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!