Primary communication resources , transmitted power , channel bandwidth , Information Capacity Theorem

By   November 12, 2019

Information Capacity Theorem , Primary communication resources , transmitted power , channel bandwidth :-
As a matter of fact, in a communication system, there are following two primary communication resources to be employed:
(i) transmitted power. and
(ii) channel bandwidth
The transmitted power refers to the average power of the transmitted signal.
The channel bandwidth is defined as the band of frequencies allocated for the transmission of the message signal.
Now, the most important system design objective is to use these two resources as efficiently as possible. In most communication channels, one resource may be considered more important than the other. Because of this, we may classify communication channels as power limited or band limited. For example, the telephone circuit is a typical band limited channel, whereas a space communication link or a satellite channel is typically power-limited channel.
Let us consider a particular case as under:
When the spectrum of a message signal extends down to zero or low frequencies, we define the bandwidth of the signal as that upper frequency above which the spectral content of the signal is negligible and therefore unnecessary for transmitting information. For example, the average voice spectrum extends well beyond 10 kHz, though most of the average power is concentrated in the range of 100 to 600 Hz, and a band from 300 to 3100 Hz gives good articulation. Accordingly, we find that telephone circuits that respond well to this latter range of frequencies give quite satisfactory commercial telephone service
Another aspect of utmost importance is the unavoidable presence of noise in a communication system. A quantitative way of accounting for the effect of noise is to introduce signal-to-noise ratio (SNR) as a system parameter. For example, we may define the SNR at the receiver input as the ratio of the average signal power to the average noise power, both being measured at the same point.*
A fundamental question that arises in the study of modulation schemes is the following:
With channel bandwidth and signal-to-noise ratio being the two principal parameters that are available to the designer of a communication system, which particular modulation scheme provides for their most efficient use? or in other words we can say for a specified channel bandwidth, which modulation scheme requires the smallest signal to nose ratio for a prescribed level of system performance.
The answer to this important question lies with information capacity theorem by Shannon.
Information Capacity Theorem
The information capacity theorem, given by Shannon, deals with a continuous channel. According to this theorem, channel bandwidth and signal-to-noise ratio are exchangeable in the sense that we may trade off one for the other for a prescribed system performance. The choice of one modulation scheme over another for the transmission of a message signal in the communication system is often dictated by the nature of this trade off. Infact, the interplay between channel bandwidth and signal-to-noise ratio, and the limitation that they impose on communication, is highlighted by the information capacity theorem.
Let B denote the channel bandwidth, and SNR denote the received signal-to-noise ratio. The information capacity theorem states that ideally these two parameters are related by
C = B log2 (1 + SNR) b/s
where C is the information capacity.
The information capacity is defined as the maximum rate at which information may be transmitted without error through the channel. It is measured in bits per second (b/s). Above equation i clearly shows that for a prescribed information capacity, we may reduce the required SNR by increasing the channel bandwidth, hence the advantage of using a broad bandwidth to transmit messages. Moreover, above equation provides an idealized framework for comparing the noise performance of one modulation scheme against another.
* The customary practice is to express the SNR in decibels (dBs), defined as 10 times the logarithm (to base 10) of the power ratio.

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