## 4 Turbo Coded OFDM with MIMO Antennas in Cooperation  
The concept of wireless communication based on three terminal networks using OFDM over frequency selective fading channels can be found in the excellent tutorial survey article detailed in [22]. The three terminals are source-S, relay-R, and destination-D, as shown in Figure 4.  
The whole code is divided in two codes C1 and C2. C1 is placed at source-S and C2 is placed in relay-R. The relay-R is mostly located near to destination-D. The whole transmission from source-S to destination-D is accomplished in two time slots. In first time slot the source-S encodes the information sequence of bits through code C1 and broadcast it towards both relay-R and destination-D. After, the corresponding de-modulation, the relay-R receives the signal in first time slot. The relay-R decodes the information sequence. Usually this decoding is assumed to be an ideal decoding due to the assumption that source-S to relay-R channel is completely noiseless. Moreover, the Relay-R encodes the information sequences with other code C2 and re-transmits them to the destination-D through a Rayleigh fading channel in second time slot after modulation. Finally, the received signals from the source-S and relay-R are demodulated by soft input soft output SISO demodulator and is estimated using joint iterating decoding employed at the destination-D. The way the turbo code is structured makes it suitable for its deployment in coded cooperative scenario. Turbo code is disturbed to source-S and relay-R in such way that the cooperation between theses nodes takes place. It forms an important class of cooperative communication commonly known as distributed turbo codes (DTC) [5]. The turbo coded OFDM with MIMO antennas are deployed in a cooperation communication scenario as shown in the Figure 5. The scheme completes the transmission of one turbo coded OFDM frame in two time slots. The source-S node consists of 1/2 rate RSC-1 encoder, mapper, OFDM block and Alamouti STBC. The information sequence of bits \(i_{1}\) is applied to RCS-1 encoder that transforms the information sequences of bits \(i_{1}\) into coded sequences of bits \(q\). The coded sequence of bits \(q\) consists of information sequence of bits \(i_{1}\) and parity sequence of bits \(\mathbf{p}_{1}\). The coded sequences of bits \(q\) are mapped into complex symbols \(a\) using different constellations such as BPSK, QPSK and 16 QAM. The coded symbols \(a\) takes the form of RSC-1 encoded OFDM symbols \(X_{k}\) as they are passed through OFDM block by incorporating N-point IDFT and appending cyclic prefix. The RSC-1 encoded OFDM symbols \(X_{k}\) are given as input to Alamouti Space time block code. Alamouti encoding [20] is applied  
Figure 4: Three-terminal coded-cooperation communication model. to RSC-1 encoded OFDM symbols \(\mathbf{X}_{k}\) that will result in two parallel sequences \(\mathbf{X}_{k}^{i}\) and \(\mathbf{X}_{k}^{i+1}\). These two Alamouti code words are broadcasted over the radio frequency (RF) channel towards both relay-R and destination-D. The signal received at the destination D during the first time slot is modelled as  
\[\mathbf{Y}_{S-D}=\mathbf{H}_{S-D}\mathbf{X}_{s}+\mathbf{N}_{S-D} \tag{26}\]  
where  
\[\mathbf{X}_{s}=\left( \begin{array}{cc}\mathbf{X}_{k}^{i}&-\mathbf{X}_{k}^{(i+1)*}\\ \mathbf{X}_{k}^{i+1}&\mathbf{X}_{k}^{i*}\end{array} \right),\;\mathbf{H}_{S-D}=\left( \begin{array} []{cc}h_{11}&h_{12}\\ h_{21}&h_{22}\end{array} \right),\;\mathbf{N}_{S-D}=\left( \begin{array}{cc}n_{11} &n_{12}\\ n_{21}&n_{22}\end{array} \right)\]  
\(\mathbf{X}_{s}\) is the Alamouti space time code word, \(\mathbf{H}_{S-D}\) is the channel matrix between source-S and destination node. The channel matrix is assumed to be a Rayleigh fading channel whose entries are independent and identically distributed (I.I.D) complex Gaussian random variables with zero mean and variance \(\frac{1}{2}\) per dimension.