comm.OVSFCode

Generate OVSF code

Description

The comm.OVSFCode System object™ generates a code from an orthogonal variable spreading factor (OVSF) matrix. Use OVSF codes to preserve orthogonality between different channels in a spread spectrum communications system. For more information, see Algorithms.

To generate an OVSF code:

Create the comm.OVSFCode object and set its properties.
Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

Creation

Syntax

ovsf = comm.OVSFCode

ovsf = comm.OVSFCode(Name=Value)

Description

ovsf = comm.OVSFCode creates a System object that generates orthogonal variable spreading factor (OVSF) codes.

ovsf = comm.OVSFCode(Name=Value) creates an OVSF code generator object with each specified property set to the specified value. For example, comm.OVSFCode(SpreadingFactor="128",SamplesPerFrame="10") outputs the first ten chips of a spreading factor length 128 OVSF code generator.

example

Properties

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Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

`SpreadingFactor` — Length of generated code
`64` (default) | positive integer

Length of the generated code, specified as a positive integer power of 2. For more information, see Spread Spectrum.

The spreading factor is the length of the code selected from the OVSF code matrix. OVSF codes are defined as the rows of an N-by-N matrix, C_N. The Index property specifies the row of the C_N matrix as the code of interest. For more information, see Orthogonal Variable Spreading Factor Codes.

`Index` — Row index of OVSF code matrix
`60` (default) | positive integer

Row index of the OVSF code matrix, specified as a positive integer in the range [0, (N – 1)]. N is the code length, as specified by the SpreadingFactor property. OVSF codes are defined as the rows of an N-by-N matrix, C_N. The value of this property specifies the row of the C_N matrix as the code of interest. For more information, see Recovering and Reconstructing OVSF Codes.

`SamplesPerFrame` — Number of OVSF chips output
`1` (default) | positive integer

Number of OVSF code chips output, specified as a positive integer. Each time the object runs, it outputs the first SamplesPerFrame chips of the OVSF code specified by the SpreadingFactor and Index property values. The OVSF code sequence repeats to fill the specified number of chips. For more information, see Spread Spectrum.

`OutputDataType` — Data type of output
`'double'` (default) | `'int8'`

Output data type, specified as 'double' or 'int8'.

Usage

Syntax

Y = ovsf()

Description

Y = ovsf() outputs a frame of the OVSF code in a column vector.

example

Output Arguments

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`Y` — Frame of OVSF code samples
column vector

Frame of OVSF code samples, returned as a column vector. Specify the data type to output with the OutputDataType property.

Data Types: double | int8

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

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Common to All System Objects

`step`	Run System object algorithm
`release`	Release resources and allow changes to System object property values and input characteristics
`reset`	Reset internal states of System object

Examples

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Generate OVSF Code

Open Live Script

Generate 10 samples of an OVSF code with a spreading factor of 32.

ovsf = comm.OVSFCode( ...
    SpreadingFactor=32, ...
    Index=12, ...
    SamplesPerFrame=10);
seq = ovsf()

Algorithms

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As discussed in [1], OVSF codes were first introduced for 3G communication systems and are primarily used to preserve orthogonality between different channels in a spread spectrum communications system.

Orthogonal Variable Spreading Factor Codes

OVSF codes with spreading factor N of an N-by-N OVSF code matrix, C_N, are the individual rows of an N-by-N matrix, C_N, which is defined recursively. First, define C₁ = [1]. Next, assume that C_N is defined and let C_N(k) denote the kth row of C_N. Define C_2N by

$C_{2 N} = [\begin{matrix} C_{N} (0) & C_{N} (0) \\ C_{N} (0) & - C_{N} (0) \\ C_{N} (1) & C_{N} (1) \\ C_{N} (1) & - C_{N} (1) \\ ... & ... \\ C_{N} (N - 1) & C_{N} (N - 1) \\ C_{N} (N - 1) & - C_{N} (N - 1) \end{matrix}]$

C_N is defined for N only as a nonnegative power of 2. It follows by induction that the rows of C_N are orthogonal.

The OVSF codes can also be defined recursively by a tree structure.

If [C] has a code length 2^r at depth r in the tree, where the root has depth 0, the two branches leading out of C are labeled by the sequences [C C] and [C –C], which have length 2^r+1. The codes at depth r in the tree are the rows of the matrix C_N, where N = 2^r.

Two OVSF codes are orthogonal if and only if neither code lies on the path from the other code to the root. Since codes assigned to different users in the same cell must be orthogonal, this requirement restricts the number of available codes for a given cell. For example, if the code C₄₁ in the tree is assigned to a user, the codes C₁₀, C₂₀, C₈₂, C₈₃, and so on cannot be assigned to any other user in the same cell.

Recovering and Reconstructing OVSF Codes

To select the OVSF code to output, you specify the spreading factor and the code index. The code index specifies how far down the column of the tree at depth r the code appears. For C_{N,
k} in the tree structure diagram, N is the spreading factor and k is the code index. The code index must be an integer in the range [0, N – 1]. If the code appears at depth r in the tree structure, the spreading factor is 2^r.

To recover the code, based on the spreading factor and the code index:

Convert the code index to the corresponding binary number.
Add 0s to the left, if necessary, so that the resulting binary sequence x₁ x₂ ... x_r has length r, where r is the logarithm base 2 of the spreading factor. This binary sequence describes the path from the root to the code.
The path takes the upper branch from the code at depth i if x_i = 0, and the lower branch if x_i = 1.

To reconstruct the code, recursively define a sequence of codes C_i:

Let C₀ be the root [1].
Assuming that C_i has been defined, for i < r, define C_i+1 by
$C_{i + 1} = {\begin{array}{l} C_{i} C_{i} & if x_{i} = 0 \\ C_{i} (- C_{i}) & if x_{i} = 1 \end{array}$
The code C_N has the specified spreading factor and code index.

For example, to find the code with spreading factor 16 and code index 6, do the following:

Convert 6 to the binary number 110.
Add one 0 to the left to obtain 0110, which has length 4 = log₂(16).
Construct the sequences C_i according to the following table.
i x_i C_i
0
C₀ = [1]
1 0
C₁ = C₀ C₀ = [1] [1]
2 1
C₂ = C₁ –C₁ = [1 1] [–1 –1]
3 1
C₃ = C₂ -C₂ = [1 1 –1 –1] [–1 –1 1 1]
4 0
C₄ = C₃ C₃ = [1 1 –1 –1 –1 –1 1 1] [1 1 –1 –1 –1 –1 1 1]

i	x_i	C_i
0		C₀ = [1]
1	0	C₁ = C₀ C₀ = [1] [1]
2	1	C₂ = C₁ –C₁ = [1 1] [–1 –1]
3	1	C₃ = C₂ -C₂ = [1 1 –1 –1] [–1 –1 1 1]
4	0	C₄ = C₃ C₃ = [1 1 –1 –1 –1 –1 1 1] [1 1 –1 –1 –1 –1 1 1]

The code C₄ has spreading factor 16 and code index 6.

Spread Spectrum

In general, spread spectrum multiplies each data message sample by a coded set of chips. To avoid confusion with samples of the data message, the term chips refers to samples or bits of a code used to spread data over a wide spectrum in digital communications. The length of the code is the spreading factor.

The spreading factor, SF = R_chip/R_data,

R_chip is the chip rate. The chip rate of a code is the number of chips per second transmitted or received. Multiple chips represent each data sample because the spreading factor must be a positive power of 2 that is greater than 1.
R_data is the sample rate of the message data.

References

[1] Kasapović, S. and N. Sarajlić. "OVSF code assignment in UMTS networks." 2010 20th International Crimean Conference "Microwave & Telecommunication Technology", 429–32. Sevastopol: IEEE^®, 2010. https://doi.org/10.1109/CRMICO.2010.5632706.

Extended Capabilities

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

Usage notes and limitations:

See System Objects in MATLAB Code Generation (MATLAB Coder).

Version History

Introduced in R2012a

comm.OVSFCode

Description

Creation

Syntax

Description

Properties

`SpreadingFactor` — Length of generated code
`64` (default) | positive integer

`Index` — Row index of OVSF code matrix
`60` (default) | positive integer

`SamplesPerFrame` — Number of OVSF chips output
`1` (default) | positive integer

`OutputDataType` — Data type of output
`'double'` (default) | `'int8'`

Usage

Syntax

Description

Output Arguments

`Y` — Frame of OVSF code samples
column vector

Object Functions

Common to All System Objects

Examples

Generate OVSF Code

Algorithms

Orthogonal Variable Spreading Factor Codes

Recovering and Reconstructing OVSF Codes

Spread Spectrum

References

Extended Capabilities

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

Version History

See Also

Objects

Blocks

comm.OVSFCode

Description

Creation

Syntax

Description

Properties

SpreadingFactor — Length of generated code 64 (default) | positive integer

Index — Row index of OVSF code matrix 60 (default) | positive integer

SamplesPerFrame — Number of OVSF chips output 1 (default) | positive integer

OutputDataType — Data type of output 'double' (default) | 'int8'

Usage

Syntax

Description

Output Arguments

Y — Frame of OVSF code samples column vector

Object Functions

Common to All System Objects

Examples

Generate OVSF Code

Algorithms

Orthogonal Variable Spreading Factor Codes

Recovering and Reconstructing OVSF Codes

Spread Spectrum

References

Extended Capabilities

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

Version History

See Also

Objects

Blocks

`SpreadingFactor` — Length of generated code
`64` (default) | positive integer

`Index` — Row index of OVSF code matrix
`60` (default) | positive integer

`SamplesPerFrame` — Number of OVSF chips output
`1` (default) | positive integer

`OutputDataType` — Data type of output
`'double'` (default) | `'int8'`

`Y` — Frame of OVSF code samples
column vector

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