Answered: We have a channel with a 5-MHz…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

We have a channel with a 5-MHz bandwidth. The SNR for this channel is 255. Assume that we choose a bit rate that is 75% of the maximum theoretical bit rate. What are the bit rate and signal level for this design? Tip: Use both Shannon formula and Nyquist formula.

Expert Solution

Step 1

In theory, bandwidth is related to data rate or we can say bit rate by:

1) Nyquist formula: bit rate = 2 * bandwidth * log2 (M) ; where M is the signal level (eg., M=4 for QPSK ).

2) Shannon formula: bit rate = bandwidth * log2(1+SNR); where SNR is the signal to noise ratio.

So using the above formulas the following answer is hence, obtained.

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