# Multi-Level Digital Modulation & Demodulation

9.1

2 May’06 / BMGC

Multi-level digital modulation & demodulation.

9.1. Introduction: So far, in looking at carrier modulated data transmission, we have concentrated mainly on binary signalling using simple forms of ASK, FSK and PSK. With a suitable pulse-shape, binary signalling can achieve a bandwidth efficiency of up to 2 bits/second per Hz using real unipolar pulses (base-band equivalent of ASK) or real bipolar pulses (base-band equivalent of PSK) at base-band. Since multiplying the base-band signal by a sinusoidal carrier doubles its bandwidth, the maximum band-width efficiency of binary ASK and binary PSK becomes one bit/second/Hz . With this band-width efficiency, a computer modem could achieve a maximum of about 3.1 kb/s over a 300-3400 kHz domestic telephone link. This is less than one tenth of what we know to be achievable. A similar calculation for the bandwidth-efficiency of binary FSK is a little more complicated, but if we take the frequency spacing used by MSK, i.e. 1/(2T) Hz, which is the minimum spacing compatible with the desirable highly property of 'orthogonality' between the 2 symbols, we may expect to achieve a maximum of slightly less than 2 bit/second per Hz. To increase the band-width efficiency over what can be achieved with binary signalling we must use multi-level modulation schemes where each symbol represents more than one bit. 9.2. Multi-level ASK and Gray coding: Perhaps the most obvious multi-level modulation technique, though rarely used, is 'M-ary ASK' which modulates the amplitude of a sinusoidal carrier with M different amplitudes. To encode N bits per symbol, rather than just one as with binary signalling, choose M=2N rather than M=2. For example, to encode 3 bits per symbol, we could have 8 rectangular symbols of heights 0, A, 2A, 3A, 4A, 5A, 6A and 7A volts. Consider what happens to the 'bit-error probability', PB , when we adopt this new signalling strategy. We can hope to keep PB...

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