An efficient analysis of time-modulated array (TMA) toward realizing less-attenuating radiation patterns with simultaneously suppressed sidelobe and sidebands is presented in this paper. In this framework, an optimal outer element-controlled time sequence is derived. The proposed time scheme, along with optimized array excitations, is profitably applied for the desired solution. TMAs are considered unconventional alternatives to the phased arrays. The desired array radiation features can be attained by periodically enabling and disabling the array elements through high-speed switches. Despite the advantages of architectural simplicity and real-time reconfigurability of periodic time sequences, time-domain antenna arrays inherently generate unavoidable sideband radiations (SRs). The undesired SRs obtained at multiple harmonics around the carrier frequency of the array resembles power loss in unintended directions. This paper aims to minimize the SRs as well as the sidelobe level (SLL) for an efficient analysis of time-modulated linear array (TMLA) with high-directive radiation patterns. The starting instants and the period of on-times are optimized to generate a unique shifted time scheme for the edge elements of the TMLA to reduce the sideband levels (SBLs). The array excitations and the uniform spacing between the elements are also optimized together with the shifted time scheme for the coveted solution. Other methods of suppressing SLLs and SBLs with shifted pulse schemes and sub-sectioned pulse schemes are also presented for a fair comparison. Modified versions of the particle swarm optimization algorithm (PSO) are applied for the desired solutions. The optimal results attained by wavelet mutation-based novel PSO is compared with the conventional PSO and the modified novel PSO-based results. The representative results are reported, and the superior performance abilities of the proposed method compared to other published studies are assessed.