OSTBC Encoder
Encode input message using orthogonal spacetime block code
Libraries:
Communications Toolbox /
MIMO
Description
The OSTBC Encoder block encodes an input symbol sequence using an orthogonal spacetime block code (OSTBC). The block maps the input symbols blockwise and concatenates the output codeword matrices in the time domain. For more information, see OSTBC Encoding Algorithm.
Examples
OSTBC Over 3by2 Rayleigh Fading Channel
Simulate orthogonal spacetime block codes (OSTBC) to achieve diversity gains in a multipleinput multipleoutput (MIMO) communications system. The example shows the transmission of data over three transmit antennas and two receive antennas using independent Rayleigh fading per link.
Explore Model
The doc_ostc32
model creates a random binary signal, modulates it using a binary phase shift keying (BPSK) technique, and then encodes the waveform using a rate 3/4 orthogonal spacetime block code for transmission over the fading channel. The fading channel has six independent links that result from the configuration of singlepath Rayleigh fading processes. The simulation adds white Gaussian noise at the receiver, and then combines the signals from both receive antennas into a single stream for demodulation. For this combining process, the model assumes perfect knowledge of the channel gains at the receiver. The simulation compares the demodulated data with the original transmitted data and computes the bit error rate. The simulation runs until it processes 100 errors or 1e6 bits, whichever comes first.
Orthogonal SpaceTime Block Code
This matrix shows the rate 3/4 code with three transmit antenna orthogonal spacetime block code configured in the OSTBC Encoder block:
where , , and correspond to the three symbol inputs for which the output is given by the matrix. The input to the OSTBC Encoder block is a 3by1 vector signal and the output is a 4by3 matrix. The number of columns in the output signal indicates the number of transmit antennas for this simulation, where the first dimension is for time. The OSTBC Combiner block outputs a 3by1 vector.
For the rate 3/4 OSTBC code modeled, the output signal power per time step is 3x(3/4) = 2.25W. A channel symbol carries 3 data bits, is 4 time steps long, and has a period of 3e3 seconds. At the receiver, two antennas result in 3/2 bits per symbol per channel (antenna). In addition,
where k is the number of bits per symbol. Since the AWGN Channel block requires perchannel values for input signal power and number of bits per symbol, set the Es/No
value to EbNo+10*log10(3/2)
to calibrate the white Gaussian noise added in the simulation.
Performance
Compare the performance of the model to theoretical results by using the Bit Error Rate Analysis app. This plot compares the simulated BER for a range of Eb/No
values with the theoretical results for a diversity order of six.
The theoretical and simulated results align well. The variation between theoretical and simulated results is primarily due to the simulated fading channel model having a small Doppler fade. Since the simulated channel varies slightly over the block symbols, the simulated and theoretical results show some variation.
Ports
Input
In — Input data
column vector  matrix
Input data, specified as a column vector or matrix of values with poweroftwo slope and zero bias. For more information, see InputtoOutput Dimensions.
This port is unnamed on the block icon.
Data Types: single
 double
 fixed point
Complex Number Support: Yes
Output
Out — Output data
matrix  3D array
Output data, returned as a matrix or 3D array. For more information, see InputtoOutput Dimensions.
The output signal inherits the data type from the input signal. For fixedpoint signals, the Saturate on integer overflow parameter specifies how the block handles integer overflows due to complex conjugation.
This port is unnamed on the block icon.
Data Types: single
 double
 fixed point
Parameters
To edit block parameters interactively, use the Property Inspector. From the Simulink^{®} Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.
MainNumber of transmit antennas — Number of transmit antennas
2
(default)  3
 4
Number of transmit antennas, specified as 2
,
3
, or 4
.
Rate — Symbol rate
3/4
(default)  1/2
Symbol rate of the code, specified as 3/4
or
1/2
. When you set Number of
transmit antennas to 2
, the symbol rate
is 1
.
Dependencies
To enable this parameter, set Number of transmit
antennas to 3
or
4
.
Saturate on integer overflow — Option to saturate on integer overflow
off (default)  on
For fixedpoint calculations, use this parameter to specify the method to be used if the magnitude of a fixedpoint calculation result does not fit into the range of the data type and scaling that stores the result.
To saturate on integer overflow, select this parameter.
To wrap on integer overflow, do not select this parameter.
For more information, see Precision and Range.
Data Types: Boolean
Block Characteristics
Data Types 

Multidimensional Signals 

VariableSize Signals 

^{a} Signed only. 
More About
InputtoOutput Dimensions
The OSTBC encoder supports time and spatial domains for OSTBC transmission and an optional dimension over which the encoding calculation is independent. This illustration indicates the supported input dimensions and resulting output dimensions.
When you input a time or spatial domain signal of size Tby
1
, the encoder outputs a (T/R)byN matrix.When you input a matrix of size FbyT, the encoder outputs an Fby(T/R)byN array.
Where:
R — Symbol rate of the code, as specified by the Rate parameter.
For N = 2, R must be 1.
For N = 3 or 4, R can be 3/4 or 1/2.
N — Number of transmit antennas, as specified by the Number of transmit antennas parameter. N can be 2, 3, or 4.
T — Input symbol sequence length for the time domain. The time domain length T must be a multiple of the number of symbols in each codeword matrix.
For N = 2 or R = 1/2, T must be a multiple of 2.
For R = 3/4, T must be a multiple of 3.
T/R — Symbol sequence length in time domain for the output signal.
F — Additional dimension; typically the frequency domain. The encoding is independent of this additional dimension. F can be any positive integer.
Algorithms
OSTBC Encoding Algorithm
The OSTBC encoder algorithm implements the five different OSTBC codeword matrices shown in this table. The number of transmit antennas and the symbol rate determine the codeword matrix that the algorithm uses to encode the input data.
Number of Transmit Antennas  Symbol Rate  OSTBC Codeword Matrix 

2  1  $$\left(\begin{array}{cc}{s}_{1}& {s}_{2}\\ {s}_{2}^{*}& {s}_{1}^{*}\end{array}\right)$$ 
3  1/2  $$\left(\begin{array}{ccc}{s}_{1}& {s}_{2}& 0\\ {s}_{2}^{*}& {s}_{1}^{*}& 0\\ 0& 0& {s}_{1}\\ 0& 0& {s}_{2}^{*}\end{array}\right)$$ 
3  3/4  $$\left(\begin{array}{ccc}{s}_{1}& {s}_{2}& {s}_{3}\\ {s}_{2}^{*}& {s}_{1}^{*}& 0\\ {s}_{3}^{*}& 0& {s}_{1}^{*}\\ 0& {s}_{3}^{*}& {s}_{2}^{*}\end{array}\right)$$ 
4  1/2  $$\left(\begin{array}{cccc}{s}_{1}& {s}_{2}& 0& 0\\ {s}_{2}^{*}& {s}_{1}^{*}& 0& 0\\ 0& 0& {s}_{1}& {s}_{2}\\ 0& 0& {s}_{2}^{*}& {s}_{1}^{*}\end{array}\right)$$ 
4  3/4  $$\left(\begin{array}{cccc}{s}_{1}& {s}_{2}& {s}_{3}& 0\\ {s}_{2}^{*}& {s}_{1}^{*}& 0& {s}_{3}\\ {s}_{3}^{*}& 0& {s}_{1}^{*}& {s}_{2}\\ 0& {s}_{3}^{*}& {s}_{2}^{*}& {s}_{1}\end{array}\right)$$ 
In each matrix, each (l, i) element indicates the symbol
transmitted from the ith antenna in the lth
time slot of the codeword block. Values for i are in the range
[1
,N], where N is
the number of transmit antennas. Values for l are in the range
[1
,L], where L is
the codeword block length.
When processing variablesize signals:
If the input signal is a column vector, the first dimension can change, but the second dimension must remain fixed at
1
.If the input signal is a matrix, both dimensions can change.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
Version History
Introduced in R2009a
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