Machine Learning Based Featureless Signalling: A Brief Review
Direct-sequence spread-spectrum (DSSS)
Many communication systems use a direct-sequence spread spectrum to avoid jamming and interference. It spreads the signal over a wider bandwidth by multiplying (element-wise) it with a spreading code (pseudo-random noise/ binary pseudo-noise) that has a higher rate than the original signal. This reduces the required transmit power per channel symbol. The spreading codes are deterministic.
We combine an N-length pseudo-noise (PN) with each encoded bit during the modulation. Symbols in the spreading sequence are called chips. We despread the received signal by multiplying (correlating) it with the same PN sequence. The correlated signal is positive for the bit value 1 and negative for the bit value 0. A predefined unique word is used to define the start of the signal.
The autocorrelation function(ACF) calculates the correlation between the signal and a time-shifted version of itself. For a spreading sequence, the ACF must have a high value at zero, and vanishing (almost zero) values for other delays.
M-sequences (a type of PN sequence) are generated using a sequence of Linear Feedback Shift Registers (LFSR). These sequences may show a periodic nature in the absence of a large number of LFSRs. Using ACF, we can detect the periodicity and thus, predict the spreading sequence. Thus, standard DSSS techniques have poor Low Probabilities of Detection (LPD).
Spreading allows us to use a low signal power to noise power ratio (SNR). The amount of reduction of SNR is equal to the spreading factor.
Our modulated signal must be indistinguishable from background noise. Thus, it must be featureless.
ML-Based Spread Spectrum (MLSS)
Instead of improving individual components of a communication system, we can optimize the whole system (transmitter, channel, and receiver) by considering it as an autoencoder. This helps us to model complex environments and channel models. Moreover, it can be dynamically adapted using real-time learning.
The hidden layer in the middle (channel) has n neurons (n can be interpreted as the number of channel symbols). For k-bit blocks (signals of length k bits), the input to the autoencoder has 2ᵏ inputs. We model the channel as Additive White Gaussian Noise (AWGN).
We use an ML model to spread data block-by-block. We input a one-hot vector of size 2ᵏ with one element +1 and others -1. The model generates a k block of data across kN chips (symbols). N = n/k, where N is the spreading factor.
Let, E/Nₒ be the energy per chip to noise power ratio. We can write the SNR in the following way.
We use cross-entropy loss as the loss function.
We can plot Bit Error Rate (BER) aginst SNR. We will take K = 8 and N = 32. Thus, n = 256. We train the network on a noise-free channel.
The MLSS system demonstrates a significant performance improvement compared to the binary phase shift keying (BPSK) modulated DSSS-PN system.
Walsh-Hadamard codes are a set of orthogonal binary sequences used in communication systems including CDMA. MLSS performs close to Walsh-Hadamard codes with maximum likelihood decoding(MLD) or soft-decision decoding(SD).
The ACF plot of MLSS shows no repetitive patterns.
However, the constellation diagram shows a non-Gaussian-like distribution. A large number of points have converged to zero.
To get a more Gaussian-like constellation diagram, we must train the model on an AWGN channel.
Computationally Efficient Architecture
Instead of using inputs of size 2ᵏ, we will use k neurons in the input. The message (bit sequence) is directly fed into the network. Elements 1 and 0 in the input are mapped into +1 and -1. The model is trained on an AWGN channel.
The model performs close to the uncoded system. Thus, we must concatenate the model with an error correction coding scheme. In the place of the sigmoid function, we use an Elliot Symmetric Sigmoid (ESS). ESS does not use exponential functions. Thus, it is computationally efficient. The mean absolute function (MAE) is used to calculate the loss value.
We can compare the distribution of the chips to the standard Gaussian distribution. The distributions look almost similar.
We can evaluate the BER performance of MLSS. We will use LPDC and extended BCH as the error-correcting codes. Both trained with and without noise, uncoded MLSS models closely follow uncoded DSSS-PN. With error correction codes, MLSS shows a significant performance improvement.
The signal constellation also shows a noise-like signal.
MLSS (received signal) has a flat power spectrum.
Thus, the received signals become indistinguishable from the background noise. This helps to avoid jamming and interference.
References
Shakeel, I. (2018). Machine Learning Based Featureless Signalling. ArXiv. /abs/1807.07260
All the images are sourced from the aforementioned paper.
