1. Signal Encoding Techniques

2. Lecture Learning Outcomes Be able to understand, appreciate and differentiate the different signal encoding criteria available.

3. Class Contents Signal Encoding Criteria Digital Data, Analogue Signals ASK FSK PSK QAM Analogue Data, Analogue Signals AM Angle Modulation Analogue Data, Digital Signals PCM Delta Modulation

4. Signal Encoding Criteria Encoding is referred in general to the process of conversion Of analogue or digital data into analogue or digital signals

5. Signal Encoding Criteria Wireless communications relevant techniques:  Digital to Analogue Conversion  Analogue to Analogue Conversion  Digital to Digital Conversion Most important factor in determining how successful was the interpretation of the signal:  SNR or E b /N 0  Data Rate (R)  Bandwidth (B)

6. Signal Encoding Criteria TermUnitsDefinition Data ElementBitsA single binary one or zero Data RateBits per second (bps)The rate at which data elements are transmitted Signal ElementDigital: a voltage pulse of constant amplitude. Analogue: a pulse of constant frequency, phase and amplitude That part of a signal that occupies the shortest interval of a signalling code. Signalling Rate or Modulation Rate Signal elements per second (bauds) The rate at which signal elements are transmitted.

7. Digital Data to Analogue Signals Amplitude Shift-Keying Frequency Shift-Keying Phase Shift-Keying Quadrature and Amplitude Modulation The principle of operation compromises the representation of a digital data stream using an analogue signal

8. Amplitude Shift-Keying (ASK) Transmitted signal for 1 bit time

9. Frequency Shift-Keying (FSK) Transmitted signal for 1 bit time Also known as Binary FSK (BFSK)

10. Multilevel FSK (MFSK) Signal more bandwidth efficient, but more susceptible to error. More than 2 frequencies are used to represent multiple levels of the signal. Each signal element represent more than 1 bit MFSK for 1 element:

11. Phase Shift-Keying (PSK) Transmitted signal for 1 bit time Phase of the carrier shifted 180 0. Also known as binary PSK (BPSK)

12. Differential Phase Shift-Keying (PSK) Transmitted signal for 1 bit time Alternative form of PSK. For a binary 0, the phase is the same as In the previous bit. For a binary 1, the phase changes 180 0.

13. Quadrature Phase Shift-Keying (QPSK) When the phase shifts occurs at 90 0 it is called QPSK Each signal element is represented by 2 bits.

14. Quadrature Phase Shift-Keying (QPSK) the amplitudes of the binary 1 and 0 are scaled and represented by and respectively

15. Multilevel Phase Shift-Keying (QPSK)  The use of multiple levels can be extended taking more than 2 Bits at a time and decreasing the phase angle used.  Further, each angle taken can have more than one amplitude. Example: a standard 9600 bps modem uses 12 phase angles, four of which have two amplitude values for a total of 16 different signal elements

16. Lets assume a bit stream of 1s and 0s at a data rate of R=1/tb. The encoded signal contains (L=4) bits in each signal element using M=16 different combinations of amplitude and phase. The modulation rate can be seen to be R/4, because each change of signal element communicates 4 bits. Therefore, the line signalling speed is 2400 bauds, but the data rate is 9600 bps Multilevel Phase Shift-Keying (QPSK) Data Rate and Modulation Rate D = modulation rate in bauds R = data rate in bps M = number of different signal elements = 2 L L = number of bits per signal element

17. Quadrature Amplitude Modulation (QAM) QAM is a combination of ASK and PSK. It is based on the fact that two signals can be transmitted simultaneously on the same carrier frequency, by using two copies of the carrier frequency, one shifted 90  with respect to the other

18. Analogue Data to Analogue Signals Reasons to do Analogue Modulation of Analogue Signals Higher frequency needed for effective transmission Modulation permits frequency division multiplexing, which is an important technique used to transmit signals simultaneously over the same communications channel. Modulation is the process of combining an input signal m(t) And a carrier frequency f c to produce a signal s(t) whose Bandwidth is usually centred in f c

19. Amplitude Modulation (AM) The amplitude of the carrier signal is altered using as guide the modulating (baseband) signal (m(t)). This signal is of lower frequency than the carrier. Where cos(2.  f.t ) is the carrier frequency and x(t) is the input signal, both normalized to unity amplitude. The parameter n a is known as the modulation index, is the ratio of the amplitude of the input signal to the carrier.

20. Amplitude Modulation (AM) Time Domain Frequency Domain

21. Amplitude Modulation (AM) Power Relationship in AM: where P t is the transmitted power in s(t), P c is the transmitted power in the carrier. The ideal would be that most of the signal power is used to transmit information (that is n a as big as possible), however, n a must remain below 1 to avoid loss of information.

22. Angle Modulation Frequency modulation (FM) and phase modulation (PM) are special cases for angle modulation Modulated Signal: For phase modulation, the phase is proportional to the modulating signal:

23. Angle Modulation (AM) For frequency modulation (FM), the time derivative of the phase is proportional to the modulating signal: Bandwidth Comparison: AM: B T =2.B Angle modulation includes a term of the form cos(  t  ), which is non linear And will produce a wide range of frequencies.

24. Bandwidth for Angle Modulation In practice, a good approximation to the bandwidth in angle modulation is known as the Carson’s rule Both FM and PM require greater bandwidth than AM

25. Digital Data to Digital Signals The digital signal can be transmitted using NRZ-L. In this case the process has gone from analogue data to a digital signal. The signal can be encoded as a digital signal using a code different from NRZ-L. This process requires an extra step The digital data can be converted into an analogue signal using one of the modulation techniques previously discussed (ASK,FSK,etc.) This process should be written as the conversion of analogue Data into digital data. This process is known as digitalization. Once data have been digitalized, the 3 most common things that happens next are:

26. Digital Data to Digital Signals The device used for converting analogue data into digital signals is called CODEC. The two principal CODEC techniques are:  Pulse Code Modulation  Delta Modulation

27. Pulse Code Modulation It is based on the sampling theorem which states: “If a signal f(t) is sampled at regular intervals of time and at a rate higher than twice the highest signal frequency, then the samples contain all the information of the original signal. The function f(t) may be reconstructed from these samples by the use of a low-pass filter”. The samples taken from the analogue signal are analogue samples called pulse amplitude modulation (PAM), to convert them to digital; each of these samples should be assigned a binary code.

28. Pulse Code Modulation A8D8 B15E6 C12F6 Sample Quantization Level Assigned

29. Using 16 levels in the sampling process, a digital binary signal coded in 4 bits is needed to represent all the possible sample levels. Pulse Code Modulation SampleBinary Code SampleBinary Code SampleBinary Code SampleBinary Code 000004010081000121100 100015010191001131101 2001060110101010141110 3001170111111011151111 The resulting PCM bit stream for the above example is: 100011111100100001100110

30. Pulse Code Modulation Typically, the PCM scheme is refined using a technique known as nonlinear encoding, which means that the quantization levels are not equally spaced. The main problem with equal spacing is that the mean absolute error for each sample is the same, regardless of signal level. Consequently, lower amplitude values are relatively more distorted. The same effect (as non-linear encoding) can be achieved by using uniform quantization but companding (compressing-expanding) the input analogue signal. Companding is a process that compresses the intensity range of a signal by imparting more gain to weak signals than to strong signals on input. At output, the reverse operation is performed. Non-linear encoding can significantly improve the PCM SNR ratio. For voice signals, improvements of 24 to 30 dB have been achieved.

31. Delta Modulation It is an alternative technique to PCM. It is easier to implement than PCM In DM, an analogue signal is approximated by a staircase function that moves up or down by one quantization level (  ) at each sampling interval T S. At each sampling time, the function moves up or down a constant amount . Thus, the output of the delta modulation can be represented as a single binary digit for each sample.

32. Delta Modulation With this technique, a bit stream is produced by approximating the derivative of an analogue signal rather than its amplitude. A binary 1 is produced is the staircase function is to go up in the next interval, and a 0 is generated otherwise:

33. Delta Modulation The two important parameters in delta modulation are:  The size of the step assigned to each binary digit (  )  The sampling rate.

34. Delta Modulation There are two types of error:  Quantization Noise: occurs when the analogue waveform is changing very slowly. This noise increases as  increases.  Slope Overload Noise: occurs when the analogue signal is changing so fast that the staircase function can not follow. This noise is increased as  is decreased.  must be chosen to produce a balance between the two noise figures. The principal advantage of DM over PCM is its simplicity in implementation. However, PCM exhibits better SNR characteristics at the same data rate.