In MIMO systems, a transmitter sends multiple streams via multiple transmit antennas. The transmission streams pass through a channel that consists of all NtNr paths between the Nt transmit antennas and the Nr receive antennas. The receiver receives the received signal vector from the multiple receive antennas and decodes the received signal vectors into information originals. A flat-fading MIMO system can be modeled as "Say no to plagiarism". Get a tailor-made essay on "Why Violent Video Games Shouldn't Be Banned"? Get an original essayy = Hx + wWhere x and y are the transmitted and received signal vectors, respectively, and H and w are the channel matrix and noise vector, respectively. x has dimension Nt _x1, y has dimension Nr x 1 and H has dimension Nr x Nt. The ergodic channel capacity of MIMO systems in the presence of perfect information about the instantaneous channel state is given by where (:)H denotes the Hermitian transposition, _ is the ratio of the transmission signal power to the noise power and CCSIperfect is the capability of the MIMO system when perfect channel state information is available. Q is the optimal covariance of the signal and is given by Q = VSVH. If the transmitter does not have information about the channel state, it can select the signal covariance Q to maximize the channel capacity in the worst case statistics, which means Q = 1 Nt I and consequently To take advantage of the advantages offered by MIMO systems diversity coding is used. In this article, a special type of Space Time Block Code (STBC), invented by Alamouti in 1998, is used. It was initially designed for a two-transmission antenna system and is represented as a matrix: Where * denotes a complex conjugate. c1 and c2 are the symbols to be transmitted at two different time instants by two antennas. Two time slots are required to transmit two symbols. In the first time interval, two symbols x1 and x2 (in OFDM language) are transmitted simultaneously by two transmitting antennas. During the second time slot, ????x_2 is transmitted from the first transmit antenna and x_1 is transmitted from the second transmit antenna. The Alamouti coding system for two transmit and two receive systems is shown in Figure 4.16. Using the optimal decoding scheme discussed below, the bit error rate (BER) of this STBC is equivalent to the 2Nr maximum branch ratio combination (MRC). Please note: this is just an example. Get a customized document from our expert writers now. Get a custom essay This is the result of perfect orthogonality between symbols after reception processing: there are two copies of each symbol transmitted and No. copies received. Where Nr is the number of receiver antennas. This is very special for STBC. It is the only orthogonal STBC that achieves rate 1. That is, it is the only STBC that can achieve full diversity gain without having to sacrifice data rate. Strictly speaking, this is only true for complex modulation symbols. Since almost all constellation diagrams are based on complex numbers. However, this property usually gives Alamouti code a significant advantage over higher-order STBCs even if they achieve better performance in terms of error rate.