## 1 Introduction
According to the sparse channel characteristics, it can be determined that the beamforming gain provided by some of the antenna-RF pairs is not high. The sub-connected structure sacrifices part of the low beamforming gain in exchange for the action in energy consumption on the RF hardware, which is exactly based on the millimeter wave channel characteristics. [PERSON] et al. [10] proposed a sub-connected structure based on the Succesive Interference Cancellation (SIC) algorithm, which has low complexity. However, it assumes that the digital precoder is a diagonal matrix and requires that the number of RF chains is equal to the number of data streams, which means the digital precoder only allocates power for different data streams. Additionally, the allocation of the RF-antenna pairs is fixed, which means that the channel characteristics are not fully utilized, which has great limitations on spectral efficiency performance. [PERSON] et al. [13] also proposed an alternating minimization algorithm based on Semi-Definite Relaxation (SDR) in sub-connected hybrid precoding, which effectively increases the spectral efficiency, but its computational complexity brought by the convex optimization toolbox during each iteration is too high and it sets an extra diagonal constraint on the analog precoder, which does not match the channel conditions perfectly, resulting in low effective channel gain being obtained. [PERSON] et al. [14] designed a heuristic algorithm to construct the analog and digital precoder of the sub-connected structure. The algorithm complexity is low, but it has a stricter quantitative relationship between the number of data streams, receiving antennas, and RF chains, which cannot be applied to all transmission scenarios. [PERSON] et al. [15] deduced the optimal solution of the dynamic sub-connected hybrid precoding scheme, but the calculation amount was too large. So, they designed a low complexity heuristic algorithm based on minimizing the Minkowski-1 norm to allocate the antennas, but the spectral efficiency of this method is not ideal because the algorithm is greedy. [PERSON] [16] also proposed a group-connected structure that compromises between the fully-connected and the sub-connected structure to find a balance between energy efficiency and spectral efficiency, but the performance was generally average. On the basis of the above analysis, most of the prior work on the sub-connected structure hybrid precoding can not obtain maximum effective channel gain due to setting extra constraints on hybrid precoder, and some have the problem of high computational complexity and too strict control of parameters. In order to avoid performance degradation and limitations of application scenarios due to these problems, this paper proposed an efficient algorithm to realize dynamic sub-connected hybrid precoding, in which an alternating minimization algorithm without any extra constraint was designed to solve the joint design problem of analog and digital precoders. By simplifying the spectral efficiency maximization problem to the effective channel gain maximization problem, we also designed a heuristic algorithm to calculate the initial value of the analog precoder and used it as the starting point of alternating minimization to speed up the convergence and prevent it from falling into a suboptimal solution. The novel contributions of this paper are as follows:  
* Leveraging the special structure of the sub-connected analog precoder, which has unit zero-norm of its row vector, the alternating minimization is completed through the quadratic programming, which maintains the low complexity when designing the analog precoder as well as obtaining higher effective channel gain compa with the traditional algorithms. * A heuristic algorithm is proposed to calculate the initial value of the analog precoder, which can speed up the convergence and improve the spectral efficiency compa with the randomly set initial value used in traditional alternating minimization.