An Efficient Wireless Channel Estimation Model
for Environment Sensing

Wireless environment sensing is a cutting-edge approach that enhances the surveillance capacity of conventional systems, e.g., sensors, without the need of additional hardware. By continuously monitoring wireless signals within and around critical facilities and infrastructure, unusual or unauthorized activities, security breaches or tampering with equipment can be identified [1, 2, 3, 4]. A number of existing methods use Channel State Indicators (CSI) [2, 3] calculated from pilot signals to detect changes in the environment. However, CSI estimation in a standard communication system is not designed to detect subtle environmental changes. Rather, it represents the cumulative impact of the surroundings on the signal and could result in erroneous sensing performance. Moreover, the background noise and the time-varying dynamics of wireless channels remain major challenges to sensing efforts.

Recently, data-driven machine learning techniques for estimating complex and non-linear system dynamics have led to the development of novel wireless channel estimation (CE) and management approaches [5, 6, 7]. However, machine learning (ML)-based channel estimation models require substantial computation time and data for training, which makes them unsuitable for real-time applications. Moreover, they are generally black-box, or non-interpretable, and the complex patterns learned by the model cannot be used to derive key insights about the radio environment.

In this paper, we propose a “gray-box” approach, where we use a Tapped-Delay Line (TDL) model of the wireless multipath channel and learn its parameters through a ML-inspired data-driven approach. Our results show that this approach not only provides better channel estimation than conventional methods, such as Least Squares, but the estimated channel state is also a more detailed measure to sense the field in an environment awareness application. The detection of anomalies from sensed data requires further development and will be discussed in future work. This paper is focused on the design and performance of our novel CE method but, as a proof of concept, we include a preliminary case study in our results section of unmanned air vehicle (UAV or drone) detection using our channel estimation model with conventional wireless signals.

Prior efforts in regards to TDL/multipath channel estimation model, include ITU’s (International Telecommunication Union) recommendations¹¹1https://www.itu.int/rec/R-REC-P.1407/en for parameterization of multipath environments, which use power thresholds to determine the number of multipath components. Not meant for real-time CE, ITU recommendations are for characterization of different scenarios. Some efforts using ML have also been proposed, e.g., [8] models the tap and gain estimation problem as multi-class classification using a deep neural network and requires training of the model by a dictionary of channel models. This work improves the CE performance of a previous method [9]. which formulates the estimation of taps for specific transmitted and received signals in a Multi-Input Multi-Output (MIMO) system, as an optimization problem.

Moreover, the existing CE approaches, in general, use statistical approaches, such as, Rayleigh or Rician fading models, to evaluate performance, which are inadequate for environment sensing experiments. In this paper, we use MATLAB’s ray-tracing tool for increased realism to evaluate our CE method and subsequent sensing experiments. Our CE approach leverages the respective strengths of classical and ML techniques and efficiently calculates channel state in sufficient detail to facilitate environment sensing. In particular, our contributions in the paper are as follows:

• •

  We propose a novel and efficient data-driven channel estimation approach based on a neural network with one hidden layer using the pilot/reference signals already available in wireless communication systems.

• •

  We evaluate the CE model using Matlab’s ray-tracing tool instead of the classical approach of employing statistical channel models, for increased realism.

• •

  Our CE model shows accurate estimation (root-mean-square error below $10^{-4}$ or $-40$dB) for different static and dynamic scenarios with reasonable SNR ($\geq 60$dB).

• •

  We also show the potential of our CE model in finding outlier events in the neighbourhood of the transmitter and receiver via a drone detection scenario.

The signal from a wireless transmitter can be represented as [10]:

where $s(t)$ is the baseband signal and $f_{c}$ is the carrier frequency. The discrete time versions of the baseband and transmitted signal are $\textbf{{s}}_{n}$ and $\textbf{{x}}_{n}$ respectively, both vectors of length $K$. Considering that the signal will reach the receiver through line-of-sight and various reflected paths, which experience different Doppler shifts, the received signal $y(t)$ can be written as [10]:

where $c_{i}(t)$, $\tau_{i}(t)$, and ${\phi}_{i}(t)$ are the gain, delay, and Doppler shift of the $i$th path, $i=0$ corresponds to the line-of-sight and there are $D(t)$ distinct multipaths. $w(t)$ is the white Gaussian noise. In a time-varying channel model, the parameters $\{c_{i}(t),\tau_{i}(t),{\phi}_{i}(t)\}~{}\forall{i}$, and $D(t)$ are random processes. The channel impulse response can be written as:

where $\theta_{h}(t)$, the parameters to describe channel impulse response, are defined as:

As can be seen in the above expression, the total phase shift experienced by the signal is $-2\pi f_{c}\tau_{i}(t)+{\phi}_{i}(t)$ due to multipaths and Doppler effect. The discrete time received signal and received baseband signal are denoted by $\textbf{{y}}_{n}$ and $\textbf{{z}}_{n}$ respectively, which are also considered as $K$ length vectors.

Figure 1 shows our approach for estimating the path delays and gains. The basic unit of our model, called TDL-NN, is a neural network (NN) with a single input and single output and one hidden layer representing $L$ taps of constant delays in multiples of $\tau$. The parameters $L$ and $\tau$ should cover all possible distinct path delays.

All wireless communication systems use pilots or reference signals, which are known sequences of symbols transmitted over the wireless channel, and the respective received signals are used for channel state estimation. Figure 1 shows $\textbf{{x}}_{m,n}$ transmitted reference signals from one primary transmitter and $M-1$ multiple interferers. The received reference signal is $\textbf{{y}}_{n}$. Our CE model is trained using $\textbf{{x}}_{m,n}$ and $\textbf{{y}}_{n}$ for $m={1,~{}\cdots,~{}M}$ and $n={1,~{}\cdots,~{}N}$, where $N$ is the available reference symbols for training. The model shifts each input or transmitted signal, $\textbf{{x}}_{m,n}$, from $0\times\tau$ to $L\times\tau$, where $\tau$ is the tap delay resolution in the hidden layer. It then computes the weights of the output layers, or coefficients $c_{m,i}$ for all taps and also for all $M$ sub-models, by minimizing the MSE (Mean Square Error) loss function, i.e.,

where $\hat{\textbf{{y}}}_{n}=\sum_{m=1}^{M}\sum_{i=0}^{L}c_{m,i}\textbf{{x}}_{m,n-i\tau}$.

Our implementation in PyTorch uses $N$ as the block-size and a learning rate of $0.01$. The computation complexity of our model grows as $\mathcal{O}(N\times L\times e)$, where $e$ is the number of epochs. As an option, we also implemented weight pruning in our model to push the smaller weights to 0. Note that our model uses the time shift idea as in conventional time delay neural networks [11], which were proposed for time series analysis, but otherwise it is a customized model to suit our application of channel estimation.

Path delays and gains change with time as mobile users or objects in the environment move. Weather conditions, such as, rain and wind also impact path gain. For a dynamic environment, the multipath delays and gains should be updated as new pilot symbols are received. Figure 1 shows a snapshot of our approach, which estimates $c_{m,i}(n)$ for each path tap $i$ at time $n$ by updating the model weights using pilot transmitted and received signals $\textbf{{x}}_{m,n}$ and $\textbf{{y}}_{n}$. Note that we are not explicitly estimating Doppler phase shift $\phi_{i}(t)$ associated with the path $i$ from the model, instead we are tracking the variations in path delays and gains.

Moreover, we remark that our TDL neural network is a realization of a typical Steepest Gradient Descent (SGD) algorithm iteratively computing coefficients of a linear predictor when the objective function is to minimize mean square error between actual observations and predictions. However, using SGD in a neural network setting with parallelization of computations is much more effective and an order of magnitude faster than the conventional iterative approach.

In this paper, we present an efficient channel estimation approach based on a TDL model for environment sensing. In our approach, the tap delays and gains are estimated through a neural network with one hidden layer. Our extensive experiments, using Matlab’s ray-tracing tool for generation of transmitted and received signal samples, show that this simple model can estimate the time-varying channel with reasonable accuracy in the presence of white noise and also in-band interference. This approach enables developing novel environmental sensing applications where interesting objects and events can be detected through the changes in the channel state. A preliminary case study is presented in the paper to show the potential of on-going research.