# A Novel Batch Streaming Pipeline for Radar Emitter Classification
## 3 The Pipeline
### Radar Deinterleaving Model  
Given the batch streaming processing approach, the DBSCAN algorithm introduced in Section 2.1 is well suited to our radar deinterleaving model. This is because in a batch streaming environment, the number of radar emitters we seek to deinterleave can vary from batch to batch. However, directly applying the DBSCAN algorithm from [27] presents two significant challenges. Firstly, finding an appropriate value of \(\epsilon\) is challenging. When we select AOA, Frequency, PW, and PA as our feature vectors for implementing DBSCAN, it is not straightforward to set an appropriate value of \(\epsilon\) in Equation (1). This is because the distance to define neighborhood is calculated by weighting each vector element equally, even though all of them have different variances and scales. Secondly, we may encounter issues related to _MinPts_. In the context of our task, despite the fact that the data have been pre-filtered for noise, if one emitter has a low frequency, the number of pulses within a given batch may not meet the _MinPts_ threshold. In this case, DBSCAN will fail to cluster these pulses into a PDW train, incorrectly identifying them as noise.  
To solve the first problem, we propose modifying Equation (1), used in DBSCAN, as follows:  
\[N_{\textit{thres}}(p)=\{q\in D\,|\,\|p-q\|\leq\textit{{thres}}\}, \tag{2}\]  
where \(p\in R^{4}\), \(q\in R^{4}\) denote the \((AOA,frequency,PW,PA)\in D\) of each PDW;  
\[\textit{{thres}}=(AOA_{\textit{thres}},Freq_{\textit{thres}},PW_{\textit{ thres}},PA_{\textit{thres}})\]  
is a threshold vector, and the norm \(\|x\|\) is defined as  
\[\|x\|\leq r\Leftrightarrow|x_{i}|\leq r_{i},i=1,\ldots,4\]  
for \(x\in\mathbb{R}^{4}\) and \(r\in(\mathbb{R}_{\geq 0})^{4}\). To account for the different variances and scales of each vector element, the distance calculation of the two vectors to define the neighborhood data is performed independently for each element, and the corresponding thresholds (_thres_) are set separately. The process of defining thresholds in Equation (2) has the advantage of enabling radar engineers to more intuitively determine the thresholds for each component based on the characteristics of each physical value.  
The second problem can be solved by increasing the batch size, to avoid data situations where the \(Min\textit{Pts}\) condition is not met, but larger batch sizes result in longer computation times and less memory efficiency. Therefore, rather than increasing the batch size, we should focus more on how to handle data that do not meet \(Min\textit{Pts}\) conditions when they occur. As illustrated in the deinterleaving model in Figure 2, we propose carrying over data with fewer numbers of PDWs than \(Min\textit{Pts}\) to the next batch, instead of classifying them as  
Figure 2: Radar recognition pipeline. The radar recognition pipeline we propose operates using a batch streaming approach. In each batch, we combine unprocessed data from the previous batch with new incoming data, to create a batch of size \(N\). This batch undergoes deinterleaving using our deinterleaving model (pink box) to transform it into PDW trains. Deinterleaved data in the form of PDW trains then move to the pattern recognition phase. The data that could not be deinterleaved are carried over to the next batch. In the pattern recognition phase, our pattern recognition model (yellow block) analyzes each de-interleaved PDW train, to uncover the frequency and PRI patterns. Each model will be defined later.  
noise. This approach stems from our assumption that the PDW data in our pipeline have already been pre-filtered for noise. Thus, rather than treating unclustered pulses as noise, we consider them as insufficient data and forward them to the next batch. The unclustered data from the previous batch are combined with new data from the next batch so that there can be enough data in that batch to satisfy the _MinPts_ condition. In other words, they can be deinterleaved into PDW trains.