Transmitter Design in Communication Systems

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Transmitter Design in Communication Systems

• Majid Fozunbal
• October 19, 2001

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Outline

• Mathematical insight to communication systems
• General scheme
• Channel
• Transmitter
• Transmission over AWGN channel
• Traditional method
• Coded modulation
• Non-ideal Gaussian channel
• Transmission over fading channels
• Encoding without CSI in transmitter
• Encoding with CSI in transmitter
• Diversity
• Multiple antenna system

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General Scheme
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Channel

• Distortion a linear operator.
• Example any causal linear filter.
• Having null space, not invertible.
• Injective, one to one, preserves dimensionality.
• Finite dimension, matrix theory.
• Perturbation
• Noise, interference.
• Uncertainty.
• No overlap, error-free inverse mapping.
• Amount of overlap, error rate.

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Channel (Cont.)
Channel Output Space
RN

• RSN and RN are normalized per dimension (infinite
  dimension).
• Gaussian noise.

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Transmitter

• An injective mapping from message space to signal
  space.
• Compensating the channel distortion.
• Finite dimension, soft balls, non-zero error
  rate.
• Tradeoff between spectral efficiency and error
  rate defined by region of decision.
• Infinite dimension, rigid spheres, zero error
  rate.
• Increasing dimension, hardening the balls,
  increasing the spectral efficiency, decreasing
  robustness to noise variance.

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Transmission over AWGN Channel

• No distortion, just additive white Gaussian
  noise.
• Band limited channel.
• Constraint Power.
• Goals
• Given an error rate, maximize the spectral
  efficiency.
• Given a spectral efficiency, minimize the error
  rate.

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Traditional Method

• Separate coding and modulation.
• Adds redundancy to maximize the minimum free
  Hamming distance.
• Information rate K/N.
• Decreases the spectral efficiency.

4K sequences (4-PSK)
4K out of 4N sequences
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Coded Modulation

• Combined coding and modulation.
• TCM, Multi-level coding, Coset codes.
• Adding redundancy by using a bigger signal
  constellation.
• Convolutional coder and nonlinear mapping.
• Maximizing the minimum free Euclidean distance.

4K Sequences (4-PSK)
4K out of 8K (8-PSK)
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Non-Ideal Gaussian Channel

• Non-ideal AWGN channels suffer ISI.
• Dividing to a bunch of ideal sub-channels.
• Multi-carrier, OFDM.
• Spectral water-filling maximizes power
  efficiency.
• Bit-loading to optimize spectral efficiency.

Power allocation for sub-channels
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Transmission over Fading Channel

• Time variable operators.
• Characterized by PDF (Rayleigh, Rician).
• Coherence time, coherence bandwidth.
• Flat fading, slowly fading.
• Channel estimation.
• Fading decreases the channel capacity.

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Encoding without CSI in Transmitter

• Ergodic channel.
• Time interleaving to achieve capacity.
• Infinite length interleaving is required.
• Suitable for data.
• Delay constraint, no good for speech.
• Uniform power distribution.
• Design criteria
• Maximizing Hamming distance.
• Product distance.
• Note Performance depends on PDF.

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Encoding with CSI in Transmitter

• Possible in slowly fading channels.
• Transmit more power and data when channel is
  good.
• Temporal water-filling.
• Bit-loading and variable size modulation skims.
• Adaptive modulation TCM and Multi-level coding.

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Diversity Techniques

• Diversity changes the statistics of the received
  signal.
• Time diversity.
• Frequency diversity.
• Space diversity
• Receiver.
• Transmitter (Needs CSI).
• Correlation decreases the diversity gain.

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Multiple Antenna Systems
X
H
Y
Y H X V
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MIMO (NO CSI in Transmitter)

• N by N MIMO.
• N times of SISO capacity (no correlation).
• Degrees of freedom
• Combat fading.
• Space-time TCM
• High efficiency.
• Complex decoder.
• Space-time Block Coding
• Maximum diversity.
• Simple decoder.
• Beam-forming.
• BLAST Source separation.

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MIMO (with CSI in Transmitter)
School of ECE
School of ECE

• Beam-forming in transmitter and receiver.
• Singular value decomposition (SVD).
• A parallel bank of SISO channels.
• Capacity is defined by PDF of singular values.
• Temporal-spatial water-filling.