1. Modulation and Coding Trade Offs 20117764 Ramesh Kumar Lama

2. Outline Defining, Designing and Evaluating Digital Communication System M-ary System Bandwidth Limited Systems Power Limited Systems Requirements for MPSK and MF SK Signaling Bandwidth Limited Un coded System Example Power limited Uncoded system Band Limited and Power Limited Coded System Example Code Selection Conclusion

3. Defining, Designing and Evaluating Digital Communication System Intended to serve as road map for outlining the typical steps that need to b e considered in meeting bandwidth, power and error requirements in digita l communications. Two primary communication resources are the received power and availab le transmission bandwidth. In many communication systems, one of these resources may be more pr ecious. Hence most systems can be classified as either band width limited or power limited. The criteria for choosing modulation and coding schemes based on whether a system is bandwidth limited or power limited are reviewed

4. M-ary System Signaling systems that process k bits at a time. Each symbol in an M-ary alphabet can be related to a unique sequence of k bits M is the size of the alphabet. gives the symbol duration Data rate R Effective time duration of each bit in terms of symbol duration Symbol rate Bandwidth efficiency

5. Bandwidth Limited Systems Any digital communication system will become bandwidth efficient as its product is decreased. Signals with Small w are often used with bandwidth limited systems like GSM with the 0.3 Hz/bits/s. For the un coded bandwidth limited systems, the objective is to maximize the transmitted information rate within the allowable bandwidth, at the expense of The efficiency of MPSK modulated signals using Nyquist filtering can be expressed as

7. Power Limited Systems Power is scarce but system bandwidth is available. Trade offs –improved with the expense of bandwidth for a fixed –Reduction of at expense of bandwidth for fixed –A natural modulation choice for a power limited system is M-ary (MFSK).  Since there are M-different orthogonal waveforms, each requiring bandwidth of Ts, B/W efficiency of non coherent MFSK is

8. Requirements for MPSK and MFSK Signaling The basic relation between the symbol transmission rate Rs and the date R

9. Bandwidth Limited Un coded System Example Given a bandwidth limited AWGN radio channel with and available bandwidth W=4000Hz The required data rate =9600bits/s. Bit error performance = Goal=>To choose the modulation scheme that meets the required performance For any digital communication system, the relationship between received power to noise power spectral density and received bit energy to noise power spectral density

10. Since the required data rate of 9600 bits/s is much larger than the available band 4000Hz, the channel can be described as bandwidth limited. Thus MPSK scheme is selected. Next smallest value of M is selected such that symbol rate is at most equal to available bandwidth. Thus M=8 is selected. Next check the bit error performance with M=8

11. Figure Basic modulator/demodulator without channel coding

12. Power limited Uncoded system The required data rate =9600bits/s Bit error performance = available bandwidth W=45kHz = 48dB-Hz. The received is found to be Since there is abundant bandwidth but a relatively small amount of This channel may be referred as power limited. Thus MFSK as modulation scheme is chosen. Next largest value of M is selected such that MFSK minimum bandwidth is not expanded M=16 is selected. Next check the bit error performance with M=16

13. Band Limited and Power Limited Coded System Example. W=4000Hz = The required data rate R =9600bits/s Bit error probability must be at most 10 -9 Since the available bandwidth is 4000Hz, the available is 13.2dB. System is both bandwidth limited and power limited. We need to consider the performance improvement by error correcting code Convolution Code or Block Codes can be used. Table presents a partial catalog for the available BCH codes in terms of n, k and t. Start with same 8-PSK in order to meet the stated bandwidth constraint. Additionally, error correction code is employed so that the bit error probability can be lowered to To make the optimum code selection from the code table we are guided by following goals

14. –The output bit error probability of the combined modulation/coding system must meet the system error requirement. –The rate of code must not expand the required transmission bandwidth beyond the available channel bandwidth. –The code should be as simple as possible. Generally, the shorter the code the simpler will be its implementation. The un coded 8 PSK minimum bandwidth requirement is 3200 Hz. And allowable channel bandwidth is specified as 4000Hz. Un coded signal bandwidth may be increased by no more than a factor of 1.25 Thus eliminate the candidates from table that would expand the bandwidth more than 25% Coding gain:

15. In table the coding gain G has been computed for MPSK at P B =10 -5 and 10 -9. thus for a particular bit error probability a given code will provide approximately the same coding gain when used with any of the modulation schemes.

16. Real time system is assumed thus cannot tolerate any message delay. The channel rate Rs must exceed the data bit rate R by factor n/k.

17. Code Selection There are two mechanism at work to influence error performance in real tim e communication system. One mechanism works to improve and other works to degrade. Improving mechanism is coding. the greater redundancy, the greater will be the error correcting capability of code. Degrading mechanism is the energy reduction per channel symbol The reduced energy causes the demodulator to make more errors. Eventually, the second mechanism wins out and thus at very low bit rate we see degradation.

18. Conclusion The criteria for choosing modulation and coding schemes based on whether a system is bandwidth limited or power limited were reviewed. The design choices that best match the channel and meet the performance requirements were determined from the given channel description

19. Question Distinguish between the Power limited syst ems and Bandwidth systems.