casmmod

CASM modulation

Since R2024b

Syntax

[modsignal,efficiency] = casmmod(signal,pin,pquad)

[modsignal,efficiency] = casmmod(signal,pin,pquad,modidx)

Description

[modsignal,efficiency] = casmmod(signal,pin,pquad) performs coherent adaptive sub-carrier modulation (CASM) on the input signal to return a multiplexed modulated signal, modsignal, and the power efficiency of the multiplexing process, efficiency. pin is the power for the in-phase (I) component of the multiplexed signal, and pquad is the power for the quadrature (Q) component of the multiplexed signal.

CASM is a constant envelope modulation (CEM) scheme to combine multiple global navigation satellite system (GNSS) signals.

For more information on the equations used to derive baseband CASM signal, see Algorithms.

[modsignal,efficiency] = casmmod(signal,pin,pquad,modidx) also specifies the modulation indices for the signals when you specify more than two signals.

Examples

Perform CASM Modulation of Four Random Signals

Generate four random signals to modulate.

numSignals = 4;
signal = 1 - 2*randi([0 1],1000,numSignals);

Set the power distribution between the in-phase and quadrature components to 40% and 60%, respectively.

Set the modulation index for the third and fourth input signal components to pi/6 and pi/7, respectively.

pin = 0.40;
pquad = 0.60;
modidx = [pi/6 pi/7];

Perform CASM modulation.

[modsignal,eff] = casmmod(signal,pin,pquad,modidx);

Perform CASM Modulation on Three QZSS Signals

Perform CASM modulation on these three Quasi-Zenith Satellite System (QZSS) signals:

• L1 C/A

• L1C data (L1CD)

• L1C pilot (L1CP)

Set the PRNID for the required satellite.

PRNID = 193; 

Set the number of C/A-code navigation data bits in the generated waveform.

numNavDataBits = 1;
% L1C requires twice the number of data bits of C/A-code for the same time duration
L1CnumNavDataBits = 2*numNavDataBits;

Initialize random data for each QZSS signal.

randLNAVData = randi([0 1],1,numNavDataBits);
randCNAV2Data = randi([0 1],1,L1CnumNavDataBits);

Generate a C/A-code for the set PRNID.

caCode = gnssCACode(PRNID,"QZSS");
tempCABits = repmat(caCode,20,1);
caBits = xor(tempCABits,randLNAVData);

Rate match the C/A-code bits with the L1CP signal by repeating each bit 24 times.

rateMatchedCABits = repelem(caBits(:),24);
caCodeSig = 1 - 2*rateMatchedCABits(:);

Generate L1C codes (data, pilot, and overlay) for the set PRNID.

[l1cd,l1cp,l1co] = gpsL1CCodes(PRNID);

Initialize the overlay code. Initialize the indices such that they circularly start from 1 after reading 1800 bits.

overlayCodeIndices = mod((1:L1CnumNavDataBits) - 1,size(l1co,1)) + 1;
overlayBits = l1co(overlayCodeIndices);

Initialize the time-multiplexed binary offset carrier (TMBOC) indices.

ut = [0; 4; 6; 29];
vt = 0:309;
boc61Indices = reshape(ut + 33*vt,[],1);      % Indices for BOC(6,1) modulation
boc11Indices = setdiff(0:10229,boc61Indices); % Indices for BOC(1,1) modulation, excluding BOC(6,1) indices

sps = 24;                                     % Samples per second
numChipsPerBit = 10230;
tmbocSig = zeros(numChipsPerBit*sps,L1CnumNavDataBits);
oneBitSig = zeros(sps,numChipsPerBit);
for ibit = 1:L1CnumNavDataBits
    l1cpo = xor(l1cp,overlayBits(ibit));
    oneBitSig(:,boc61Indices+1) = reshape(-1*bocmod(l1cpo(boc61Indices+1),6,1),sps,[]);
    oneBitSig(:,boc11Indices+1) = reshape(-1*bocmod(l1cpo(boc11Indices+1),1,1,6*2),sps,[]);
    tmbocSig(:,ibit) = oneBitSig(:);
end

l1cdBits = xor(l1cd,randCNAV2Data);
l1cdSig = -1*bocmod(l1cdBits(:),1,1,6*2);

Set the CASM signal in-phase power as 20% and the quadrature power as 80%.

inphasePower = 0.20;
quadraturePower = 0.80;
m = pi/4;               % Modulation index for third signal component

Perform CASM modulation.

[QZSSL1BBWaveform,efficiency] = casmmod([caCodeSig,l1cdSig,tmbocSig(:)],inphasePower,quadraturePower,m); 

Visualize the modulated waveform.

% Set sample rate for plotting waveform
fs = 24*1.023e6;
% Visualize the QZSS Waveform
bbscope = spectrumAnalyzer(SampleRate=fs, ...
    Title="Power spectrum of QZSS signals");
bbscope(QZSSL1BBWaveform)

Perform CASM Modulation on Three NavIC Signals

Perform CASM modulation on these three Navigation with Indian Constellation (NavIC) signals to generate a complex baseband waveform.

• Standard Positioning Service (SPS) signal

• Restricted Service (RS) data signal

• RS-pilot signal

Set the PRNID for the satellite.

PRNID = 1;

Set the number of navigation data bits in the generated waveform.

numNavDataBits = 3;

NavIC uses course acquisition codes (C/A-codes) for spreading the navigation data spectrum at a chipping rate of 1.023 Mcps.

numCAChipsPerDataBit = 1023*20;
randNavICData = 1 - 2*randi([0 1],1,numNavDataBits);
caCode = 1 - 2*double(gnssCACode(PRNID,"NavIC L5-SPS"));

% Each navigation data bit corresponds to 20 repetitions of C/A-code
caBits = repmat(caCode,20,1);
SPSsig = caBits.*randNavICData; % Spread SPS data

Generate random data bits for the RS-pilot and RS-data signals.

dummyRSP = randi([0,1],numCAChipsPerDataBit*numNavDataBits,1); % RS pilot signal
dummyRSD = randi([0,1],numCAChipsPerDataBit*numNavDataBits,1); % RS data signal

Modulate the RS signals by using binary offset carrier (BOC) modulation. Rate-match the SPS signals with the BOC-modulated RS signals.

RSPsig = bocmod(dummyRSP,5,2);
RSDsig = bocmod(dummyRSD,5,2);
RateMatchedSPSsig = repelem(SPSsig(:),10,1);

Set the amplification factors for the RS-data, SPS, and RS-pilot signals, in that order.

ampfactors  = [2/3 sqrt(2)/3 sqrt(2)/3];

Derive the modulation index, in-phase power, and quadrature power.

m = atan(ampfactors(3)/ampfactors(1)); % Modulation index
inphasePower = ampfactors(2)/cos(m);
quadraturePower = ampfactors(1)/cos(m);

Perform CASM modulation of the SPS, RS-pilot, and RS-data signals.

[NavICBBwaveform,efficiency] = casmmod([RSDsig,RateMatchedSPSsig,RSPsig],inphasePower^2,quadraturePower^2,m);

Visualize the complex NavIC baseband waveform.

fs = 10*1.023e6;                             % Sample rate
bbscope = spectrumAnalyzer(SampleRate=fs, ...
Title = "Power spectrum of NavIC signals");
bbscope(NavICBBwaveform)

Input Arguments

signal — Input signal

matrix

Input signal, specified as a matrix with 5 or fewer columns.

In the matrix, the number of rows represents the length of the input signal, and the number of columns represents the number of input signals to multiplex.

Data Types: double
Complex Number Support: Yes

pin — Power of in-phase component

real scalar

Power of the in-phase (I) component, specified as a real scalar.

pin and pquad together define the power distribution between IQ components, which the function uses to generate the modsignal.

Data Types: double

pquad — Power of quadrature component

real scalar

Power of the quadrature (Q) component, specified as a real scalar.

Data Types: double

modidx — Modulation indices of input signals

scalar | vector

Modulation indices of the input signals, specified as one of these options.

Note

To specify modidx, you must specify more than two input signals.

• Scalar — Assigns the same value to each input signal.

• Vector — Assigns an individual value to each input signal. Because modulation indices are required when size(signal,2) is greater than 2, the length of this vector is in the range [1, 3].

Data Types: double

Output Arguments

modsignal — Multiplexed modulated signal

column vector

Multiplexed modulated signal, returned as a column vector of length size(signal,1). The modsignal argument is of the same data precision as the input signal.

For more information on the equations used to derive baseband CASM signal, see Algorithms.

Data Types: double
Complex Number Support: Yes

efficiency — Efficiency of modsignal

real scalar in the range [0, 1]

Efficiency of modsignal, returned as a real scalar in the range [0, 1].

The function computes efficiency as a ratio of total signal power to the total transmitted power.

Data Types: double

Algorithms

The general CASM equation is given by this formula.

$$s(t)=I_o(t)\cos ({\omega }_{c}t+{\varphi }_s(t))-Q_o(t)\sin ({\omega }_{c}t+{\varphi }_s(t))$$

Here:

• I_o is the in-phase signal component and is calculated by:

  $$I_o(t)=\sqrt{P_I}{s}_2=\sqrt{P}{s}_2\sin {\theta }_2$$

• ω_c is the carrier frequency.

• ϕ_s(t) is the phase of the multiplexed signal s(t) and is calculated by:

  $${\varphi }_s(t)={\displaystyle \sum _{n=3}^N{\theta }_n{s}_1(t)}{s}_n(t)$$

• Q_o is the quadrature-phase signal component and is calculated by:

  $$Q_o(t)=\sqrt{P_Q}{s}_1=\sqrt{P}{s}_1\cos {\theta }_2$$

where:

• P_I is the in-phase signal component power and P_Q is the quadrature-phase signal component power.

• s_i is the square wave of unit amplitude, denoting the subcarrier signal. i is an integer in the range [1, N], where N represents the total number of signals to be multiplexed.

• θ_n is the modulation index of the nth signal component.

Considering the first equation, this is the equivalent baseband CASM signal equation.

$$\begin{array}{l}{s}_{CASM}(t)=(I_o\cos {\varphi }_s(t)-Q_o\sin {\varphi }_s(t))+j(I_o\sin {\varphi }_s(t)+Q_o\cos {\varphi }_s(t))\\ \\ \end{array}$$

References

[1] Dafesh, P. A., T. M. Nguyen, and S. Lazar. “Coherent Adaptive Subcarrier Modulation (CASM) for GPS Modernization,” 649–60, 1999.

Extended Capabilities

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

Version History

Introduced in R2024b