Barker Code Generator

Barker sequence generation.

barker code generator

Description

Block Barker Code Generator generates a Barker sequence. The short length and minimal side lobes of the autocorrelation function allow Barker sequences to be used for frame synchronisation in communication systems.

Ports

Output

Output - Barker sequence frame
`vector-column

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

Dependencies

The output data type is specified by the Output data type parameters.

Parameters

Code length - length of the generated sequence
7 (by default) | 1 | 2 | 3 | 4 | 5 | 11 | 13

The length of the generated sequence is 1, 2, 3, 4, 5, 7, 11, or 13.

Example: the value 2 specifies the sequence [-1;1].

Sample time - sampling period
1 (by default) | -1 | positive scalar

The sampling period specified as a positive number. To inherit the sampling period, set this parameter to -1.

Samples per frame - number of samples in the output frame
1 (by default) | -1 | positive number

The number of samples in the output frame as a positive integer. If Samples per frame is M, the block outputs a frame containing M samples consisting of Barker sequences of length N. N is the length of the generated sequence, which is specified by the Code length parameters. When M is not a multiple of N, consecutive frames maintain Barker sequence continuity across frame boundaries.

Data types: Int64

Output data type - output data type
double (by default) | Int8

Output data type. Available data types: double or Int8.

Barker Sequences

A Barker sequence is a finite sequence of values +1 and -1 having an autocorrelation function whose side lobe level does not exceed .

The Side lobe of the autocorrelation function is the correlation of the codeword with a time-shifted version of itself. The side lobe of the correlation, , for a shift of symbols in a -bit code sequence is equal to

For is an individual code symbol equal to +1 or -1.

The output sequence has a bipolar format, where 0 and 1 are mapped to 1 and -1. The maximum known length of the Barker sequence is 13. The short length and low side lobes of the autocorrelation function make Barker sequences useful for frame synchronisation in digital communication systems. The Barker sequence generator produces the following sequences:

Length	Barker sequence	Side lobe 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; 1]	-16.9 dB
11	[-1; −1; −1; 1; 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; 1; −1]	-22.3 dB

Length

Barker sequence

Side lobe level

[-1]

0 dB

[-1; 1]

-6 dB

[-1; − 1; 1]

-9.5 dB

[-1; −1; 1;-1]

-12 dB

[-1; −1; −1; 1; −1]

-14 dB

[-1; −1; −1; 1; 1; 1; −1; 1]

-16.9 dB

[-1; −1; −1; 1; 1; 1; 1; 1; −1; 1; 1; 1; 1; −1; 1]

-20.8 dB

[-1; −1; −1; −1; −1; 1; 1; 1; −1; −1; 1; −1; 1; 1; −1]

-22.3 dB

Time selection

The time between output updates is equal to the product of the Samples per frame and Sample time parameters. For example, if Sample time and Samples per frame are equal to 1, the unit outputs a frame every second. If Samples per frame is increased to 10, the block will output a 10-element vector every 10 seconds. This ensures that the equivalent output rate is independent of the Samples per frame parameters.