## 1 Introduction  
An array of the antennae can offer an efficient way for processing and detecting the signals coming from some different orientations. Contrasted to a single antenna, a specific array of sensors is able to have its own beam pattern modified through the amplitude and phase distribution named the weights of this array. In order to achieve an array beam pattern of the antennae, the signals could be power weighted and accumulated once the pre-process on the antenna outputs is over. The problem on the antenna array pattern synthesis includes how to get the weights to satisfy a series of specifications over the beam pattern. In this paper, we make the purpose of proposing a specific modular algorithm on the basis of the genetic algorithms (GAs) for various restrictions, just like the array thinned, the linear dimension minimization, the side-lobes peak minimization, BP (beam pattern) shape modeling, etc. Some completely experimental instances show that the method presented can work well. The presented GAs-based processing method is suitable and flexible to the antenna array. Contrasted to the traditional SISO system (single-input single-output system), the MIMO system (multiple-input multiple-output system) can provide a huge capacity gain [1; 2]. Assuming that only the receiver has known the channel state information, the MIMO system has two modulation methods: Diversity and multiplexing [3; 4]. The orthogonal space-time block codes do not achieve the overall channel capacity in the MIMO channels in spite of its advantage of maximizing the diversity. Scientists [PERSON] and [PERSON] [5] firstly presented the revolutionary linear dispersion codes (LDCs). The researcher [PERSON] [6] proposed a family of LDC designs on the basis of the frame theory, which certifies good performance in terms of the diversity advantage. While the MIMO system can increase system capacity and assure communication quality, but an introduction of multiple RF (Radio Frequency) links requires additional requirements according to volume, power consumption, and costs of the hardware. Therefore, antenna selection becomes a cheap and low-complexity application method [5]. Space-time coding schemes, involved in STTC (space-time trellis codes) [6; 7] and STBC (space-time block codes) [8; 9], have also been studied. Reference [10] proposes a BLAST-TAS (Bell Labs layered space time transmitting antenna selection) system for zero-force (ZF) receivers. The multiple antenna system can improve the reliability and increase the capacity in the mobile communication. However, the RF chains are expensive depending on size, the hardware and the power. Consequently, the antenna selection intends to be the lower cost and lower complexity alternative scheme to catch a lot of the merits of the MIMO systems [11]. In order to apply multiple antennae, some articles [11; 12; 13; 14; 15] have already come out lately in the research report in which the conception over the antenna selection was proposed for the space-time codes. Other authors [16; 17] proposed a complete performance analysis on orthogonal STBCs using the antenna selection. The quasi-orthogonal STBCs were researched in some papers [18; 19]. In order to increase the transmission rate and improve the diversity gain of the system, the article used a transmit antenna selection [11; 12] scheme based on linear dispersion code (LDC-TAS). This system scheme adopts the minimum posterior signal to noise ratio (SNR) criterion, which can be applied to any configuration of the number of antennae at both transmitters and receivers, so as to provide diversity capability [13; 14] under the condition of maximizing mutual information between transmitters and receivers. The computer simulation results illustrate that the minimum posterior SNR criterion outperform the other criterions under the different modulation ways just like 8 PSK, 16 QAM, and QPSK.