comm.BarkerCode

Generate bipolar Barker code

Description

The comm.BarkerCode System object™ generates a bipolar Barker code. Barker codes have low autocorrelation properties. The short length and low correlation sidelobes make Barker codes useful for frame synchronization in digital communications systems. For more information, see Barker Codes.

To generate a Barker code:

1. Create the comm.BarkerCode object and set its properties.

2. Call the object, as if it were a function.

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

Creation

Syntax

barkerCode = comm.BarkerCode

barkerCode = comm.BarkerCode(Name,Value)

Description

barkerCode = comm.BarkerCode creates a bipolar Barker code generator System object to generate a Barker code.

barkerCode = comm.BarkerCode(Name,Value) sets properties using one or more name-value pairs. For example, comm.BarkerCode('Length',11,'SamplesPerFrame','11') configures a bipolar Barker code generator System object to output a length 11 Barker code in an 11-sample frame. Enclose each property name in quotes.

Properties

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.

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: 'Length',2 outputs the Barker code [–1;1].

Data Types: double

SamplesPerFrame — Samples per output frame

1 (default) | positive integer

Samples per output frame, specified as a positive integer. If SamplesPerFrame is M, the object outputs a frame containing M samples comprised of length N Barker code sequences. If necessary, the object repeats the code sequence to reach M samples. N is the length of the generated code, which is set by the Length property.

Data Types: double

OutputDataType — Output data type

double (default) | int8

Output data type, specified as double or int8.

Data Types: char | string

Usage

For versions earlier than R2016b, use the step function to run the System object algorithm. The arguments to step are the object you created, followed by the arguments shown in this section.

For example, y = step(obj,x) and y = obj(x) perform equivalent operations.

Syntax

y = barkerCode

Description

y = barkerCode outputs a Barker code frame, as a column vector. If the frame length exceeds the Barker code length, the object fills the frame by repeating the Barker code.

Set the data type of the output with the OutputDataType property.

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)

Specific to comm.BarkerCode

clone	Create duplicate System object
isLocked	Determine if System object is in use

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

Generate Barker Code Sequence

Create a Barker code System object with 10 samples per frame.

  barker = comm.BarkerCode('SamplesPerFrame',10)

barker = 
  comm.BarkerCode with properties:

             Length: 7
    SamplesPerFrame: 10
     OutputDataType: 'double'

Generate multiple frames by using the default Barker code sequence of length 7. The code wraps within the frame and continues in the next frame.

  for ii = 1:2
      seq = barker()
  end

seq = 10×1

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

seq = 10×1

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

Compute Barker Code Sidelobe Level

Compute the peak sidelobe level for each Barker code.

CodeLength = [1 2 3 4 5 7 11 13]';
psl = zeros(length(CodeLength),1);
barker = comm.BarkerCode;
for ii=1:length(CodeLength)
    spf = CodeLength(ii);
    barker.Length = CodeLength(ii);
    barker.SamplesPerFrame = spf;
    seq = barker();
    sll_dB = 20*log10(abs(xcorr(seq)));
    psl(ii) = -(max(sll_dB));
    release(barker);
end
Sidelobe_dB = psl;
T = table(CodeLength,Sidelobe_dB)

T=8×2 table
    CodeLength    Sidelobe_dB
    __________    ___________

         1                0  
         2          -6.0206  
         3          -9.5424  
         4          -12.041  
         5          -13.979  
         7          -16.902  
        11          -20.828  
        13          -22.279  

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

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).