# Theoretical Derivation and Optimization Verification of BER for Indoor SWIPT Environments
## 1 Introduction  
Simultaneous wireless information and power transfer (SWIPT) has been widely investigated recently [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12]. SWIPT does not only provide a high spectral efficiency of wireless systems, but it also provides energy via ambient radio frequency electromagnetic waves. SWIPT is able to support various sensor networks, the Internet of Things (IoT), and cellular systems [13]. In SWIPT systems, signals with information are used for communication and for energy extraction. Energy harvesting can allow for a longer lifetime of energy-constrained wireless devices.  
A trade-off between the data rate and energy transfer for a narrow band signal was proposed in the literature [1]. Then, the authors of [2] used a frequency-selective channel with additive Gaussian noise. Another piece of research proposed a dynamic power splitting receiver to spilt the signal and decoded information, with a variable ratio of power to harvest energy [3]. A broadband system with multiplexing of the orthogonal frequency division and beamforming of the transmission was used for SWIPT. [4] However, the direct transmission of the wide band was not considered in the paper (without carrier). The authors of [5] studied a multiple-input multiple-output (MIMO) SWIPT system. The beamforming technique transmitted to the energy and the information receiver of the narrow band signal. Robust beamforming was studied on the assumption of imperfect channel state information at the transmitter in the literature [6]. In the work of [7], the analytic solution was used to optimize the beamforming technology of the SWIPT system. In the literature [10], the allocation of a multi-object resource for secured communication in recognizable radio networks was studied. However, the study only used an analytic solution to calculate the bit error rate (BER) with a statistical channel. In the work of [14], precoding optimization research reduced the resources required for computing, but energy was not taken into consideration.  
Most papers deal with the optimal analytic solution with the signal-to-noise ratio constraint for narrow-band signals. However, there are no analytic solutions for BER in the wideband system. For wide-band signals, the weighting vector is assumed to be adjusted according to the different frequencies, and BER should consider the inter symbol interference. In this paper, for design simplicity, we controlled the feed line length and current of the antenna element by beamforming techniques, based on the frequency selective effect of the multipath channel instead of the digital phase shifters. The circular antenna array is useful for adjustment with multiple receivers, as the deployment is symmetrical. Moreover, the bit error rate performance was considered in the wireless wideband communication system. In this paper, a wideband circular array was used to synthesize the array pattern to maximize the energy harvesting efficiency with the BER constraint using evolution algorithms. In Section 2, we explain the model for our wide band system. In Section 3, we introduce the criterion for different objective function optimization. In Section 4, the mechanisms of the algorithms are introduced for optimization. Section 5 includes the discussion on the simulation results, and Section 6 concludes with the key point. The definition of parameters are conclude in Appendix A.