In this paper, we propose a cross subcarrier precoder design (CSPD) for massive multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. The aim is to maximize the weighted sum-rate (WSR) performance while considering the smoothness of the frequency domain effective channel. To quantify the smoothness of the effective channel, we introduce a delay indicator function to measure the large delay components of the effective channel. An optimization problem is then formulated to balance the WSR performance and the delay indicator function. By appropriately selecting the weight factors in the objective function and the parameters in the delay indicator function, the delay spread of the effective channel can be reduced, thereby enhancing the smoothness of the effective channel. To solve the optimization problem, we apply the symplectic optimization, which achieves faster convergence compared to the gradient descent methods. Simulation results indicate that the proposed algorithm achieves satisfying WSR performance while maintaining the smoothness of the effective channel.

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