Double sideband-suppressed carrier modulation
The carrier wave, let us represent it by c(t), in full AM is completely independent of the message signal m(t). This shows us a shortcoming of amplitude modulation, that is, only a fraction of the total transmitted power is affected by m(t). To overcome this shortcoming, the carrier component from the modulated wave is suppressed, resulting in a double sideband-suppressed carrier or DSB-SC modulation. A modulated signal that is proportional to the product of the carrier wave and the message signal is obtained by suppressing the signal, therefore, a DSB-SC modulated signal as a function of time can be described as follows :
s(t) = c(t)m(t)
= A cos(wt) m(t)
A phase reversal is done on the modulated signal whenever the message signal m(t) crosses zero, and the envelope of a DSB- SC modulated signal is entirely different from that of the message signal, which is contrary to the amplitude modulation.
Frequency domain description
The suppression of the carrier from the modulated signal in the above-mentioned equation can be confirmed by examining its spectrum.
The generation of a DSB-SC modulated wave consists simply of the product of the message signal m(t) and the carrier wave Acos(wt). A device called the product modulator is used for achieving this requirement, which is works as a straightforward multiplexer.
Coherent detection
To recover the message signal m(t) from a DSB-SC modulated signal s(t) we first multiply s(t) with a locally generated sinusoidal wave and then apply a low-pass filter to the product.
We also assume in prior that the source of the local oscillator, which can be defined as a locally generated sinusoidal wave, is exactly coherent or synchronized, in both frequency and phase, with the carrier wave c(t) used in the product modulator of the transmitter to generate s(t). This phenomenon is known as coherent detection or synchronous demodulation.
Coherent detection is a special case of the more general demodulation process and is done using a local oscillator whose output has the same frequency, but arbitrary phase difference ∅, measured with respect to the carrier wave c(t).
It is denoted by the coherent detection that the local oscillator output in the receiver by cos(wt + ∅) is assumed to be of unit amplitude for convenience. The product modulator output is represented using the following:
v (t) = cos (wt + ∅) s(t)
= A cos (wt) cos (wt + ∅) m(t)
= ½ A cos (∅) m(t) + ½ A cos (2wt + ∅) m(t)
½ A cos (∅) m(t), that is the first term on the right-hand side, represents a scaled version of the original message signal m(t), and ½ A cos (2wt + ∅) m(t), that is the second term represents a new DSB-SC modulated signal with carrier frequency 2w.
When the phase error ∅ is a constant the demodulated signal v(t) is proportional to m(t). The amplitude of this demodulated signal is a minimum of zero when ∅ – 1pi / 2 and maximum when ∅ = 0. The zero demodulated signal, which occurs for ∅= + or – pi/2 represents the quadrature-null effect.
The detector output is attenuated by a factor equal to cos ∅, this is caused due to the phase error ∅ in the local oscillator. The detector output provides an undistorted version of the original message signal m(t), as long as the phase error is constant. In practical life, however, it is found that the phase error ∅ varies randomly with time, due to random variations in the communication channel. It causes the detector output, and the multiplying factor cos ∅ to also vary randomly with time, which is not a favorable situation. Therefore, the circuitry must be provided in both frequency and phase in the receiver to maintain the local oscillator in perfect synchronism with the carrier wave used to generate the DSB-SC modulated wave in the transmitter. This results in an increase in the complexity of the receiver.
Costas receiver
Costas receiver is used to obtain a practical synchronous receiver system suitable for demodulating DSB-SC waves. The Costas receiver consists of two well-organized detectors, that are supplied with the same incoming DSB-SC wave, with individual local oscillator signals that are in phase quadrature with respect to each other. The frequency of the local oscillator is adjusted so that it can be the same as carrier frequency f. The in-phase coherent detector or Q-channel refers to the detector in the upper path. A negative-feedback system is formed when the two detectors are coupled together, it is designed in such a way as to maintain the local oscillator synchronous with the carrier wave.
Reference