multirate modulation
DESCRIPTION
Multirate modulation A Bandwidth and power efficient Modulation schemeTRANSCRIPT
Multi-rate Modulation:
A Bandwidth and Power efficient Modulation Scheme
By: Khalid Ibrahim
MS Electronics Engg. (IIUI)
Modulation
• Binary sequence can't be transmitted
• Compatible format
• Mapping the information sequence into the signal waveforms.
(Also called Digital modulation)
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.
Multirate Modulation
• Resembles Partial Response Modulation.
• Both use doubinary signaling.
• An Extension of Partial Response Modulation.
PR
• BW efficient
• Use Doubinary signaling
– Can transmit 2 times the minimum BW W(sym/s)
– With controlled ISI
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
Advantages of
MR over PR Modulation
• NO Loss of synchronization or Gain control.
• NO Error propagation
• Improved Gain of 1.5dB
• Improved BW efficiency
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
Main Idea of MR
• Transformation of input block ta a different output block [using Matrix C]
– y = C x
• To create a NYQUIST NULL
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= 𝐶 𝑥
• Nyquist Null at:
• No Output block contain all 0’s. No loss of synchronization
• dH=2, dmin=2 2
MR filter structure for matrix transformation
Cascade of MR filter with Analog filter
• Impulse response of ideal low pass filter
• Impulse response of cascaded system.
• Fourrier transform
Spectral Null
• Spectral null is obtained when
• Condition on y
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}
Generalized MR Filter
Decoding
• Remove last component of y and last row of C to make C a k-1 x k-1 Matrix.
Bandwidth efficiency: 𝐾−1
𝐾
BW Efficiency
• For k=10
• Slightly higher bandwidth
• For K>10
• Better bandwidth efficiency
Power Efficiency for M=2
Power Efficiency for M=4
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
Thanks!