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Neural Network Detection of Data Sequences in Communication Systems

Nariman Farsad, Andrea Goldsmith

arXiv:1802.02046v3eess.SPcs.ITcs.LG

TL;DR

The paper addresses communication detection when channel models are unknown or CSI is unavailable. It trains neural detectors, including a real-time SBRNN, from transmitted and received data and evaluates them on Poisson and experimental molecular channels. SBRNN performs well across changing conditions, with BER better than Viterbi detection using imperfect CSI and other evaluated neural detectors.

  • Problem

    Detection is difficult when channel models are unknown or intractable, and CSI estimation adds pilot overhead while potentially reducing accuracy.

  • Method

    The paper trains neural-network detectors from transmitted and received samples, including an SBRNN that detects symbols in real time as the stream arrives.

  • Results

    SBRNN performs well without channel-model knowledge or CSI, and its BER is better than Viterbi detection with imperfect CSI and other evaluated neural detectors.

  • Takeaways & Limitations

    SBRNN supports computationally efficient detection across changing channels and can be trained from limited measurements when analytical molecular-channel models are unavailable.

Abstract

from arXiv · show

We consider detection based on deep learning, and show it is possible to train detectors that perform well without any knowledge of the underlying channel models. Moreover, when the channel model is known, we demonstrate that it is possible to train detectors that do not require channel state information (CSI). In particular, a technique we call a sliding bidirectional recurrent neural network (SBRNN) is proposed for detection where, after training, the detector estimates the data in real-time as the signal stream arrives at the receiver. We evaluate this algorithm, as well as other neural network (NN) architectures, using the Poisson channel model, which is applicable to both optical and molecular communication systems. In addition, we also evaluate the performance of this detection method applied to data sent over a molecular communication platform, where the channel model is difficult to model analytically. We show that SBRNN is computationally efficient, and can perform detection under various channel conditions without knowing the underlying channel model. We also demonstrate that the bit error rate (BER) performance of the proposed SBRNN detector is better than that of a Viterbi detector with imperfect CSI as well as that of other NN detectors that have been previously proposed. Finally, we show that the SBRNN can perform well in rapidly changing channels, where the coherence time is on the order of a single symbol duration.

I. INTRODUCTION

The paper frames detection as recovering transmitted data from noisy observations when channel models or instantaneous CSI may be unavailable. It proposes data-driven neural detectors, including SBRNN, and evaluates them on modeled and experimental communication channels.

  • Detection estimates transmitted signals from noisy, corrupted receiver observations, traditionally using mathematical channel models.
  • CSI estimation requires pilot transmissions, reducing data rate and potentially degrading detection when the estimate is inaccurate.
  • The proposed approach trains neural detectors directly from transmitted and received samples, without requiring channel-model knowledge.
  • SBRNN performs real-time sequence detection as a data stream arrives and can be trained on diverse channel conditions to avoid instantaneous CSI estimation.
  • In Poisson-channel evaluations, SBRNN is more computationally efficient than Viterbi detection for long-memory channels and outperforms Viterbi with CSI estimation error and other neural detectors.
  • Unknown or intractable channel models make conventional detection design unclear, while long channel memory can make optimal Viterbi detection computationally infeasible.

III. DETECTION USING DEEP LEARNING

The paper trains neural-network detectors with supervised examples of transmitted and received sequences. The trained networks output symbol-probability estimates that support hard decisions and soft channel decoding.

  • Detection uses an offline training phase followed by deployment of the trained neural network for detection.
  • Known symbol sequences are transmitted or generated through models, simulations, experiments, or field measurements to create training data.
  • A deep neural classifier maps received signals or extracted features to probability vectors over the transmission-symbol set.
  • The probability outputs support soft-decision channel decoding, while the maximum-probability symbol provides a hard decision when channel coding is absent.
  • The network is optimized using known transmission sequences, stochastic-gradient methods, backpropagation, and cross-entropy loss.

B. Symbol-by-Symbol Detectors

Symbol-by-symbol detectors use fully connected or convolutional neural networks to estimate symbol probabilities from received signals or extracted features. Their softmax outputs form probability mass functions over the symbol set.

  • Fully connected detectors accept received signals or features and use a softmax output of length m to produce a symbol probability mass function.
  • CNN detectors learn filters that extract relevant detection features before a dense softmax layer estimates the symbol probabilities.
  • For symbol-by-symbol detection, the estimated probability vector contains one neural-network probability for each possible transmitted symbol.
  • Detection quality depends on how well the neural-network structure captures the physical channel characteristics.

C. Sequence Detectors

Sequence detectors use recurrent architectures to account for intersymbol interference, while bidirectional processing incorporates future observations. The proposed SBRNN slides a fixed-length BRNN window to provide real-time estimates with complexity that grows linearly with window length.

  • RNN and BRNN: RNN detectors estimate each symbol from current and prior observations, but feed-forward processing omits future observations that may contain information because of delayed channel effects.RNN state summarizes prior observations for streaming detection, whereas future observations are excluded during estimation.
  • RNN and BRNN: BRNNs process the received sequence both forward and backward, combining the two directions so symbol estimates can use future signal observations.This addresses the feed-forward limitation of ordinary RNNs in the presence of intersymbol interference.
  • BRNN constraints: A fixed maximum BRNN length L limits computation; it should ideally match channel memory, or be tuned as a training hyperparameter when memory is unknown.Without a fixed length, re-estimating the entire growing stream becomes infeasible for long sequences.
  • SBRNN detector: The SBRNN slides the BRNN window one symbol at a time and combines estimates from all valid overlapping windows for each symbol.The final symbol probability mass function is formed from weighted estimates associated with the relevant window positions.
  • SBRNN detector: After the first L symbols arrive, SBRNN immediately estimates each new symbol while dynamically updating the previous L −1 estimates.This gives the detector a dynamic-programming-like streaming operation.
  • Complexity and evaluation: SBRNN complexity increases linearly with the BRNN window length and therefore with the channel memory length.The evaluation uses both the Poisson model and an experimental molecular-communication platform with an unknown underlying model.

IV. THE POISSON CHANNEL MODEL

The Poisson channel models particle-count communication in optical and molecular systems, with observations determined by transmitted symbols, channel response, and additive Poisson noise. Optical and molecular responses have similar shapes but differ in rise time and tail duration.

  • Channel formulation: The Poisson channel represents information through the intensity of photons or particles released by the transmitter and observed at the receiver.The model is used for both optical and molecular communication systems.
  • Modulation: On-off keying uses the symbol set S = {0, 1}, transmitting a fixed-intensity pulse for 1 and no pulse for 0.The paper later treats OOK as the m = 2 special case of m-PAM.
  • Sampling and response: The number of samples per symbol is a = ωτ, where ω is the sampling rate and τ is the symbol interval.The transmitted 1-bit pulse determines the system response λ(t), whose sampled averages characterize observations.
  • Channel responses: Optical responses are proportional to a Gamma distribution, whereas molecular responses are proportional to an inverse Gaussian distribution.Their channel parameters can change over time.
  • Channel responses: Optical and molecular responses are similar in shape, but optical channels rise faster and molecular channels have longer tails.The example parameters illustrate the distinct time scales of the two systems.
  • Noise and CSI: Poisson observations include independent additive noise with mean η, representing background interference or receiver noise.The same noise term is also known as dark current in optical communication.
  • Noise and CSI: The model CSI consists of ΘOP = [α, β, η] for optical channels and ΘMO = [c, µ, η] for molecular channels; some parameters may vary with conditions.The evaluation also considers the assumption that these parameters are known perfectly.

A. The Viterbi Detector

The Viterbi detector performs sequence detection on a trellis whose states encode the previous M transmitted bits. It updates state likelihoods over two possible transitions and uses the most likely path to estimate the sequence.

  • Channel-memory assumption: The Viterbi detector assumes that each current observation depends only on the current symbol and the previous M transmitted symbols.If the memory-length estimate is inaccurate, the resulting likelihood model is also inaccurate.
  • Trellis construction: Each trellis state represents the previous M estimated bits, giving 2^M possible binary states.A next state has two predecessor states corresponding to the two possible incoming bits.
  • Likelihood recursion: For each next state, the detector updates log-likelihoods by adding the transition log-likelihood to the predecessor state's accumulated likelihood.The two candidate predecessor transitions are compared through the Viterbi recursion.
  • Sequence estimation: The most likely transmitted sequence is recovered with the Viterbi algorithm after initializing the zero state with likelihood 0 and other states with −∞.The transition likelihoods are derived from the Poisson observation model.
  • Computational limitation: When memory is long, exhaustive trellis evaluation becomes computationally infeasible because the number of states grows exponentially with memory length.The paper therefore implements a Viterbi beam-search algorithm.

V. EVALUATION BASED ON POISSON CHANNEL

This section evaluates SBRNN and other neural-network detectors using the Poisson channel model for optical and molecular communication. It compares their performance with Viterbi detection and summarizes the evaluation settings.

  • The evaluation uses the Poisson channel model for both optical and molecular communication channels.
  • The section evaluates SBRNN performance and compares it with the Viterbi detector.
  • Table I summarizes the results presented in the evaluation section.
  • Table II reports Viterbi beam-search performance as a function of the number of retained states N.

A. Training and Simulation Procedure

The detectors are evaluated on optical and molecular Poisson channels using specified channel parameters, CSI scenarios, recurrent architectures, and randomized training sequences. SBRNN training uses variable subsequence lengths and 500k sequences.

  • The optical channel uses ΘOP = [β, η], while the molecular channel uses ΘMO = [c, µ, η].
  • The Viterbi detector uses beam search that retains the top N = 100 states during each time slot.
  • RNN and SBRNN detectors use LSTM cells and three layers, with output sizes chosen to give roughly equal parameter counts.
  • Training data consists of random transmitted-bit sequences and corresponding Poisson-generated received signals.
  • SBRNN training randomly breaks 100-bit sequences into subsequences with lengths from 2 through 50.
  • The detectors are trained with Adam using learning rate 10^-3, batch size 500, and 500k sequences of 100 bits.

B. Effects of Sequence Length, Symbol Duration, and Noise

The evaluation examines memory length, sequence length, symbol duration, noise, and channel-parameter variation. Across these conditions, SBRNN remains competitive with or better than Viterbi detection when CSI or memory estimates are imperfect.

  • Memory length and sequence length: For the optical channel, the impulse response implies a memory length of approximately M ≈ 51 symbols at τ = 0.05 µs.The response falls to 0.01% of its peak after τ0.0001 = 2.55 µs.
  • Memory length and sequence length: SBRNN outperforms the Viterbi detector with perfect CSI when the Viterbi memory-length estimate is inaccurate.
  • Symbol duration: 2.5% CSI estimation error is sufficient for SBRNN to achieve better BER than the Viterbi detector across the evaluated settings.
  • Symbol duration: At τ = 0.1 µs in the optical channel, all detectors achieve zero error on the evaluated 1000 sequences.
  • Noise: At larger η values, corresponding to lower SNR, RNN and SBRNN outperform the Viterbi detector with CSI estimation error.
  • Channel-parameter variation: Across changing optical and molecular channel parameters, SBRNN performs as well as or better than Viterbi detection with 2.5% estimation error.

D. Effects of Symbol Set Size, Transmission Length, and RNN Cell Type

The section evaluates larger symbol sets, transmission lengths, recurrent cell types, and rapidly changing optical channels. SBRNN performance remains strong across these settings, while sequence-boundary errors and channel drift shape detection results.

  • Symbol Set Size: 4-PAM achieves the best BER with perfect CSI, whereas OOK achieves the best BER when CSI estimation contains errors.
  • RNN Cell Type: The LSTM-based SBRNN achieves better SER than the GRU- and vanilla-RNN-based SBRNN detectors.The 4-PAM SBRNN also outperforms Viterbi detection with CSI estimation error and approaches Viterbi detection with perfect CSI.
  • Transmission Length: SER decreases as transmission-sequence length increases because errors are more likely for symbols at the sequence beginning and end.The first symbols are affected by the rapidly rising initial signal, whose structure differs from later symbols.
  • Rapidly Changing Channels: The rapidly changing-channel model varies β and η between successive symbol intervals using diffusion with drift.The parameters may degrade or improve over time depending on the drift direction.
  • Rapidly Changing Channels: SBRNN performs well under rapidly changing conditions, while Viterbi detection degrades significantly when the channel drifts over time.The SBRNN was trained with fixed channel parameters and tested on sequences of length 200, despite training sequences having length 100.

F. Computational Complexity

The section compares computational complexity across SBRNN, RNN, and Viterbi detectors, alongside the molecular-platform evaluation setup. RNN is most efficient, while traditional Viterbi complexity grows exponentially with channel memory.

  • Computational Complexity: SBRNN complexity is O(L(n −L + 1)), Viterbi complexity is O(Nn), and RNN complexity is O(n).Here n is sequence length, L is sliding-BRNN length, and N is the number of retained trellis states.
  • Computational Complexity: Traditional Viterbi detection has exponential complexity in channel memory M because N = 2^M.The paper therefore describes traditional Viterbi detection as impractical for the considered channels.
  • Molecular Platform: The molecular platform uses timeslotted acid and base injections, with a pH probe detecting the received chemical signals.Four guard durations represent bit rates from 2 to 4 bps.
  • Dataset: The molecular dataset contains 100 transmissions of random 120-bit sequences per symbol duration, with 84 transmissions for training and 16 for testing.The resulting data includes 12k bits per symbol duration.
  • Real-Time Detection: Sequence detectors estimate incoming bits one by one using SBRNN-style testing, supporting real-time detection on data streams of any length.The evaluated sequence networks include LSTM- and bidirectional-LSTM-based architectures.

A. System’s Memory and ISI

The molecular communication platform exhibits long memory and intersymbol interference, making sequence detection important. SBRNN-based detectors are more resilient than RNNs under degraded channel conditions and support real-time messaging.

  • System’s Memory and ISI: BER falls from 0.1010 to 0.0333 at 4 bps and from 0.0167 to 0.0005 at 2 bps when LSTM state carries across detections.Resetting the state ignores system memory and ISI, whereas passing it forward incorporates them.
  • System’s Memory and ISI: BER decreases as SBLSTM length increases, indicating that the molecular channel has memory extending beyond four symbols for the 500 ms duration.BER values below 5 × 10^-3 are less accurate because fewer than 10 test errors were observed.
  • Performance and Resiliency: Sequence-detection algorithms generally outperform symbol-by-symbol detectors, including the baseline algorithm.
  • Performance and Resiliency: With a degraded pH probe, SBLSTM3-Net10 achieves BERs of 0.0883 and 0.0142 at 250 ms and 500 ms, compared with 0.1254 and 0.0504 for LSTM3-Net120.These results are reported as evidence of greater resilience to changing channel conditions.
  • Real-Time Communication: The SBRNN supports reliable text-message transmission at 2 bps on the molecular communication platform.The reported rate is an order of magnitude higher than previous molecular-communication systems.

APPENDIX

The appendix describes features extracted from each received symbol interval for neural-network detection. These features summarize intensity changes and may include normalized bin statistics.

  • FEATURE EXTRACTION: The received symbol interval is divided into B equal bins, whose averaged values form the vector b.
  • FEATURE EXTRACTION: The rate of change during a symbol duration is extracted by differentiating the bin values.
  • FEATURE EXTRACTION: For Poisson and experimental pH signals, intensity increases indicate transmitted 1-bits, while decreases or unchanged intensity indicate 0-bits.
  • FEATURE EXTRACTION: Additional features include the first and last bin values, plus the mean and variance of the bin vector.
  • FEATURE EXTRACTION: Because intersymbol interference can make intensity large, the bin vector may be normalized as b̂ = b/γ before extracting statistics.
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