casmmod
Syntax
Description
[
performs coherent adaptive sub-carrier modulation (CASM) on the input signal to return a
multiplexed modulated signal, modsignal
,efficiency
] = casmmod(signal
,pin
,pquad
)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.
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
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 than2
, 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.
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
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
See Also
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