Soft Demodulation Using Neural Networks

Tammie Yang

EE132A

Professor Lorenzelli

Overview

GOAL: Build neural networks for 5 different modulation schemes to softly demodulate symbols by calculating the bit log-likely ratios (LLRs): BPSK, 8PSK, 4QAM, 16QAM, and 64QAM.

• Generated data in MATLAB
• Created the neural networks in Python
• Calculated exact & approximate bit LLRs
• Tested and chose optimal parameters
• Trained with 15 dB SNR, evaluated with 20, 15, 10, 5 dB SNR data sets
• Plotted accuracy and loss for each modulation scheme
• Implemented a Rayleigh Fading Channel
• Compared modulation schemes
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Data Generation

MATLAB portion

Simulated Channel

• Used randi to generate symbols from 0 to M-1 with gray coding for ‘c’ vector
• Used pskmod, qammod to modulate symbols
• Added AWGN noise with variance calculated from specified SNR value to get ‘s-hat’ vector
• Demodulated by calculating exact and approximate LLRs to get ‘l’ vector
• Saved data in .mat files to import into Python

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LLR Calculations

(Log-likelihood ratio)

Exact log-MAP

• logarithmic max a-posteriori algorithm
• More accurate, slower to calculate
• Logarithm of the ratio of probabilities of a 0 bit being transmitted over that of a 1 bit for a received signal

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• Assuming equal probability for all symbols, and variance is denoted by sigma squared and calculated from specified SNR
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Approximate max-log-MAP

• Maximum logarithmic max a-posteriori algorithm
• Approximation, faster to calculate
• Computed using only the nearest constellation point to the received signal

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Calculation

• BPSK, 8PSK calculated manually for both
• 4QAM, 16QAM calculated manually and using qamdemod
• 64QAM calculated using qamdemod

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Exact vs Approximate LLR

• Linear 1-1 relation proves accurate, correct results
• All modulation schemes shown

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LLRnet overview

Input Layer

• Takes in two inputs
• Received symbol (s-hat) split into two components
• In-phase
• quadrature

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Hidden Layer

• Has K neurons
• Uses ReLU activation function

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Output Layer

• Outputs M-bit LLRs based on M-modulation scheme

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Python code (4QAM example)

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Optimal Parameters

Tested each while keeping all other parameters constant

Optimizer Choice

• Tried multiple different optimizers from Keras options
• Adam gave most optimal results for all modulation schemes
• Organized data from worst to best performance

Performance data for BPSK modulation scheme

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Number of Symbols

• loss increased as the number of symbols decreased
• would like to use higher number of symbols but took much longer to run
• Used 10,000 symbols for BPSK
• 100,000 symbols for rest

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Validation Split

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• denotes how much of the inputted data will be used to train versus validating the model
• found 0.2 to be the optimal split, as the training and validation loss performed most similarly

Number of Neurons

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• More neurons
• longer training/validation time
• Training loss plateaued while validation loss kept decreasing
• More complicated modulation schemes required more neurons

Modulation Schemes

BPSK

Binary Phase-shift Keying

Constellation Plots

Clearly shows two constellation points at 1 and -1

The model showed very low loss after just 50 epochs

Evaluating the BPSK Keras model with the same SNR it was trained at showed the least loss

Evaluation

Training

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8PSK

8 Phase-shift Keying

Constellation Plots

Shows 8 constellation points around a circle, blurring out with lower SNR values

The model showed very low loss after just 10 epochs

Training

Because the accuracy is not 100%, the linear relation is more spread out, showing the effect of the noise

Evaluation

4QAM

4 Quadrature Amplitude Modulation

Constellation Plots

Shows 4 constellation points around a circle, blurring out with lower SNR values

The model showed very low loss after just 10 epochs

Training

The thin linear relation showcases the high accuracy

Evaluation

16QAM

16 Quadrature Amplitude Modulation

Constellation Plots

Shows 16 constellation points around a circle, blurring out with lower SNR values

The model showed very low loss after just 10 epochs

Training

Because the accuracy is not 100%, the linear relation is more spread out, showing the effect of the noise

64QAM

64 Quadrature Amplitude Modulation

Constellation Plots

Shows 64 constellation points as predicted

The model showed very low loss after around 20 epochs

Training

The thin linear relation showcases the high accuracy

Rayleigh Fading Channel

Simulation

• Rayleigh fading is a reasonable model when there are many objects in the environment that scatter the radio signal before it arrives at the receiver
• Generated Rayleigh distributed random amplitudes to multiply sent symbol vector with
• Used scale param value of 1
• Generated uniform random phase from 0 to 2pi to phase shift all sent symbols with
• Added AWGN noise

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Rayleigh Results

• The noise proved to be too much to create a neural network to train
• Symbols all overlapping in the constellation
• Phase shift is very apparent in the angle of the plotted shape
• Further extension of the project I would attempt to implement phase estimation or receiver equalization

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Overall Results

Modulation Scheme Comparison

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BEST: 64QAM

• High accuracy and low loss for all SNR values

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WORST: 8PSK

• High levels of loss compared to other modulation schemes at all SNR values

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Thank you!

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