| Analog-Digital
Hybrid Modulation for Improved Efficiency over Broadband Wireless Systems |
This
paper seeks to present ways to eliminate the inherent quantization noise component
in digital communications, instead of conventionally making it minimal. It deals
with a new concept of signaling called the Signal Code Modulation (SCM) Technique.
The primary analog signal is represented by: a sample which is quantized and encoded
digitally, and an analog component, which is a function of the quantization 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 analog residual
allows for the system performance to improve when excess channel SNR is available.
The digital component provides increased SNR and makes it possible for coding
to be employed to achieve near error-free transmission.
Introduction Let
us consider the transmission of an analog signal over a band-limited channel.
This could be possible by two conventional techniques: analog transmission, and
digital transmission, of which the latter uses sampling and quantization principles.
Analog Modulation techniques such as Frequency and Phase Modulations provide significant
noise immunity as known and provide SNR improvement proportional to the square
root of modulation index, and are thus able to trade off bandwidth for SNR.
The SCM Technique : An Analytical Approach
Suppose we are given a bandlimited signal of bandwidth B Hz, which needs to be
transmitted over a channel of bandwidth Bc with Gaussian noise of spectral density
N0 watts per Hz. Let the transmitter have an average power of P watts. We consider
that the signal is sampled at the Nyquist rate of 2B samples per second, to produce
a sampled signal x(n). Next, let the signal
be quantized to produce a discrete amplitude signal of M=2b levels. Where b is
the no. of bits per sample of the digital symbol D, which is to be encoded. More
explicitly, let the values of the 2b levels be, q1, q2, q3, q4…qM which are
distributed over the range [-1, +1], where is the proportionality factor determined
relative to the signal. Given a sample x(n) we find the nearest 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 accomplish the transmission of this information over the noisy channel by
dividing it into two channels: one for analog information and another for digital
information. The analog channel bandwidth is Ba= aB, and the digital channel bandwidth
being Bd= dB, where Ba+Bd=Bc, the channel bandwidth. Let =Bc/B, be the bandwidth
expansion factor, i.e. the ratio of the bandwidth of the channel to the bandwidth
of the signal.
Similarly, the variables a and d are the ratios of Ba/B and
Bd/B. Here we will assume that a=1 so that d= -1. The total power is also divided
amongst the two channels with fraction pa for the analog channel and fraction
pd for the digital one, so that pa+pd=1.
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