Energy-Efficient Optimization for Downlink Massive MIMO FDD Systems With Transmit-Side Channel Correlation

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The energy-efficient resource allocation problem is investigated for the downlink massive multiple-input–multiple-output (MIMO) frequency-division duplexing (FDD) system under a correlated Rayleigh fading channel. Our objective is to maximize energy efficiency by adjusting the training duration, training power, and data power, under the constraint of the total transmit energy and spectral efficiency requirement for the user, which evaluates the impacts of the training and data transmission phases simultaneously. The optimization problem is established in a complicated form, where the difficulties lie in the nonanalytic expression of the involved objective function, as well as the nonconvex nature of the optimization problem. To solve it, the deterministic equivalent approximation methodology is introduced to obtain an accurate analytical expression of the cost function. Based on this, the optimization problem in a nonconvex fractional form is transformed into an equivalent optimization problem with a parametric subtractive form, which is still nonconvex. Thus, the objective function is lower bounded by a concave function, which leads to the availability of standard convex theory, and finally, an iterative resource allocation algorithm is proposed. Moreover, we obtain the closed-form solutions using the Lambert W function for some special channel cases. Numerical results validate the benefits of the proposed scheme and illustrate the tradeoff between training and data transmission.