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In MIMO systems, a transmitter sends multiple streams by multiple transmit antennas. The transmit streams go through a channel which consists of all NtNr paths between the Nt transmit antennas and Nr receive antennas. The receiver gets the received signal vector by the multiple receive antennas and decodes the received signal vectors into the original information. A flat fading MIMO system can be modeled as
y = Hx + w
Where x and y are transmitted and received signal vectors, respectively, and H and w are the channel matrix and the noise vector, respectively. x has a dimension of Nt _x1, y has dimension of Nr x 1 and H has the dimension of Nr x Nt. The ergodic channel capacity of MIMO systems in the presence of perfect instantaneous channel state information is given by
where (:)H denotes Hermitian transpose, _ is the ratio between transmit signal power and noise power, and CCSIperfect is the capacity of the MIMO system when the perfect channel state information is available. Q the optimal signal covariance and is given by Q = VSVH.
If the transmitter has no channel state information it can select the signal covariance Q to maximize channel capacity under worst-case statistics, which means Q = 1 Nt I and accordingly
To exploit the benefits offered by MIMO systems diversity coding is employed. In this paper a special type of Space Time Block Code (STBC), invented by Alamouti in 1998, is used. It was first designed for a two-transmit antenna system and is represented as a matrix:
Where * denotes complex conjugate. c1 andc2 are the symbols to be transmitted at two different time instances by two antennas. It takes two time-slots to transmit two symbols. In the first time slot, two symbols x1 and x2 (in parlance to OFDM) are transmitted simultaneously from two transmit antennas. During the second-time slot, ????x_2 is transmitted from first transmitter antenna and x_1is transmitted from second transmit antenna. The Alamouti encoder system for two transmit and two receive system is shown in Figure 4.16. Using the optimal decoding scheme discussed below, the bit-error rate (BER) of this STBC is equivalent to 2Nr-branch maximal ratio combining (MRC).
This is a result of the perfect orthogonality between the symbols after receive processing — there are two copies of each symbol transmitted and Nr copies received. Where Nr is the number of receiver antennas. This is a very special to STBC. It is the only orthogonal STBC that achieves rate-1. That is to say that it is the only STBC that can achieve its full diversity gain without needing to sacrifice its data rate. Strictly, this is only true for complex modulation symbols. Since almost all constellation diagrams rely on complex numbers. However, this property usually gives Alamouti’s code a significant advantage over the higher-order STBCs even though they achieve a better error-rate performance.
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