**FPGA Implementation of MIMO-OFDM STBC Systems**

Multiple-input multiple-output (MIMO) combined with
Orthogonal Frequency Division Multiplexing (OFDM) techniques has been received
a great attention in recent years. It is also well-known that Space-Time Block
Coding (STBC) is the typical approach to significantly increase diversity gain.
In this project, we present design of MIMO-OFDM STBC systems based on VLSI
platform which consists of Verilog HDL and Matlab Program. The project is
designed based on MIMO OFDM STBC system using Radix-4 256 Point FFT and 4QAM
modulation with different numbers of receiver antennas in MIMO multipath fading
environments. Radix-4 FFT is used to achieve low power design. The design is
simulated using Matlab with Modelsim and performance is evaluated based of BER
for various inputs such as image and text.

**MIMO STBC**

A block diagram of a MIMO STBC system
with 2 transmit antennas and NR
receive antennas is shown in below Fig.

Block diagram of a MIMO STBC
system

At transmitter
side, input data is encoded by Alamouti STBC as follows:

x

_{1}(T)=s(T)
x

_{2}(T)=s(T+1) (3.1)
x

_{1}(T+1) =-s*(T+1)
x

_{2}(T+1) =s*(T) (3.2)
Where

*s*(*T*) and*s*(*T+1*) denote input data symbols at symbol duration*T*and*T+*1,*x*(*T*) and*x*(*T*+1) denote encoded data symbols at the symbol duration*T*and*T*+1. Encoded data then are transmitted through two transmit antennas.
At the receive
side, received signals at the symbol duration

*T*and*T*+1 are given by:
r

_{i}(T)=r_{i1}.x_{1}(T)+h_{i2}.x_{2}(T)+n_{i}(T)
=h

_{i1}s(T)+h_{i2}s(T+1) +n_{i}(T) (3.3)
r

_{i}(T+1) =h_{i1}.x_{1}(T)+h_{i2}.x_{2}(T+1) +n_{i}(T+1)
=h

_{i1}s*(T+1) +h_{i2}s*(T) +n_{i}(T+1) (3.4)
where

*y*i(*T*) and*y*i(*T*+1) denote received signals obtained at the*i*th receive antenna at the duration*T*and*T*+1,*hij*denotes the channel response from the*j*th transmit antenna to the*i*th receive antenna,*n*i(*T*) and*n*i(*T*+1) denote AWGN noise at the*i*th receive antenna at the duration*T*and*T*+1.
After simply
exchanging in (3) and (4), we can get following equations:

h

_{i1}*r_{i}(T). h_{i2}*r_{i}(T+1)=(| h_{i1}|^{2}+| h_{i2}|^{2})s(T)+ h_{i1}*n_{i}(T)+ h_{i2}*n_{i}(T+1)^{ }(3.5)
h

_{i2}*r_{i}(T). h_{i1}*r_{i}(T+1)=(| h_{i1}|^{2}+| h_{i1}|^{2})s(T+1)+ h_{i2}*n_{i}(T)+ h_{i1}*n_{i}(T+1)^{ }(3.6)
Here, we can see
the advantage of the STBC technique is that we can get transmitted signals
without any inter-symbol interference with a simple process at transmitter side
and receive side. The signal to noise at the

*i*th receive antenna is given by:
Î³

_{i}= (| h_{i1}|^{2}+| h_{i2}|^{2})P_{s}/P_{n }(3.7)
The summation of
signal to noise ratio of

*N*R receive antennas in the system is thus given by:_{ }(3.8)

**MIMO-OFDM STBC block diagram**

A
block diagram of MIMO-OFDM STBC systems is shown in above figure. At the transmit
side, a high-speed input data stream is divided into many sub-streams according
to the number of subcarriers of the systems. On each subcarrier, input data
will be encoded by STBC encoder, then data on each transmit antenna will be
processed by IFFT before transmitting. At the receive side, received signals
will be done by an FFT process and applied STBC decoder on each subcarrier. The
decoded data will be multiplexed to obtain transmitted data. MIMO OFDM STBC is
divided into two,

- Transmitter Side
- Receiver Side

Block diagram
of 2x2 MIMO-OFDM STBC hardware system

**Simulation Video Demo**

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