Analog-Digital Hybrid Modulation for improved efficiency over Broadband Wireless Systems
Abstractâ€ 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
Index Termsâ€SCM, Hybrid Modulation, Quantized residual amplification.
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. On the other and, Digital techniques of transmission can utilize error- correction codes that provide performance close to theoretical prediction.
However, the major disadvantage of digital transmission techniques is the inherent quantization error introduced, which is imminent all the while the signal
is relayed. This
However, the SNR improvement provided by these techniques is much lower than the ideal performance as shown by the Shannon's capacity theorem .
error causes distortion in the original signal being relayed and cannot be later recovered by any means possible.
If we quantize the sampled signal using QAM or any other method, using a fixed number of bits, a fixed digital distortion is introduced in the developmental
stage itself. This distortion is present regardless of the transmission quality of the channel being used. Thus the original signal can be considered to be
Communications systems are normally constructed for SNR much higher than the minimum that is required, so as to leave a margin for fading and other effects
which might occasionally reduce the SNR .
So, it is essential to design a communications system where the output SNR increases as the channel SNR increases. While, as already stated, this technique
is not feasible through digital modulation, it is an inherent property in analog modulation.
Here, we introduce the concept of Signal Code Modulation (SCM) which utilizes both the analog, as well as, digital modulation techniques. The primary analog
input signal is sampled at the appropriate rate and quantized. The digital samples are denoted by symbols D. The resulting D symbols are then transmitted
using digital transmission techniques (like QAM) optimized for that channel. Those D symbols represent N bits per analog input sample.
The quantization residual, which is not left behind, is transmitted over the noisy channel as an analog symbol A, corresponding to the digital symbol D, as
shown in the proportional factor that will optimize the voltage swing of the signal with that of the channel).
D symbols. However, the 2N amplitude gain of the analog components provides a noise immunity of 22N to boost the SNR and provide a near ideal scheme for
2. 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 oc[-1, +1], where a 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=paB, and the digital channel bandwidth being Bd=pdB, where Ba+Bd=Bc, the channel bandwidth. Let
p=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 Pa and pd are the ratios of Ba/B and Bd/B. Here we will assume that Pa=1 so that pd=P-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.
The SNR of the channels is first conveniently defined where no bandwidth expansion is used
4. 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.
Output SNR versus y (channel SNR) different bandwidth expansion factors
4.1 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) e [-a, +a]. 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 [-a, +a] 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 [-a, +a] 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
5. PROSPECTIVE APPLICATIONS
5.1 Broadband Wireless Transmission
An SCM-based communications link is basically a transparent, band-limited analog pipe with near-ideal performance in noisy channels. Every analog signal
could potentially use SCM because it can outperform other existing modulation schemes. However, SCM has a compelling advantage for digital communications
applications as well.
For example, SCM can pass digital information by acting as a repeater of a digital channel. This application provides a wireless extension of cable modem
digital information. As illustrated in Figure 8, a cable modem termination system
(CMTS) transmits a 42 Mb/s 256-QAM signal in a 6 MHz
cable channel shared among the cable modems located at the subscribers' premises. The return upstream path from the cable modems is a 10 Mb/s 16-SQAM signal
in a 3.2 MHz cable channel. The signals are carried by a combination of fiber and coax referred to as a hybrid fiber/coax (HFC) network.
The fiber delivers a large amount of bandwidth over long distances with strong noise immunity. Coax cables distribute the signal between the fiber and each
subscriber. To reach a station located beyond the reach of the existing HFC network, the cable operator installs an SCM-based point-to-multipoint wireless
access system at any point on the HFC network that has line-of-sight to the unreachable station. All customers located at a particular site share the SCM
radio located at that site. The subscribers simply use low-cost cable modems that connect to the SCM radio via a shared coax cable. The wireless subscribers
can even share the same cable channels with purely wired subscribers because the wireless link is transparent to the cable equipment. The significance of SCM
in this application is its ability to take a 256-QAM signal and transport it over a wireless link suitable only for a lower modulation scheme, such as 16-
QAM. SCM provides significant additional noise immunity, as is depicted in Figure 2 because it uses bandwidth expansion to improve the destination SNR.
There is a non-SCM alternative: the 256-QAM signal could first be demodulated back to the original data bits, then modulated as 16-QAM, transmitted over the
wireless link, demodulated at the destination, and finally remodulated using 256-QAM. This alternative would be much more costly, given the amount of
processing required. It would also add significant latency to the information transported because an efficient channel must perform the error correction of
the original signal before transmitting it over the wireless link.
Furthermore, because SCM provides a transparent link that is not sensitive to protocol evolution or variations, it
is more future-proof and versatile than specific digital standards.
I would like to acknowledge the inspiration given by Mr. Ravi Billa, Head of the Electronics and Communications Department, MGIT and the influential
motivation of our principal Mr. Komaraiah in completing this paper on time.
 B.P. Lathi, Modern Digital and Analog Communication Systems, Oxford Press, 1998 : p.711
 Simon Haykin, Communication Systems, 4th Edition, John Wiley & Sons, 2000 : p.542
 Simon Haykin, Communication Systems, 4th Edition, John Wiley & Sons, 2000 : p.151 and p.164, Fig. 2.55
 B. Friedlander and E. Pasternak's published work at the Asilomar Conference on Signals, Systems and Computers, November 2001.
2. Superior Digital Audio Recording and Playback
Figure 8. Communication using the SCM technique could increase efficiency and reliability while reducing interface and processing costs
A new-generation audio CD could include a digital track identical to and compatible with the existing CD tracks, and in addition, have an analog track to
provide the enhanced quantization error. Such an analog track would provide audio performance that depends on the quality of the recording and of the disc
player. The most discriminating audio enthusiasts could use the more sophisticated player for true analog reproduction, while the less discriminating users
would enjoy the low-cost CD technology in its current format.