Background

Accurate positioning in scenarios with predominant multi-path propagation and non-line-of-sight (NLOS), such as an indoor factory with dense clutter shown in Figure 1, is a challenging task. Conventional positioning methods like trilateration based on time of arrival (TOA) usually perform poorly in these scenarios. In recent years, artificial intelligence or machine learning (AI/ML) based approaches have shown promising results on NLOS-heavy scenarios. On the other hand, AI/ML based positioning has been approved in the 3rd generation partnership project (3GPP) as one of the three representative cases to apply AI in wireless networks.

Figure 1. Illustration of NLOS-heavy indoor factory scenario.

However, in AI/ML based positioning studies so far, the raw channel information, e.g., channel impulse response (CIR) or channel frequency response (CFR), is still commonly used as it covers all features on the wireless channel and may unleash the full potential of AI/ML ability [1]. Nonetheless, using raw channel information based AI/ML may suffer from the curse of dimensionality due to the increasing sampling rate in the spatial, frequency, and time domains for the increasing requirements of positioning accuracy. Moreover, the enormously enlarged number of features when using raw channel information as model input directly increases model complexity and computational complexity, which also lowers the training speed and becomes vulnerable to overfitting. Clearly, designing the proper data input is essential to the practical implementation of AI for positioning.

In this blog, we present the log signature transform based (SIG based) data processing of wireless channels before feeding into the AI/ML model. The log signature transform is the mapping from a path (continuous mapping) to the logarithm of its signature, and the signature of a path, which originally introduced in [2], can be seen as a collection of features extracted from the path by iterated integrals [3]. Our experimental results shown that our method can drastically reduce the number of input features and the computational complexity of the AI/ML model without compromising the positioning accuracy.

Method

Figure 2. The block diagram for the proposed method and a visualization of main steps.

The original discrete sample from the collected dataset consists of raw CIRs for all links between transmission reception points (TRPs) and any user equipment (UE), with its location being the label. The normative AI-based positioning commonly utilizes such samples/labels for the full knowledge but redundancy for model training and inference. Therefore, the SIG based method is proposed to enable lightweight AI-based positioning. The exemplary process is illustrated in Figure 2.

In order to be qualified for the signature transform derivation and maintain the necessary information for positioning as much as possible. The vital step is to construct a proper path from the original sample. We present the specifically constructed time-augmented cumulative sum of energy (CSE) path of each CIR, which can keep the critical information (power and time) for the positioning purpose and also becomes suitable for feature derivation.

Figure 3. Geometrical interpretations of the first two levels of signature features.

Given the time-augmented CSE path, its signature features can be obtained by iterated integrals and well interpreted from the geometrical structure point of view with corresponding physical meanings, as shown in Figure 3. S₁ is the energy span of the path, which equals CIR total energy and contains information on large-scale fading like path loss and shadowing. S₂ is the time span of the path, which contains the time information of CIR. CIR with a sizable absolute delay plus delay spread will have a large value of S₂. S_1,2 is the blue area containing information about the CIR line-of-sight (LOS) tap. The CSE path of CIR with LOS tap will climb up earlier than that of CIR without LOS tap, resulting in a larger value of the blue area S_1,2. S_2,1 is the goldenrod area, which equals the sum of energy-weighted time with an extra linear interpolation of time, and can be interpreted as the average time of arrival of CIR taps.

Experiments

The proposed method is evaluated in the scenario of the 3GPP indoor factory with dense clutter and high base station height (InF-DH) [4]. The dataset consists of 18K and 2K samples for training and testing. Each sample consists of CIRs from 18 TRPs with the dimensionality of 18×256×2 (256 denotes the number of CIR taps, and 2 indicates real and imaginary parts) and a two-dimensional UE location as the corresponding label. Each CIR is first normalized to have a total energy of one and then transformed into six log signature features as model input. Thus, the input dimensionality of AI/ML models has been reduced to 18×6. As for the AI/ML model training configurations, the Adam optimizer is used, the batch size is 32, and the learning rate is 1e-3. Furthermore, 90 percent of the training samples are used for training and 10 percent for validation. The mean-squared-error (MSE) based loss function is applied to train the model.

Figure 4. Comparison on positioning accuracy, input data size, and FLOPs.

Figure 4 shows the comparison results on positioning accuracy, input data size, and floating-point operations (FLOPs) between SIG based and CIR based ResNet. It can be seen that the proposed method can drastically reduce the input feature number and the computational complexity of subsequent AI models while maintaining similar positioning accuracy.

Conclusion

In this blog, we describe a novel dimensionality reduction technique that uses log signature-based operation to extract features of wireless channels for AI-based positioning. With its elegant feature extraction capability, about 98 percent reduction can be achieved regarding the input feature number and the computational complexity of the subsequent AI/ML model without compromising the positioning accuracy, which greatly builds upon the confidence for practical implementation of AI-based positioning.