with the non-convex nature. To solve it, an analytical expression is derived first by the virtue of the deterministic equivalent approximation technology, which is shown to be a tight approximation. Based on this, the structure of the EE maximization-based pilot signal matrix is proved to be column orthogonal, where the column corresponds to the dominant eigendirections of channel spatial correlation matrix. By use of the derived pilot structure, the primal non-convex fractional optimization problem is recast to an equivalent optimization problem with the objective function in a subtractive form, which can be solved by deliberately manipulating the Lagrangian function. Finally, an iterative algorithm is proposed to obtain the closed-form solution and further insights are extracted. Numerical results validate the performance gain of our proposed near-optimal pilot scheme in terms of the energy efficiency and spectral efficiency compared with the classical mean squared error-based pilot scheme.