Space Time Block Codes Essay

778 words - 4 pages

Space time block codes operates on sending a block of data at once to create spatial diversity represented by a matrix where time is represented by the number of columns and the number of rows represents the number of antennas[1]. This allow the system to have a better performance in a fading environment. Its main features are the provision of full diversity with a very minimal decoding scheme and it can achieve maximum diversity gain but it doesn't provide coding gain. STBC provides coding gain if and only if it is merged with a different code [2]. Space time block codes is commonly used in downlink of UMTS third Generation cellar systems, and in OFDM applications such as Long Term ...view middle of the document...

The below figure represent two transmitters – One receiver system.

Figure 1:2-Transmit, 1-Receive Alamouti STBC coding;Reproduced fromhttp://www.dsplog.com/2008/10/16/alamouti-stbc/
Let h1 denote the path gain from Tx1 to the receiver and h2 the path gain from Tx2 to the receiver. The received vector in the first time slot is written as
y1 = h1 (x1) + h2 (x2) + n1, (2.01)
As for the second time slot, the received vector is
y2 = h1 (-x2*) + h2 (x1*) + n2. (2.02)
Where n1 and n2 stand for the additive white Gaussian noise (AWGN). The matrix equation can be written as following
[█(y1@y2)]= [■(h1&h2@h2*&-h1*)][█(x1@x2)]+ [█(n1@n2)] (2.03)
We are interested in detecting x1 and x2. Since the columns of the square matrix are orthogonal, finding x1 and x2 is divided into two different, orthogonal, scalar problems. After projecting the output y on each of the two columns, we obtain the sufficient statistics
r_i=‖h‖ x_i+n_i with i=1,2 (2.04)
h = [h1 , h2]tand n1 and n2 are independent withn_(i )~ CN(0,N_0). Two messages with half the power each are transmitted over two symbol times rather than one only. The...

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