The first idea that comes to my mind is using Amplitude Modulation.

Then, instead of transporting the information in the frequency of the signal, doing it in the amplitude of the signal; different amplitudes meaning different values (taking into account that in analog there is no sampling, hence no discrete but continuous values).

Dear Professor Abdelhalim Zekry, Since measurement of occupied BW generally implies a power percentage or ratio. Therefore, BW can be traded.

Thank you Rafel and Afaq for your answers.

To be specific, i will give an example. To transmit speech occupying frequency band from .3 to 3.4 kHz in its analog form we use a twisted wire pairs having the same bandwidth. Converting this signal into standard pcm binary digital format results in a bit stream having a rate fb=64 kb/s. Transmitting this signal in its binary form requires a minimum bandwidth of 32 kHz and certain minimum Eb/No for a given bit rate.

Using higher order amplitude and phase shift keying M PSK and MQAM we can build transmission symbols having 2,3,4,...etc bits per symbol that have smaller bandwidth as the modulation order increases but at the same time needs higher Eb/No for the same bit error rate. So, the binary digital form of the signal is flexible enabling the trade off between the signal power and bandwidth.

Th observation is that:

-The A/D conversion of the analog signal stretches the samples in the sampling time between samples increasing its maximum frequency.

-This time starched binary form can be easily reformed by amplitude and phase shift keying to contract them in time and in this way reduces their maximum frequency with increasing the modulation order as it is well known.

My question is about analogous processes for the analog signal form?

I hope it is now more clear!

Dear Professor Zekry,

You touched interesting theme. Classic Shannon’s formula says that spectrum expansion increases capacity C of the channel and this permits to reduce the power W of emitted signals without change of capacity and vice versa. This trade off is universal and does not depend on the analog signals or bit sequences are transmitted. But it depends on the method of transmission.

A shortage of “usual” AM transmission is that it does not expand the spectrum: one-side channel bandwidth is equal to the signal baseband. For this reason, SNR at the demodulator output, bit rate and capacity can be increased only by the increase of the power of transmitter. The result is low resistance to noise influence and no trade off (the latter would require changes of input signals spectrum what is hardly acceptable). The nonlinear FM and PM expand the spectrum and have greater noise resistance but have limitations on the spectrum expansion due to appearance of abnormal errors in demodulator.

In turn, digital communication systems (CS) have almost unlimited freedom in regulation of power–bandwidth trade off using different signal digitizing, coding and modulation (keying) units. This radically extends possibilities of designers and permitted to approach the bit rate of transmission within 1 dB to the Shannon’s limits under BER of ~ 10e-5 order and smaller (high noise resistance).

Currently, equivalent but more convenient for applications form of this trade off is used, which connect energy (E-) efficiency (ratio Eb [J/bit ] /No [W/Hz]) and spectral (S-) efficiency (C/Fo [bit/s/Hz]; Fo is channel bandwidth). The aim is to approach real power - bandwidth (point E-bit/R, R

Thank you Prof. Platonov. You always enrich our discussions on the communication systems.As i understand from your answer, the concept of trade off between the power and bandwidth is a universal one in the sense that it is independent of the type of the base band signal whether it is analog or digital.

There exist methods to implement this trade off between power and bandwidth for the sane information capacity. The first practical method is modulate the analog information signal on either the frequency or the phase of a sinusoidal carrier as is well known. With such angle modulation the signal bandwidth can be stretchered without changing the power of the carrier. Really , such FM and PM modulation require much less S/N ratio than the AM to achieve the same quality thanks to the bandwidth enlarging effect of such modulation techniques. While PM has relatively bandwidth spreading effect, the FM has a greater capability to spread the spectrum of the signal. FM can be a practical tool to trade off the power and the bandwidth of the analog signals.

The other method introduced by professor Platonov is to an analog communication system with a forward channel and an associated feedback channel to retransmit samples of the received signals to the transmitter. In this way the receiver can estimate the mean square error in the received signal and the overall system can be adjusted for the lowest power and the highest band width efficiency with a given allowed error or distortion.Such system resembles the ARQ system in digital communications.My question now to the colleague Platonov, did you implement such system practically ?

Best regards.

Thank you, Professor Zekry for development of the question,

Answering on your question, I may say only that I have no laboratory nor funds to realize and a prototype of AFCS. For this reason, I’ve concentrated on the theory, and my small team helps me to study particularities of AFCS functioning in advanced simulations.

This is interesting: 3/4 of reviewers on my papers and grant applications ask: “why do you try to restore the past? Digital CS proved, far ago, their superiority over analog systems”.

I used to see such reaction. This is echo of not noticed event in development of communications: after many years work of many researchers in AFCS theory, the work was almost ceased at the beginning of 70th. The reasons I’ve described in the mentioned above paper. It is not easy understanding that else 3-5 years of work at the same intensity and level could make AFCS important part of modern communications.

In last three years, instead of writing not accepted large papers, I began to publish the results in small papers and at the conferences. This helped – I see growing acceptation of research by CS community that makes more and more realistic hardware implementation of AFCS. It will be not too difficult task – majority of practical questions are already solved by digital CS theory and technology.

Concerning ARQ: this method of transmission radically differs from that used in AFCS: The ARQ repeats transmission of the same signal (package) on the request from the receiver, if this signal was recovered with error. Unlike ARQ, AFCS does not repeat signals but transmit, cycle by cycle, quickly diminishing and amplified in modulator difference between the value of input sample and its estimate formed by receiver in previous cycle (and delivered to the transmitter over feedback channel). Therefore, each new signal delivers (some distorted by noise) error of estimate formed in the previous cycle, further processed and added to previous estimate that quickly increases its accuracy. Each cycle is similar. After n cycles, final estimate of the sample is routed to addressee, and AFCS begins transmission of the next sample.

It might be nice to consider so called "soliton networks" too. They were descrtibed first in 19th century and mathematically proven in about 1922 (roughly). According to the general description the signal goes through optical fibre practically without any attenuation and distortion. It seems field tests proved transmission of optical signals over distance 1 400 km without any amplifiers or chromatic dispersion cancellers.

Hi all, Is this question referring to wired ? or, wireless ?

If you are talking about wired, I am thinking about the PAM-5 that is used in 1000BASE-T. ......http://en.wikipedia.org/wiki/PAM-5

The amplitude is split into 5 discrete levels, and 4 pairs of wire are used. the noise immunity of each twisted pair is improved with low-voltage differential signaling (LVDS) at the cable. PAM-5 used 5 voltage levels on 4 twisted pairs, allowing 5^4=625 symbols, 256 of which are valid symbols, and the remaining 369 are invalid and synchronization symbols ... This standard uses 125MHz.

PAM-16, on the other hand, allows us to go to 10GBASE-T at 500MHz. It uses 16 voltage levels, which significantly lowers the noise margins, but, part of the noise margins are boosted back from higher voltages (thus, higher power), and part of it is remedied by much more sophisticated 2D matrix-based coding, DSQ128.

At silicon, 10GBASE-T consumes much higher power. I met a VLSI designer from Canada last year at the SOCC conference, I can't remember his company, he was telling me that, the chip they were working on (10GBASE-T synthesized IC), was consuming around 10W, whereas 1000BASE-T is less than a Watt.

So, there, you traded power for bandwidth on the same wire ...

Just a note from broader scope.

Nice thing about dial-up connection was there was no power consumption in inactivity state. Upgrade to higher bandwiths needs powering 24/7 and transmission power is only part of the whole consumption. PCs need cooling etc. Before LED based monitors and low-povered comps somebody calculated that in order to achieve full switch to BB, England would need to build two completely new power plants.

Dear Tolga,

The question concerns the two types of transmission channels. According to shanon theory the maximum channel capacity C= B log2 (1+S/N), for the same channel capacity C , one can trade B for S and vice verse.

What do you talk about Tolga is the power required for processing different signal speeds. The power required for processing the signal is proportional to the the frequency of the that signal which in this case the signal bit rat e. In CMOS circuits the power consumption is = CVDD^2 f, where f is the frequency of the signal to be processed.

Here no trade off between the power and the band width. HERE the as the bandwidth of the signal increases the power consumption increases too.Here there is no trade off. Higher speed necessitates larger power consumption.

The note of Tomy is in the same direction. More processing speed needs more power.

Thank you Tolga and Tomy for your contributions.

Four years later.

It required definite work, but now I may answer on the question of professor Zekry: „…colleague Platonov, did you implement such system practically?”

- Yes.

My young team realized two hardware prototypes of “perfect” adaptive CS with feedback (AFCS). The results of experiments showed that both prototype transmit signals without coding, in real time, with minimal MSE (rate distortion in terms of inf. theory), bit rate equal to the capacity of the system (R=C), and with limit power (Eb/No) and bandwidth (C/Fo) efficiency.

Optimally adjusted PAM modulator works in AFCS as ideal coder. A probability to receive the distorted samples (“word error rate” – WER

It is quite impressing to read all of those answers and comments, very informative and insightful. I think I actually have a question which goes pretty much in line with Prof. Zeckry's main question. Here goes:

A capacity-achieving communication system operates in an AWGN channel of bandwidth W, using a transmitter with total power 31 times higher than that of the noise. An engineer has the option of replacing the transmitter either with one of the same total power, but twice the bandwidth, or one with the same bandwidth, but twice the total power. What should he/she do? Justify mathematically.

I would endlessly appreciate it if I can get an answer on this soon.

Thanks in advance :)