1. When a signal is transmitted over a channel, the frequency band and bandwidth of the channel must match the signal frequency characteristics. Usually, it is necessary to modify the signal for transmission in order to maximise the efficiency of the communication. Analogue Modulation is a process whereby the ‘baseband’ signal is ‘shifted’ to a different frequency band for transmission by controlling the amplitude, the frequency, the phase, or all of these parameters associated with a ‘carrier’ wave.

2. If the baseband signal is digital, then the carrier parameters are modulated to discrete values by the signal. The process is the same as analogue modulation but the terminology is different: Amplitude Modulation (AM) becomes Amplitude Shift Keying (ASK) Frequency Modulation (FM) becomes Frequency Shift Keying (FSK) Phase Modulation (PM) becomes Phase Shift Keying (PSK) Some digital modulation schemes operate at baseband (eg Pulse Code Modulation) and have no analogue parallel.

3. There is a RECIPROCAL relationship between TIME & FREQUENCY Reducing the signal duration increases the necessary transmission bandwidth Reducing the signal risetime increases the necessary transmission bandwidth T 1/T Time Frequency A AT Time signalSpectrum Fourier Transform

4. Frequency 2B Time 1 0 1 1 The maximum speed of transmission over a channel of bandwidth B (Hz) without ‘inter-symbol’ interference ( ISI ) is 2B pulses/sec (Nyquist) INPUT DATA OUTPUT DATA Channel bandwidth=B (Hz)

5. Note that the perfect ‘brick-wall’ frequency spectrum is not practical. The data pulse is ‘shaped’ to minimise ISI prior to transmission. This can be achieved by controlling the time waveform of each pulse or by shaping the frequency spectrum of the data. Common shaping functions are: time frequency ‘Gaussian’& ‘Raised Cosine’

6. The maximum theoretical error free information capacity for a channel of bandwidth B (Hz) with Signal to ratio S/N in the presence of Gaussian noise is given by: Bits/second To increase the capacity, the bandwidth must increase, or the signal to noise ratio must be improved. (Shannon-Hartley)

7. The spectral efficiency of a modulation scheme is just the ratio of the achieved data rate to the required transmission bandwidth D/B (bits/sec/Hz). Hence the maximum theoretical spectral efficiency of a simple binary baseband transmission is 2 (bits/second/Hz) A simple ‘Pulse Amplitude Modulation’ (PAM) scheme can increase the spectral efficiency by allowing each pulse to represent more than one bit. To keep the error rate low, more signal power is required to maintain the ‘distance’ between signal levels.

8. D/B is a measure of the spectral efficiency of a modulation scheme. Another important parameter is the energy per transmitted bit (Eb joules) required to achieve a specified probability of bit error (Pb) in the presence of gaussian noise (No watts/Hz). The product of spectral efficiency with Eb/No gives the system signal to noise ratio (SNR)

9. Consider a simple ‘sampled’ & ‘quantised’ analogue signal: Provided the sample period T<1/2B, where B is the signal bandwidth, the original signal can be reconstructed (Nyquist) subject to quantisation noise. Samples could be sent as discrete pulses at a maximum rate of 2B pulses/second over a channel with bandwidth B (Hz). If there are 2 n quantisation levels, the data rate would be 2nB bits/second, giving a spectral efficiency = 2n bps/Hz. time T<1/2B Quantisation levels

10. Pulse Amplitude Modulation is converted to Pulse Code Modulation (PCM) if the n bits associated with each amplitude level are transmitted in series as a binary code. The spectral efficiency then reverts to 2 bps/Hz but lower signal power is required to maintain the error rate. (PCM) Each sample transmitted as n binary digits. 2 bps/Hz (PAM) Each sample transmitted at a discrete level. 2n bps/Hz Original signal

11. The amplitude of the carrier is varied in proportion to the baseband signal amplitude. The effect on the spectrum is simply to shift the baseband spectrum from dc (0 Hz) to the carrier frequency (fc Hz) frequency Baseband Signal Spectrum 0(Hz) Baseband bandwidth B(Hz) frequency fc(Hz) Modulated Signal Spectrum RF bandwidth 2B(Hz) RF bandwidth = 2 x baseband bandwidth

12. The frequency of the carrier is varied in proportion to the baseband signal amplitude, to a peak deviation  f (Hz). The effect on the spectrum is to change its form and shift it from dc (0 Hz) to the carrier frequency (fc Hz). frequency Baseband Signal Spectrum 0(Hz) Baseband bandwidth B(Hz) frequency RF bandwidth fc Modulated Signal Spectrum RF bandwidth given by ‘Carson’s rule =

13. The phase of the carrier is varied in proportion to the baseband signal amplitude, to a peak deviation  (rads). The effect on the spectrum is to change its form and shift it from dc (0 Hz) to the carrier frequency (fc Hz). Instantaneous frequency is the differential of phase with respect to time. Hence the peak phase deviation and the peak frequency deviation for a sinusoidal modulation are related by:

14. 2n bps/Hzn bps/Hz The amplitude of the carrier is modulated to 2 n discrete levels. OOK = On Off Keying, a binary form of ASK The spectrum is similar to that of the baseband pulse spectrum, shifted to the carrier frequency fc. frequency fc(Hz) Modulated Signal Spectrum RF bandwidth 2B=1/T (Hz) frequency Baseband Signal Spectrum 0(Hz) Baseband bandwidth B=1/2T (Hz) T symbol OOK spectral efficiency = 1 bps/Hz (max), 0.8bps/Hz (practical)

15. The frequency of the carrier is modulated to 2 n discrete levels. Usually used in binary form where n=1. The spectrum associated with each transmission frequency is similar to that of ASK, the overall spectrum depending upon the separation of the two frequencies. Hence spectral efficiency is variable & usually less than PSK f1f1 fofo fcfc frequency FSK bandwidth

16. The phase of the carrier is modulated to 2 n discrete levels. PRK = Phase Reversal Keying, a binary form of PSK. QPSK = Quadrature Phase Shift Keying, a 4 level version. The spectrum is similar to that of ASK but the carrier frequency component is usually removed by the phase reversal for PRK & QPSK. PRK spectral efficiency = 1 bps/Hz (max), 0.8bps/Hz (practical) QPSK spectral efficiency = 2 bps/Hz (max), 1.9bps/Hz (practical)

17. MSK = Minimum shift keying, binary FSK with the minimum distance between the two transmission frequencies. The frequency deviation is: GMSK = Gaussian Minimum Shift Keying, MSK with Gaussian pulse shaping. fcfc frequency fc+3/4Tfc-3/4T 1.5/T Practical Spectral efficiency = 1.9 bps/Hz Rapid decay of spectrum improves spectral efficiency

18. APK = Amplitude Phase Keying APK is a combination of APK and PSK This is easy to visualise with a ‘signal space’ diagram. QPSK8 level APK