Incremental small sphere and large margin for online recognition of communication jamming

Abstract

In the anti-jamming field of radio communication, the problem of online and multiclass jamming recognition is fundamental to implement reasonable anti-jamming measures. The incremental small sphere and large margin (IncSSLM) is proposed, this model can learn the compact boundary for own communication signals and known jamming, which relieves the open-set problem of radio data. Meanwhile it can also update the model of classifier in real time, which avoids the large memory requirement for vast jamming data and saving much time for training. The core of proposed method is the small sphere and large margin (SSLM) approach, which makes the spherical area as compact as possible, like support vector data description (SVDD), and also makes the margin between them as far as possible, like support vector machine (SVM). In other words, it can minimize intra-class divergence and maximize inter-class space. Therefore, there is a significant enhancement of recognition performance when compared with open classifiers such as SVM, and considerable superiority of training efficiency when compared with the canonical SSLM algorithm. Numerical experiments based on synthetic data, practical complex feature data of high-resolution range profile (HRRP), and jamming data of radio communication demonstrate that IncSSLM is efficient and promising for multiple and online recognition of vase and open-set radio jamming.

Appendix

The derivation of $\overline {G}$ is written as:

$$ \begin{array}{l} \overline{G}={{\left[ \begin{array}{cc} Q & {{\eta }_{c}} \\ {\eta_{c}^{T}} & 2{{H}_{cc}} \end{array} \right]}^{-1}}\text{=}{{\left[ \begin{array}{cc} {{G}^{-1}} & {{\eta }_{c}} \\ {\eta_{c}^{T}} & 2{{H}_{cc}} \end{array} \right]}^{-1}} \\ \text{ } \text{ } \text{ =}\left[ \begin{array}{cc} G+G{{\eta }_{c}}{{\left( 2{{H}_{cc}}-{\eta_{c}^{T}}G{{\eta }_{c}} \right)}^{-1}}{\eta_{c}^{T}}G & -G{{\eta }_{c}}{{\left( 2{{H}_{cc}}-{\eta_{c}^{T}}G{{\eta }_{c}} \right)}^{-1}} \\ -{{\left( 2{{H}_{cc}}-{\eta_{c}^{T}}G{{\eta }_{c}} \right)}^{-1}}{\eta_{c}^{T}}G & {{\left( 2{{H}_{cc}}-{\eta_{c}^{T}}G{{\eta }_{c}} \right)}^{-1}} \end{array} \right] \\ \text{ } \end{array} $$

(34)

Let $\kappa =2{{H}_{cc}}-{\eta _{c}^{T}}G{{\eta }_{c}}$, β_c = −Gη_c, the (31) can be rewritten as:

$$ \begin{array}{l} \overline{G}=\left[ \begin{array}{cc} G+\frac{1}{\kappa }{{\upbeta }_{c}}{{\upbeta}_{c}^{T}} & \frac{1}{\kappa }{{\upbeta }_{c}} \\ \frac{1}{\kappa }{{\upbeta}_{c}^{T}} & \frac{1}{\kappa } \end{array} \right] \\ \text{ }\text{ }=\left[ \begin{array}{cc} G & 0 \\ 0 & 0 \end{array} \right]+\frac{1}{\kappa }\left[ \begin{array}{cc} {{\upbeta }_{c}} \\ 1 \end{array} \right]\left[ \begin{array}{cc} {{\upbeta}_{c}^{T}} & 1 \end{array} \right] \end{array} $$

(35)

The derivation of κ is written as:

$$ \begin{array}{l} \kappa =2{{H}_{cc}}-{\eta_{c}^{T}}G{{\eta }_{c}}=2{{H}_{cc}}\text{+}{\eta_{c}^{T}}{{\upbeta }_{c}} \\ \text{ } \text{ }=2{{H}_{cc}}\text{+}{{\left[ \begin{array}{cc} {{y}_{c}} \\ 2H_{cs}^{T} \end{array} \right]}^{T}}\left[ \begin{array}{cc} {{\upbeta }_{\mu }} \\ {{\upbeta }_{s}} \end{array} \right] \\ \text{ } \text{ }=2{{H}_{cc}}\text{+}2{{H}_{cs}}{{\upbeta }_{s}}+{{y}_{c}}{{\upbeta }_{\mu }} \\ \text{ }\text{ } \text{ =}{{\gamma }_{c}} \end{array} $$

(36)