OVSF Code Generator

Generate orthogonal variable spreading factor (OVSF) code from set of orthogonal codes

Library

Spreading Codes

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Description

The OVSF Code Generator block generates an OVSF code from a set of orthogonal codes. OVSF codes were first introduced for 3G communication systems. OVSF codes are primarily used to preserve orthogonality between different channels in a communication system.

OVSF codes are defined as the rows of an N-by-N matrix, C_N, which is defined recursively as follows. 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

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

Note that C_N is only defined for N a 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, as shown in the following figure.

If [C] is 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.

Note that 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 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.

Block Parameters

You specify the code the OVSF Code Generator block outputs by two parameters in the block's dialog: the Spreading factor, which is the length of the code, and the Code index, which must be an integer in the range [0, 1, ... , N - 1], where N is the spreading factor. If the code appears at depth r in the preceding tree, the Spreading factor is 2^r. The Code index specifies how far down the column of the tree at depth r the code appears, counting from 0 to N - 1. For C_{N, k} in the preceding diagram, N is the Spreading factor and k is the Code index.

You can recover the code from the Spreading factor and the Code index as follows. Convert the Code index to the corresponding binary number, and then 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 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 for as follows. Let C₀ be the root [1]. Assuming that C_i has been defined, for i < r, define C_i+1 by

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

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.

Parameters

Spreading factor

Positive integer that is a power of 2, specifying the length of the code.

Code index

Integer in the range [0, 1, ... , N - 1] specifying the code, where N is the Spreading factor.

Sample time

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

Samples per frame, specified as a positive integer indicating the number of samples per frame in one channel of the output data. For information on the relationship between Sample time and Samples per frame, see Sample Timing.

Output data type

The output type of the block can be specified as an int8 or double. By default, the block sets this to double.

Simulate using

Select the simulation mode.

Code generation

On the first model run, simulate and generate code. If the structure of the block does not change, subsequent model runs do not regenerate the code.

If the simulation mode is Code generation, System objects corresponding to the blocks accept a maximum of nine inputs.

Interpreted execution

Simulate model without generating code. This option results in faster start times but can slow subsequent simulation performance.

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 a sample every second. If you increase Samples per frame to 10, then the block outputs a 10-by-1 vector every 10 seconds. This ensures that the equivalent output rate is not dependent on the Samples per frame parameter.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using Simulink® Coder™.

Does not support integer only code generation.

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 the frame attribute in the R2015b Release Notes. For more information on block forwarding, see Maintain Compatibility of Library Blocks Using Forwarding Tables (Simulink).