Pass band data transmission

1. Pass band data transmission • In digital pass band data transmission the transmitted data bits are modulated onto a carrier • There are three basic signaling schemes used in pass band these are • Amplitude shift keying (ASK), the data bits modulates the amplitude of the carrier

2. Pass band data transmission • Frequency shift keying (FSK), the data bits modulates the frequency of the carrier • Phase shift keying (PSK), the data bits modulates the phase of the carrier • Those three keying schemes are illustrated graphically in next slide

3. Graphical representation of ASK, FSK and PSK ASK PSK FSK

4. Hierarchy of digital modulation techniques • Digital modulation techniques can be classifieds into • Coherent • Non coherent • This classification depends on whether the receiver contains a phase recovery or not

5. Hierarchy of digital modulation techniques In general coherent detection has a better immunity to noise (better average probability of error) but requires a complicated circuit compared with non coherent demodulation schemes

6. M-ary signaling schemes In many applications where the channel bandwid this limited (always the channel bandwidth is smaller than the desired needs for most applications) it is desired to transmit more than one bit using a single carrier Modulation schemes designed in this manner are called M-ary signaling scheme

7. M-ary signaling schemes In pass band transmission these schemes are known as M-ary ASK, M-ary FSK and M-ary PSK It is possible to generate M-ary signals by combining more than one modulation scheme such as amplitude and phase shift keying which is know as APK A special form of this hybrid modulation is M-ary quadrature amplitude shift keying (QAM)

8. Pass band Transmission model The pass band channel can be modeled as illustrated in the block diagram shown The main difference between pass band and base band model is the presence of modulator and demodulator (detector)

9. Geometric Representation of Modulation Signal • Digital Modulation involves • Choosing a particular signal waveform for transmission for a particular symbol or signal • For possible signals, the set of all signal waveforms are: • The elements of , ,, …., , represent signal levels in multilevel (M-ary) decoding • Also the elements of represents vectors in the vector space

10. Geometric Representation of Modulation Signal For binary modulation, each bit is mapped to a signal from a set of signal set that has M signals We can view the elements of as points in vector space

11. Geometric Representation of Modulation Signal Vector space We can represented the elements of as linear combination of basis functions For example The general form for any signal (symbol or M-Ary level) in can be given by

12. Graphical example of vector representation A given vector here is represented by three orthonormal basis functions ,

13. Geometric Representation of Modulation Signal Vector space The coefficients represents the projection of the symbol on the basis function The coefficients can be found from The number of basis functions are the dimension of the vector space

14. Geometric Representation of Modulation Signal Vector space Basis functions are orthogonal to each-other Each basis function is normalized to have unit energy If the basis functions are normalized, then the basis functions are said to be orthonormal The basis functions can be found by using a procedure called Gram-Schmidt procedure

15. Gram-Schmidt Procedure • In this procedure the basis functions can be found as follows • Find the first basis function

16. Gram-Schmidt Procedure

17. Gram-Schmidt Procedure

20. orthogonality

21. Below, Below,