OSTBC Encoder

Encode input message using orthogonal space-time block code

Libraries:
Communications Toolbox / MIMO

Description

The OSTBC Encoder block encodes an input symbol sequence using an orthogonal space-time block code (OSTBC). The block maps the input symbols block-wise and concatenates the output codeword matrices in the time domain. For more information, see OSTBC Encoding Algorithm.

Examples

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OSTBC Over 3-by-2 Rayleigh Fading Channel

Open Model

Simulate orthogonal space-time block codes (OSTBC) to achieve diversity gains in a multiple-input multiple-output (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 space-time block code for transmission over the fading channel. The fading channel has six independent links that result from the configuration of single-path 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 Space-Time Block Code

This matrix shows the rate 3/4 code with three transmit antenna orthogonal space-time block code configured in the OSTBC Encoder block:

$\pmatrix{s_{1} & s_{2} & s_{3} \cr -s_{2}^* & s_{1}^* & 0 \cr s_{3}^* &
0 & -s_{1}^* \cr 0 & s_{3}^* & -s_{2}^*}$

where $s_{1}$ , $s_{2}$ , and $s_{3}$ correspond to the three symbol inputs for which the output is given by the matrix. The input to the OSTBC Encoder block is a 3-by-1 vector signal and the output is a 4-by-3 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 3-by-1 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 3e-3 seconds. At the receiver, two antennas result in 3/2 bits per symbol per channel (antenna). In addition,

$\frac{E_s}{N_o} = \frac{E_b}{N_o} + 10log_{10}(k)$

where k is the number of bits per symbol. Since the AWGN Channel block requires per-channel 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

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In — Input data
column vector | matrix

Input data, specified as a column vector or matrix of values with power-of-two slope and zero bias. For more information, see Input-to-Output Dimensions.

This port is unnamed on the block icon.

Data Types: single | double | fixed point
Complex Number Support: Yes

Output

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Out — Output data
matrix | 3-D array

Output data, returned as a matrix or 3-D array. For more information, see Input-to-Output Dimensions.

The output signal inherits the data type from the input signal. For fixed-point 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

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To edit block parameters interactively, use the Property Inspector. From the Simulink^® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Main

Number 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.

Data Types

Saturate on integer overflow — Option to saturate on integer overflow
off (default) | on

For fixed-point calculations, use this parameter to specify the method to be used if the magnitude of a fixed-point 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	`double` \| `fixed point^a` \| `single`
Multidimensional Signals	`yes`
Variable-Size Signals	`yes`
^a Signed only.

More About

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Input-to-Output 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 T-by-1, the encoder outputs a (T/R)-by-N matrix.
When you input a matrix of size F-by-T, the encoder outputs an F-by-(T/R)-by-N 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

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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	$(\begin{matrix} s_{1} & s_{2} \\ - s_{2}^{} & s_{1}^{} \end{matrix})$
3	1/2	$(\begin{matrix} s_{1} & s_{2} & 0 \\ - s_{2}^{} & s_{1}^{} & 0 \\ 0 & 0 & s_{1} \\ 0 & 0 & - s_{2}^{*} \end{matrix})$
3	3/4	$(\begin{matrix} s_{1} & s_{2} & s_{3} \\ - s_{2}^{} & s_{1}^{} & 0 \\ s_{3}^{} & 0 & - s_{1}^{} \\ 0 & s_{3}^{} & - s_{2}^{} \end{matrix})$
4	1/2	$(\begin{matrix} s_{1} & s_{2} & 0 & 0 \\ - s_{2}^{} & s_{1}^{} & 0 & 0 \\ 0 & 0 & s_{1} & s_{2} \\ 0 & 0 & - s_{2}^{} & s_{1}^{} \end{matrix})$
4	3/4	$(\begin{matrix} s_{1} & s_{2} & s_{3} & 0 \\ - s_{2}^{} & s_{1}^{} & 0 & s_{3} \\ s_{3}^{} & 0 & - s_{1}^{} & s_{2} \\ 0 & s_{3}^{} & - s_{2}^{} & - s_{1} \end{matrix})$

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 variable-size 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

OSTBC Encoder

Description

Examples

OSTBC Over 3-by-2 Rayleigh Fading Channel

Ports

Input

In — Input data
column vector | matrix

Output

Out — Output data
matrix | 3-D array

Parameters

Number of transmit antennas — Number of transmit antennas
`2` (default) | `3` | `4`

Rate — Symbol rate
`3/4` (default) | `1/2`

Dependencies

Saturate on integer overflow — Option to saturate on integer overflow
off (default) | on

Block Characteristics

More About

Input-to-Output Dimensions

Algorithms

OSTBC Encoding Algorithm

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

See Also

Blocks

Objects

OSTBC Encoder

Description

Examples

OSTBC Over 3-by-2 Rayleigh Fading Channel

Ports

Input

In — Input data column vector | matrix

Output

Out — Output data matrix | 3-D array

Parameters

Number of transmit antennas — Number of transmit antennas 2 (default) | 3 | 4

Rate — Symbol rate 3/4 (default) | 1/2

Dependencies

Saturate on integer overflow — Option to saturate on integer overflow off (default) | on

Block Characteristics

More About

Input-to-Output Dimensions

Algorithms

OSTBC Encoding Algorithm

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Version History

See Also

Blocks

Objects

In — Input data
column vector | matrix

Out — Output data
matrix | 3-D array

Number of transmit antennas — Number of transmit antennas
`2` (default) | `3` | `4`

Rate — Symbol rate
`3/4` (default) | `1/2`

Saturate on integer overflow — Option to saturate on integer overflow
off (default) | on

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.