what is hybrid modulation and technical background

In digital communication, the 3 basic modulation techniques are frequency shift modulation, phase shift modulation, and amplitude shift modulation. A hybrid modulation is a modulation that uses more than one, the most common is quadrature amplitude modulation (QAM), where it is modulated using amplitude and phase. The primary analog signal is represented by: a digitally quantized and digitally encoded sample, and an analog component, which is a function of the quantizing component of the digital sample.

The advantages of such a system are two-sided offering advantages of both analog and digital signaling. The presence of the analogue residual allows to improve the performance of the system when excessive channel SNR is available. The digital component provides a higher SNR and makes it possible for the encoding to be used to achieve almost error-free transmission.
Suppose we are given a B Hz broadband signal, which needs to be transmitted over a Bc bandwidth channel with Gaussian noise of spectral density N0 watts per Hz. Let the transmitter have an average power of P watts. We consider that the sample is sampled at the Nyquist velocity of 2B samples per second to produce a sampled signal x (n).

Next, the signal is quantized to produce a discrete amplitude signal of M = 2b. Where b is the no. Bit per sample of digital symbol D, to be encoded. More explicitly, let the values of levels 2b be q1, q2, q3, q4 ... qM that are distributed in the range [-1, +1], where is the given proportionality factor in relation to the signal . Given a sample x (n) we find the closest level qi (n). Here, qi (n) is the digital symbol and xa (n) = x (n) -qi (n) is the analog representation. The exact representation of the analog signal is given by x (n) = qi (n) + xa (n).

We can achieve the transmission of this information on the noisy channel by dividing it into two channels: one for analog information and one for digital information. The bandwidth of the analog channel is Ba = aB, and the bandwidth of the digital channel is Bd = dB, where Ba + Bd = Bc, the bandwidth of the channel.

Sea = Bc / B, the bandwidth expansion factor, ie the relationship between the channel bandwidth and the bandwidth of the signal. Analogously, the variables a and d are the relations of Ba / B and Bd / B. Here we assume that a = 1 so that d = -1. The total power is also divided between the two channels with the fraction pa for the analog channel and the fraction pd for the digital, so that pa + pd = 1.