27-06-2013, 12:52 PM
Analog-Digital Hybrid Modulation for improved efficiency over Broadband Wireless Systems
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Abstract
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
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).
PERFORMANCE COMPARISON
SCM offers near ideal communications performance. To
show this is true, let us consider the role of a
communications link designer who has a noisy transmission
channel of bandwidth B and limited SNR. Let us choose a
digital link as a first and best choice. Here, the analog
samples are converted to digital with a resolution of b bits
per sample.
According to Shannon’s principle of the capacity of a noisy
transmission channel, by using an ideal error correction
coding technique the information can be passed error free at
a bit rate equal to channel capacity, given by equation (7).
If the analog signal is sampled at a rate of R samples per second. Then, the number of bits per symbol cannot exceed b= C/R. Thus M=2b is fixed and quantization error is unavoidable. The designer may consider analog modulation,
such as FM, which is known to increase the output SNR. FM accomplishes this advantage at the expense of bandwidth increase. FM is inferior to PCM at the minimum channel SNR. This is because FM suffers from a threshold phenomenon where the performance decreases drastically with channel SNR.[3]
The Ideal SCM
Now let us consider the SCM technique with the mixed analog/digital link: Assume for the moment that the digital symbols are transmitted error free. Note: the analog symbol xa(n) produced by the SCM process described above, has a
smaller variance than the original symbol x(n).
Ideal SCM with Power Optimization
The performance of the SCM technique can be further improved by adjusting the power allocation between the analog and digital channels so as to maximize the output SNR. Figures 5 and 6 depict the performance of the ideal SCM for allocation of optimal power, computed by adjusting pd in equation (17) so as to maximize SNR0.