Coherent Detection of DSBSC Modulated Wave

Coherent detection of DSBSC (Double Sideband Suppressed Carrier) modulated wave involves the use of a carrier signal that is coherent with the carrier frequency used in the modulation process. The coherent detection process is based on multiplying the received DSBSC signal with the coherent carrier signal and passing the resulting product through a low-pass filter.

The coherent carrier signal is generated by a local oscillator at the receiver, which is synchronized with the carrier frequency used in the modulation process. The local oscillator generates a signal that has the same frequency and phase as the carrier signal used in the modulation process. This coherent carrier signal is then mixed or multiplied with the received DSBSC signal, resulting in the product of the two signals. Mathematically, the coherent detection process can be represented as:

r(t) = s(t) * cos(2πfct) = Ac/2 * m(t) * cos(2πfct)^2

where r(t) is the received DSBSC signal, s(t) is the transmitted DSBSC signal, Ac is the amplitude of the carrier signal, and cos(2πfct) is the coherent carrier signal generated by the local oscillator.

Multiplying the received DSBSC signal by the coherent carrier signal results in a signal that contains only the two sidebands of the modulating signal, with the carrier component canceled out or suppressed. This signal is then passed through a low-pass filter to extract the modulating signal, which is then demodulated to recover the original information signal.

Coherent detection of DSBSC modulated wave has several advantages over non-coherent detection techniques. It is less sensitive to noise and distortion, as the use of a coherent carrier signal enables the receiver to extract the modulating signal more accurately. Coherent detection also allows for the recovery of the carrier signal, which can be useful in applications such as frequency and phase synchronization.

The message signal m(t) can be uniquely recovered from a DSBSC wave s(t) by first multiplying s(t) with a locally generated sinusoidal wave and then low pass filtering the product as shown.

Coherent Detector

It is assumed that the local oscillator signal is exactly coherent or synchronized, in both frequency and phase, with the carrier wave c(t) used in the product modulator to generate s(t). This method of demodulation is known as coherent detection or synchronous detection.

Let 𝐴′𝑐 cos(2𝜋𝑓 𝑡 + 𝜙) be the local oscillator signal, and 𝑠(𝑡) = 𝐴𝑐 cos(2𝜋𝑓𝑐 𝑡) 𝑚(𝑡) be the DSBSC wave. Then the product modulator output 𝑣(𝑡) is given by

The first term in the above expression represents a DSBSC modulated signal with a carrier frequency2𝑓𝑐, and the second term represents the scaled version of message signal. Assuming that the message signal is band limited to the interval– 𝑤 <𝑓 < 𝑤, the spectrum of 𝑣(𝑡) is plotted as shown below.

Spectrum of output of the product modulator

From the spectrum, it is clear that the unwanted component (first term in the expression) can be removed by the low-pass filter, provided that the cut-off frequency of the filter is greater than W but less than 2fc-W. The filter output is given by

The demodulated signal vo(t) is therefore proportional to m(t) when the phase error ϕ is constant.