OVSF Code Generator

Generate OVSF code

• 

Libraries:
Communications Toolbox / Comm Sources / Sequence Generators

Description

The OVSF Code Generator block 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.

Examples

Generate OVSF Code in Simulink

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

The cm_generate_ovsf_code model sets Code length to 32, Code index to 12, and Samples per frame to 10. Other parameters use the default settings.

Run the model and display the generated OVSF code.

ans =

     1
     1
    -1
    -1
    -1
    -1
     1
     1
     1
     1

Ports

Output

Out — Output data

column vector

Output data, returned as a binary-valued column vector containing the OVSF code generated from a set of orthogonal codes.

Data Types: double | int8

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.

Code length — Code length

64 (default) | positive integer

Length of the generated code, specified as a positive integer power of 2. The code length value is the spreading factor of the code. 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 Code index parameter specifies the row of the C_N matrix as the code of interest. For more information, see Orthogonal Variable Spreading Factor Codes.

Code index — Row index of OVSF code matrix

60 (default) | integer

Row index of the OVSF code matrix, specified as an integer in the range [0, (N – 1)], where N is the spreading factor as specified by the value of the Code length parameter. 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.

Sample time — Sample time, in seconds

1 (default) | positive scalar

Positive scalars specify the time in seconds between each sample of the output signal. If you set the sample time to -1, the output signal inherits the sample time from downstream. For information on the relationship between the Sample time and Samples per frame parameters, see Sample Timing.

Samples per frame — Number of OVSF chips output

1 (default) | positive integer

Number of OVSF code chips output, specified as a positive integer. Each time the block runs, it outputs the first Samples per frame chips of the OVSF code specified by the Code length and Code index property values. For more information, see Spread Spectrum.

For information on the relationship between Sample time and Samples per frame, see Sample Timing.

Output data type — Output type

double (default) | int8

Output data type, specified as double or int8.

Simulate using — Type of simulation to run

Code generation (default) | Interpreted execution

Type of simulation to run, specified as Code generation or Interpreted execution.

• Code generation — Simulate the model by using generated C code. The first time you run a simulation, Simulink generates C code for the block. The model reuses the C code for subsequent simulations unless the model changes. This option requires additional startup time, but the speed of the subsequent simulations is faster than with the Interpreted execution option.

• Interpreted execution — Simulate the model by using the MATLAB^® interpreter. This option shortens startup time, but the speed of subsequent simulations is slower than with the Code generation option. In this mode, you can debug the source code of the block.

For more information, see Interpreted Execution vs. Code Generation (Simulink).

Block Characteristics

Data Types	double | integer
Multidimensional Signals	no
Variable-Size Signals	no

More About

Sample Timing

The time between output updates is equal to the product of the Samples per frame and Sample time parameter values. For example, if Sample time and Samples per frame each equal 1, the block outputs one sample every second. If you increase Samples per frame to 10, then the block outputs a 10-by-1 vector every 10 seconds. This timing ensures that the equivalent output rate is not dependent on the Samples per frame parameter.

Algorithms

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

$$C_{2N}=\left[\begin{array}{cc}{C}_N(0)& C_N(0)\\ C_N(0)& -C_N(0)\\ C_N(1)& C_N(1)\\ C_N(1)& -C_N(1)\\ \mathrm{...}& \mathrm{...}\\ C_N(N-1)& C_N(N-1)\\ C_N(N-1)& -C_N(N-1)\end{array}\right]$$

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:

1. Convert the code index to the corresponding binary number.

2. 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.

3. 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

  $$C_{\text{i}+1}=\{\begin{array}{ll}{C}_{\text{i}}{C}_{\text{i}}\hfill & \text{if }{x}_{\text{i}}=0\hfill \\ C_{\text{i}}(-C_{\text{i}})\hfill & \text{if }{x}_{\text{i}}=1\hfill \end{array}$$

• 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:

1. Convert 6 to the binary number 110.

2. Add one 0 to the left to obtain 0110, which has length 4 = log₂(16).

3. Construct the sequences C_i according to the following table.

   i	xi	Ci
   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 Simulink® Coder™.

Version History

Introduced before R2006a

R2020a: Existing models automatically update this block to current version

Starting in R2020a, Simulink no longer allows you to use the OVSF Code Generator block version available before R2015b.

Existing models automatically update to load the OVSF Code Generator block version announced in Source blocks output frames of contiguous time samples but do not use frame attribute. For more information on block forwarding, see Maintain Compatibility of Library Blocks Using Forwarding Tables (Simulink).