bocmod

Binary offset carrier modulation

Since R2022a

Syntax

y = bocmod(x,m,n)

y = bocmod(x,m,n,halfcyclesps)

y = bocmod(x,m,n,halfcyclesps,phasing)

Description

y = bocmod(x,m,n) performs binary offset carrier (BOC) modulation on the input bits x by using a square wave and returns the modulated symbols y. m is the square wave frequency indicator. n is the input bit rate indicator.

By default, the phasing of the square wave is set to the phase of the sine curve.

To explore the characteristics of a BOC‑modulated signal and examine its spectrum, see BOC Modulated Signal Characteristics.

y = bocmod(x,m,n,halfcyclesps) specifies the number of samples per half cycle of the square wave.

y = bocmod(x,m,n,halfcyclesps,phasing) specifies the phase of the square wave.

Examples

Apply BOC Modulation Using Default Phasing

Generate a random stream of input data bits to modulate.

numBits = 5;
bits = randi([0,1],numBits,1);

Set the values of m and n for the subcarrier square wave.

m = 2; % Square wave frequency is m*1.023e6 Hz
n = 2; % Square wave input bit rate is n*1.023e6 Hz

Modulate the input bits with the square wave using the BOC modulation technique.

sym = bocmod(bits,m,n) % Default phasing is of a sine curve

sym = 20×1

    -1
    -1
     1
     1
    -1
    -1
     1
     1
     1
     1
    -1
    -1
    -1
    -1
     1
      ⋮

Apply BOC Modulation Using Cosine Curve Phasing

Generate a random stream of input data bits to modulate.

numBits = 10;
bits = randi([0,1],numBits,1);

Set the values of m and n for the subcarrier square wave. Also specify the number of samples per square wave half cycle, spshc.

m = 5;
n = 2;
spshc = 4;

Modulate the input bits with the square wave using the BOC modulation technique.

sym = bocmod(bits,m,n,spshc,"cos");

Input Arguments

x — Input bits

column vector of binary values

Input bits, specified as a column vector of binary values.

The function maps an input bit value of 0 to +1 and an input bit value of 1 to -1. It then multiplies the mapped symbols with a square wave by using the BOC modulation technique.

Data Types: double | int8 | logical

m — Square wave frequency indicator

positive scalar

Square wave frequency indicator, specified as a positive scalar.

The frequency of square wave is m*1.023e6 Hz.

Note

The value of 2*m/n must always be an integer. This value represents the number of square wave half cycles per input bit, x.

Data Types: double

n — Input bit rate indicator

positive scalar

Input bit rate indicator, specified as a positive scalar.

The input bit rate is n*1.023e6 Hz.

Data Types: double

halfcyclesps — Number of samples per half cycle of the square wave

2 (default) | integer greater than or equal to 2

Number of samples per half cycle of the square wave, specified as an integer greater than or equal to 2.

Data Types: double | uint8

phasing — Phase of square wave

"sin" (default) | "cos"

Phase of the square wave, specified as "sin" or "cos".

• "sin" — Set the phase of the square wave to the phase of a sine curve.

• "cos" — Set the phase of the square wave to the phase of a cosine curve.

Data Types: char | string

Output Arguments

y — BOC modulated symbols

column vector with values +1 or -1

BOC modulated symbols, returned as a column vector with values +1 or -1. The length of the vector is equal to length(x)*halfcyclesps*2*m/n.

The data type of the returned modulated symbols is same as that of the input bits, x.

To explore the characteristics of a BOC‑modulated signal and examine its spectrum, see BOC Modulated Signal Characteristics.

More About

BOC Modulated Signal Characteristics

BOC modulation is a technique in modern Global Navigation Satellite Systems (GNSS) to optimize spectral sharing. In this scheme, multiplying the spreading code with a square-wave subcarrier shifts signal energy away from the carrier, and creates two distinct symmetric spectral lobes. These lobes allow new GNSS signals to coexist with legacy waveforms on the same carrier frequency without significant interference. These are the key characteristics of this modulation technique.

• Spectral Separation — BOC modulation shifts the signal power away from the center frequency into two distinct sidebands. This shift reduces mutual interference with legacy binary phase shift keying (BPSK) signals that occupy the carrier center frequency.

• Inter-System Compatibility — Spilt-spectrum energy enables multiple constellations to operate simultaneously without performance degradation.

• Backward Compatibility — Utilization of existing carrier frequencies maintains support for the established market of GPS receivers.

BOC modulation improves tracking accuracy and mitigates multipath effects. However, these benefits increase receiver complexity. Accurate symbol processing requires a higher sampling rate. This is typically mitigated using high-performance processing hardware and optimized algorithms. To mitigate this, you can use specialized receiver architectures, such as dual BPSK tracking, sideband processing, or band-pass sampling.

This visualization compares the spectrum of a BPSK modulated GPS C/A-code signal and a BOC modulated GPS L1C signal.

For theoretical derivation of the spectrum equations, refer to the technical paper [1].

References

[1] Betz, John W. "Binary Offset Carrier Modulations for Radionavigation." Navigation 48, no. 4 (2001): 227-246.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2022a