Zero-Forcing (ZF) has been considered as one of the potential practical precoding and detection method for massive MIMO systems. One of the most important advantages of massive MIMO is the capability of supporting a large number of users in the same time-frequency resource, which requires much larger dimensions of matrix inversion for ZF than conventional multi-user MIMO systems. In this case, Neumann Series (NS) has been considered for the Matrix Inversion Approximation (MIA), because of its suitability for massive MIMO systems and its advantages in hardware implementation. The performance-complexity trade-off and the hardware implementation of NS-based MIA in massive MIMO systems have been discussed. In this paper, we analyze the effects of the ratio of the number of massive MIMO antennas to the number of users on the performance of NS-based MIA.In addition, we derive the approximation error estimation formulas for different practical numbers of terms of NS-based MIA. These results could offer useful guidelines for practical massive MIMO systems.

Massive Multiple-Input Multiple-Output (MIMO) systems, dense Small-Cells (SCs), and full duplex are three Simulation results demonstrate that SC in-band wireless backhaul has the potential to improve the throughput for massive MIMO systems. Specifically, among the three strategies, CTDD is the simplest one and could achieve decent throughput improvement. Depending on conditions, with the self-interference cancellation capability at SCs, ZDD could achieve better throughput than CTDD, even with residual self-interference. Moreover, ZDD-IR requires the additional interference rejection process at the BS compared to ZDD, but it could generally achieve better throughput than CTDD and ZDD.

Hybrid beamforming (HB) has been widely studied for reducing the number of costly radio frequency (RF) chains in massive multiple-input multiple-output (MIMO) systems. However, previous works on HB are limited to a single user equipment (UE) or a single group of UEs, employing the frequency-flat first-level analog beamforming (AB) that cannot be applied to multiple groups of UEs served in different frequency resources in an orthogonal frequency-division multiplexing (OFDM) system. In this paper, a novel HB algorithm with unified AB based on the spatial covariance matrix (SCM) knowledge of all UEs is proposed for a massive MIMO-OFDM system in order to support multiple groups of UEs. The proposed HB method with a much smaller number of RF chains can achieve more than 95% performance of full digital beamforming. In addition, a novel practical subspace construction (SC) algorithm based on partial channel state information is proposed to estimate the required SCM. The proposed SC method can offer more than 97% performance of the perfect SCM case. With the proposed methods, significant cost and power savings can be achieved without large loss in performance. Furthermore, the proposed methods can be applied to massive MIMO-OFDM systems in both time-division duplex and frequency-division duplex. Index TermsHybrid beamforming, unified analog beamforming, massive MIMO, spatial covariance matrix, partial CSI, OFDM, multiple group of UEs, a reduced number of RF chains

This paper solves the drawbacks of traditional intelligent optimization algorithms relying on 0 and has good results on CEC 2017 and benchmark functions, which effectively improve the problem of algorithms falling into local optimality. The sparrow search algorithm (SSA) has significant optimization performance, but still has the problem of large randomness and is easy to fall into the local optimum. For this reason, this paper proposes a learning sparrow search algorithm, which introduces the lens reverse learning strategy in the discoverer stage. The random reverse learning strategy increases the diversity of the population and makes the search method more flexible. In the follower stage, an improved sine and cosine guidance mechanism is introduced to make the search method of the discoverer more detailed. Finally, a differential-based local search is proposed. The strategy is used to update the optimal solution obtained each time to prevent the omission of high-quality solutions in the search process. LSSA is compared with CSSA, ISSA, SSA, BSO, GWO, and PSO in 12 benchmark functions to verify the feasibility of the algorithm. Furthermore, to further verify the effectiveness and practicability of the algorithm, LSSA is compared with MSSCS, CSsin, and FA-CL in CEC 2017 test function. The simulation results show that LSSA has good universality. Finally, the practicability of LSSA is verified by robot path planning, and LSSA has good stability and safety in path planning.

In this paper, a lens learning sparrow search algorithm (LLSSA) is proposed to improve the defects of the new sparrow search algorithm, which is random and easy to fall into local optimum. The algorithm has achieved good results in function optimization and has planned a safer and less costly path to the three-dimensional UAV path planning. In the discoverer stage, the algorithm introduces the reverse learning strategy based on the lens principle to improve the search range of sparrow individuals and then proposes a variable spiral search strategy to make the follower's search more detailed and flexible. Finally, it combines the simulated annealing algorithm to judge and obtain the optimal solution. Through 15 standard test functions, it is verified that the improved algorithm has strong search ability and mining ability. At the same time, the improved algorithm is applied to the path planning of 3D complex terrain, and a clear, simple, and safe route is found, which verifies the effectiveness and practicability of the improved algorithm.