0.9 Carrier recovery  (Page 3/19)

Drawing on the code in pulseshape.m , and modulating with the carrier c , pulrecsig.m creates the two different received signals. The pam command creates a random sequence of symbols drawn from the alphabet $\pm 1$ , $\pm 3$ , and then uses hamming to create a pulse shape. This is not a common (or a particularly useful) pulse shape. It is just easy to use.Good pulse shapes are considered in detail in Chapter [link] . The oversampling factor M is used to simulate the “analog” portion of the transmission, and $M{T}_s$ is equal to the symbol time  $T$ .

[link] plots the spectra of both the large and suppressed carrier signals and . The carrier itselfis clearly visible in the top plot, and its frequency and phase can readily be found by locating the maximum valuein the FFT: fftrlc=fft(rlc);                    % spectrum of rlc [m,imax]=max(abs(fftrlc(1:end/2))); % index of max peak ssf=(0:length(t))/(Ts*length(t));   % frequency vectorfreqL=ssf(imax)                     % freq at the peak phaseL=angle(fftrlc(imax))          % phase at the peak Changing the default phase offset phoff changes the phaseL variable accordingly. Changing the frequency fc of the carrier changes the frequency freqL at which the maximum occurs. Note that the max function used in this fashion returns both the maximum value m and the index imax at which the maximum occurs.

On the other hand, applying the same code to the FFT of the suppressed carrier signal does not recover the phaseoffset. In fact, the maximum often occurs at frequencies other than the carrier, and the phase values reportedbear no resemblance to the desired phase offset phoff . There needs to be a way to process the received signal to emphasize the carrier.

A common scheme uses a squaring nonlinearity followed by a bandpass filter, as shown in [link] . When the received signal $r\left(t\right)$ consists of the pulse modulated data signal $s\left(t\right)$ times the carrier $\cos (2\pi f_{c}t+\Phi )$ , the output of the squaring block is