The document discusses multi-rate modulation, a bandwidth and power efficient modulation scheme. Multi-rate modulation resembles block coded modulation and partial response modulation, using encoding matrices to transform input blocks into output blocks with different sampling rates. This creates a Nyquist null to improve bandwidth efficiency. Advantages over partial response modulation include no loss of synchronization or error propagation, and improved gain of up to 1.5dB.

1. Multi-rate Modulation:
A Bandwidth and Power efficient
Modulation Scheme
By: Khalid Ibrahim
MS Electronics Engg. (IIUI)

3. Modulation
• Binary sequence can't be transmitted
• Compatible format
• Mapping the information sequence into the
signal waveforms.
(Also called Digital modulation)

4. Multirate Modulation
• Resembles Block Codded Modulation.
• Encoding matrices are used for transformation.
– y = C x
• To provide
– Spectral Shaping: H(-1)=0
– Euclidean distance: 2 2
– Encoding Matrix is implemented using MR digital
filters of low complexity.

5. Multirate Modulation
• Resembles Partial Response Modulation.
• Both use doubinary signaling.
• An Extension of Partial Response Modulation.

6. PR
• BW efficient
• Use Doubinary signaling
– Can transmit 2 times the minimum BW W(sym/s)
– With controlled ISI

7. Continued….
• Yk= xk + xk-1
– [input signal + its delayed version]
– H(z)=1+z-1
– Using Sinc(πt/T) pulse (controlled ISI)
– Precoding is needed to avoid error propagation

8. Advantages of
MR over PR Modulation
• NO Loss of synchronization or Gain control.
• NO Error propagation
• Improved Gain of 1.5dB
• Improved BW efficiency

9. Multirate
• Output sampling rate of MR varies from input
sampling rate.
• Similar to PR,MR Filter give spectral Null at
Nyquist frequencies. ( f=1/2T )
MR Digital
filter
Ideal Low
Pass Analog
Filter
Dobinary
Impulse
response

10. Main Idea of MR
• Transformation of input block ta a different
output block [using Matrix C]
– y = C x
• To create a NYQUIST NULL

11. Example
• Input sequence {+1,-1} [+(2k-1),-(2k-1)]
• Input Block length x=3
• Output Block length y =4 {-2,0,+2}
• [+(2k+1-2),0,-(2k+1-2)]
• 3T=4T’
• Using y= 퐶 푥

12. • No Output block
contain all 0’s. No loss
of synchronization
• dH=2, dmin=2 2
• Nyquist Null at:

13. MR filter structure for matrix
transformation

14. Cascade of MR filter with Analog filter

15. • Impulse response of ideal low pass filter
• Impulse response of cascaded system.

16. • Fourrier transform

17. Spectral Null
• Spectral null is obtained when
• Condition on y

18. Matrix C
• Every column correspond to system function
that is zero for z=-1
• Each row contains zero entries except two
entries from {+1,-1}

19. Generalized MR Filter

20. Decoding
• Remove last component of y and last row of C
to make C a k-1 x k-1 Matrix.

21. Bandwidth efficiency:
퐾−1
퐾

22. BW Efficiency
• For k=10
• Slightly higher bandwidth
• For K>10
• Better bandwidth efficiency

23. Power Efficiency for M=2

24. Power Efficiency for M=4

25. Improved Gain of 1.5dB
• Computer simulations [ciacci]
– For K=10
– AWGN channel
– BER = 10-6
• MR with Wagner Decoding:
– Better Gain of 1.3dB(M=2) & 1.5dB(M=4)
• PR with symbol by symbol detection

26. Thanks!