12-04-2013, 03:30 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
et 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.
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).
Consider the case when x(n) is a uniformly distributed
random variable. Assuming that x(n) є [-, +]. As there are
2B symbols/sec and C bits/sec, we have b=C/2B bits per
symbol. Now the analog sample in the range [-, +] is not
transmitted in full, instead it is divided into M=2b equal
segments and only one segment consists of the analog
information. This segment is magnified to the range [-, +]
and transmitted with PAM. The b bits associated with it are
transmitted through the digital channel and recovered. The
receiver in turn will take the analog signal, shrink it by 2b
times and translate it to its original level.