Cell-free (CF) networks are a promising architecture poised to revolutionize future wireless communication systems. To enhance performance, designing effective transmission strategies for CF networks is of practical significance. In this paper, we study the downlink beamforming design to maximize the resource efficiency (RE) of CF networks, which encompasses both energy efficiency (EE) and spectral efficiency (SE) optimization, thereby enabling the realization of an EE-SE tradeoff. Specifically, we formulate a RE maximization problem taking into account both the quality of service (QoS) requirements of the users and the power constraint of the network. The RE optimization problem is a non-convex fractional program. To solve it efficiently, we first equivalently decompose the challenging RE problem into two more tractable problems, a subproblem and a primary problem. Then, we show that the subproblem is equivalent to a power minimization problem and propose two effective methods to obtain the optimal primal and dual solutions simultaneously. After that, we derive the gradient of the optimal value function of the subproblem exploiting the obtained primal and dual solutions that facilitates the design of efficient algorithms with rapid convergence to address the primary problem. Finally, numerical results demonstrate that the proposed algorithms can effectively balance the EE-SE tradeoff, surpassing existing approaches in terms of either EE or SE.

In this paper, we address the peak-to-average power ratio (PAPR) reduction problem of an orthogonal frequency division multiplexing (OFDM) system under error vector magnitude (EVM) and out-of-band emissions (OOBE) constraints. Unlike the existing methods, we first equivalently transform the non-convex objective function—PAPR into the difference between the numerator and denominator, and then analyze its monotonicity of the auxiliary variable. Subsequently, we propose a novel algorithm based on bisection searching to tackle the equivalent PAPR optimization problem. Furthermore, an efficient PAPR reduction algorithm is developed to overcome the challenge of high computational complexity, and a simplified version of this algorithm is provided. Finally, the performance of the proposed algorithms is compared with the state-of-the-art schemes. The simulation results demonstrate the superiority of the proposed algorithms.