Barker Code Generator

Generate bipolar Barker Code

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Libraries:
Communications Toolbox
Communications Toolbox / Comm Sources / Sequence Generators

Description

The Barker Code Generator block generates a bipolar Barker code. The short length and low correlation sidelobes make Barker codes useful for frame synchronization in digital communications systems. For more information, see Barker Codes.

Examples

Generate Barker Code With Various Code Lengths

The cm_ex_various_barker_code_length model shows the output from Barker Code Generator blocks configured for 15 samples per frame at a sample time of 1, and code lengths set to 3, 4, 7, and 13. The plot shows that the code sequence repeats, as needed, to fill a 15 sample frame.

Plot the Barker code sequences. Each Barker Code Generator block outputs one frame with 15 samples. Comparing the code sequences you can see the code is repeated to fill the frame.

Detect Barker Code Preamble in Frames

Construct two frames consisting of a 7-bit Barker code preamble and a 14-bit payload field. Detect the preamble locations by using the Preamble Detector block.

Based on detection of a Barker code preamble by the Preamble Detector block, the model displays the index location of the last bit in each preamble detected. To load the model and to configure the runtime preamble setting, callback functions are used. For more information, see Model Callbacks (Simulink).

• When loading the model, a PostLoadFcn callback initializes the preamble value of the Preamble Detector block.

• For runtime execution, an InitFcn callback gets the runtime setting for the preamble from the Barker Code Generator block.

The Barker Code Generator block outputs a bipolar (-1,1) signal that must be converted to unipolar (0,1) for the Preamble Detector block. When you run the model, the display shows the numbers 7 and 28 corresponding to the locations at the end of the two preambles.

Extended Examples

Frame Synchronization Using Barker Code Preamble

Use a length 13 Barker code frame preamble for frame synchronization of data bits.

• Open Model

Ports

Output

output — Barker code frame

column vector

Barker code frame, returned as a column vector. If the frame length exceeds the Barker code length, the block fills the frame by repeating the Barker code.

Dependencies

Set the data type of the output with the Output data type parameter.

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 — Length of generated code

7 (default) | 1 | 2 | 3 | 4 | 5 | 11 | 13

Length of the generated code, specified as 1, 2, 3, 4, 5, 7, 11, or 13. For more information, see Barker Codes.

Example: 2 outputs the Barker code [–1;1].

Sample time — Output sample time

1 (default) | -1 | 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 — Samples per output frame

1 (default) | positive integer

Samples per output frame, specified as a positive integer. If Samples per frame is M, the block outputs a frame containing M samples comprised of length N Barker code sequences. N is the length of the generated code, which is set by the Code length parameter. When M is not an integer multiple of N, consecutive frames maintain continuity of the Barker code across frame boundaries.

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

Output data type — Output data 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

Barker Codes

Barker codes have a maximum autocorrelation sequence, which has off-peak autocorrelations no larger than 1.

A correlation sidelobe is the correlation of a codeword with a time-shifted version of itself. The correlation sidelobe, C_k, for a k-symbol shift of an N-bit code sequence, {X_j}, is

$$C_k={\displaystyle \sum _{j=1}^{N-k}{X}_j{X}_{j+k}}$$

For j=1, 2, 3,..., N, X_j is an individual code symbol that is equal to +1 or –1. The adjacent symbols are assumed to be 0.

The output code is in a bipolar format with 0 and 1 mapped to 1 and –1. The maximum known Barker code length is 13. The short length and low correlation sidelobes make Barker codes useful for frame synchronization in digital communications systems. The Barker code generator outputs the Barker codes listed in this table.

Barker Code Length	Barker Code	Sidelobe Level
1	[–1]	0 dB
2	[–1; 1]	–6 dB
3	[–1; –1; 1]	–9.5 dB
4	[–1; –1; 1; –1]	–12 dB
5	[–1; –1; –1; 1; –1]	–14 dB
7	[–1; –1; –1; 1; 1; –1; 1]	–16.9 dB
11	[–1; –1; –1; 1; 1; 1; –1; 1; 1; –1; 1]	–20.8 dB
13	[–1; –1; –1; –1; –1; 1; 1; –1; –1; 1; –1; 1; –1]	–22.3 dB

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.

Extended Capabilities

C/C++ Code Generation

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

Usage notes and limitations:

• 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 Barker Code Generator block version available before R2015b.

Existing models automatically update to load the Barker 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).