OFDM Receiver Design and Complex Convolutional Networks

Deep-Waveform

Deep-Waveform: A Learned OFDM Receiver Based on Deep Complex-Valued Convolutional Networks. Zhongyuan Zhao et.al. IEEE Journal on Selected Areas in Communications, August 2021 (pdf) (Citations 25)

Open-source software

提出了一种利用deep complex-valued convolutional network 实现直接从时域信号解调OFDM bits的方案

  • 结合CP-exploitation, channel estimation, and intersymbol interference，一起取得了比较好的效果
  • 指导了新的方法进行复数运算
    • 传统方案一：拼成两列
    • 传统方案二：two channel
  • Two stages for training in fading channel.
  • 代码开源

Quick Overview

  • Use a deep complex-valued convolutional network (DCCN) to recover bits from time-domain OFDM signals without relying on any explicit DFT/IDFT.
  • has the advantage of combining CP-exploitation, channel estimation, and intersymbol interference.
  • guidelines of exact and approximate implementations of a complex-valued convolutional layer are provided for the design and analysis of convolutional networks for wireless PHY.
  • a suite of novel training techniques are developed to improve the convergence and generalizability of the trained model in fading channels.

The Authors claimed that process complex data in the $\mathbb{R}^2$ is differs from field in multiplicative operations.

And DCCN can:

  • a learned linear transform to replace DFT/IDFT by exploiting its cyclic prefix (CP).
  • a data-driven interpretable DCCN channel equalizer that outperformances the legacy receivers and lower complexity. Combine CP exploitation, intersymbol interference mitigation and channel estimation.
  • a training methods to improve the convergence and generalizability of the DNN-based receiver in fading channel.

OFDM system

Diagram of legacy OFDM PHY

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Exemplary OFDM coherence slot and time-domain waveform

image-20240118153824808

An OFDM symbol contains subcarriers, and DC guard band and edge guard band among the subcarriers.

A subcarrier in an OFDM symbol (the yellow column) is refereed to as a resource element (RE). And a coherence slot contains OFDM symbols, with pilot REs and data REs, respectively.

The length of a time-domain full OFDM symbol is .

Channel estimation

image-20240118161650143

Pilot signals are of either constant signal or low auto-correlation sequence (e.g., Zadoff-Chu sequence) known at the receiver. The basic pilot-aided channel equalizer in OFDM system is based on the least square (LS) estimator.

Whole Structure

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And two stage training.

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Simplify

Using the legacy data REs extraction and demodulation (Equalizer?)

image-20240118163730156

Another paper/ old version https://arxiv.org/abs/1810.07181v3

  • The model contains both dense and convolutional layers which are mostly linear activated, and new structures of residual and skip connections. (different from other works which only contain Fully-Connected layer and Relu activation.)
  • complex convolutional layer is implemented within Tensorflow to process complex IQ data, instead of treating it as two independent real numbers.

Typical pilot patterns in OFDM system are: block, comb, and scattered

image-20240305111123753

It is recommended to keep the CP while recovering the bits from the time-domain waveform.

Basic OFDM Receiver (AWGN)

Firtstly, the author trains the basic DCCN OFDM receiver (i.e., without channel equalizer) for bit recovery.

image-20240305175722646

  • The first part includes first 3 layers, which is intended to transform time-domain OFDM symbol into frequency-domain. The major component of the first part is a Complex Conv (C-Conv) layer of size N × S(N) × 1.
    • DCCN can drop CP by configuration. Dropping the CP before Complex 1D-Conv.
  • The second part contains layers 4 to 6, which is intended to extract all the data cells of an OFDM frame, this is implemented by an FC layer.
    • the real part and imaginary part are stored in the last dimension of the tensors.
  • Part 3 is for demodulation, which is convert the complex IQ data into soft bits. The output of softmax activation are soft bits, which represents each bit with 2 real numbers (e.g. Log-Likelihoods of 0 and 1).

OFDM receiver Equalizer

  • The equalizer usually located in the frequency domain to avoid the convolutional operator. Thus, the DFT-like component is located before the LS-like Equalization.

image-20240305181423944

  • The first (layer 0-5) and fourth parts (last 4 layers) are DFT/IDFT-like complex Conv layers intended to perform time/frequency domain transformation. The layer 3 and last 2 layer are used for CP removing and adding back.
  • Part 2, from layers 6 to 19, is for channel estimation.
  • Part 3, layer 20, is frequency domain channel equalization implemented by complex division: the output of part 1 (frequency domain receive signal) over the output of part 2 (channel estimates).
    • LS-like channel equalizer

Training configurations

The Two-stage training configurations:

image-20240305182353730

  • It’s too complex to be trained together at one time.
  • Firstly, training the basic OFDM receiver in AWGN channel without fading
  • Then, Load the pre-trained basic OFDM receiver and insert the DCCN Equalizer before the DCCN OFDM receiver.
  • Lastly, generate the Rx data with fading, and only the DCCN Equalizer is trained.
  • Some tracks:
    • mini batch
    • to tensor
    • small and decaying learning rate
    • early stopping

The same loss function is used in the two stages. And the loss function is:

image-20240305182603431

  • The logarithmic BER could prevent diminishing gradient due to tiny changes of CE when BER is very small.
  • Training SNR:

image-20240305183646134