## 2 System Model
### Linear Attention Mechanism  
The RIMformer architecture employs a trainable dual attention mechanism to discern complex dependencies between elements of the input sequence, which is crucial for capturing intricate relational information. However, the computational complexity of conventional transformers scales quadratically with the number of signal frames \(n\) in the input sequence. This quadratic scaling becomes impractical for an enormous \(n\). The quadratic computational complexity makes the straightforward use of global receptive fields in self-attention intractable, which leads to excessively high computational costs. While this problem can be addressed by designing sparse global attention patterns or using smaller attention windows, it is often limited by the intricacies of the attention patterns designed and may compromise the ability to model long-term dependencies. In contrast, linear attention is an efficacious alternative and reduces the computational complexity from \(O(n^{2})\) to \(O(n)\). In the paper, a method for estimating the softmax and Gaussian kernels using positive orthogonal random features is applied to the RIMformer, employing FAVOR+ [31] for the robust and unbiased estimation of standard (softmax) attention. Specifically, a kernel function is introduced to approximate the original similarity function, which can enhance computational efficiency while preserving the accuracy of the attention mechanism. The standard scaled-dot attention can be described as follows:  
\[\text{Attention}(\mathbf{Q},\mathbf{K},\mathbf{V})=\text{softmax}\left(\frac{\mathbf{Q}\mathbf{K} ^{T}}{\sqrt{d}}\right)\mathbf{V}, \tag{3}\]  
where the inputs \(\mathbf{Q},\mathbf{K},\mathbf{V}\in\mathbb{R}^{n\times d}\) are queries, keys, and values derived from the input by different linear transformations. \(d\) is the number of feature dimension of signal frames. Radar signals, after applying the sliding window, are transformed into a structured format with overlapping segments. These segments capture the localized temporal and spatial features of the signals, including interference and target echoes. The query Q and key K metrics represent the characteristics of these segments. Their dot product measures the similarity between different signal segments, which is the key to identifying interference patterns and correlations in the radar data. Given that subscripting a matrix with i returns the i-th row as a vector, Equation (3) can be written as follows:  
\[\text{Attention}(\mathbf{Q},\mathbf{K},\mathbf{V})_{i}=\frac{\sum_{j=1}^{n}\mathbf{q}^{i}\mathbf{ k}_{j}^{T}\mathbf{v}_{j}}{\sum_{j=1}^{n}\mathbf{e}^{i}\mathbf{k}_{j}^{T}}=\frac{\sum_{j=1}^{n} \text{sim}\left(\mathbf{q}_{i},\mathbf{k}_{j}\right)\mathbf{v}_{j}}{\sum_{j=1}^{n}\text{ sim}\left(\mathbf{q}_{i},\mathbf{k}_{j}\right)}, \tag{4}\]  
where \(\mathbf{q}_{i}\) and \(\mathbf{k}_{j}\) are the i-th and j-th row vectors in matrices \(\mathbf{Q}\) and \(\mathbf{K}\), respectively. For the sake of brevity, \(\sqrt{d}\), which can be treated as a constant, is omitted here. According to the  
Figure 4: Structure of RIMformer block. positive random features (PRFs) [31] for softmax, \(e^{\phi\cdot k^{T}}\) can be converted approximately to a product of \(\phi(\mathbf{q})\) and \(\phi(\mathbf{k})\), as in the following equation:  
\[\text{sim}(\mathbf{q},\mathbf{k})=e^{\mathbf{q}\cdot k^{T}} =\mathbb{E}_{\mathbf{\omega}\sim\mathcal{N}(\omega\mathbf{0},\mathbf{I}_{d })}\Big{[}e^{\mathbf{\omega}\cdot\mathbf{q}-\|\mathbf{q}\|^{2}/2}\times e^{\mathbf{\omega} \cdot\mathbf{k}-\|\mathbf{k}\|^{2}/2}\Big{]}\] \[\approx\underbrace{\frac{1}{\sqrt{m}}\left( \begin{array}{c}e^ {\mathbf{\omega}_{1}\cdot\mathbf{q}-\|\mathbf{q}\|^{2}/2}\\ e^{\mathbf{\omega}_{2}\cdot\mathbf{q}-\|\mathbf{q}\|^{2}/2}\\ \vdots\\ e^{\mathbf{\omega}_{m}-\|\mathbf{q}\|^{2}/2}\end{array} \right)}_{\phi(\mathbf{q})}^{T} \cdot\underbrace{\frac{1}{\sqrt{m}}\left(