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Spectrum Sensing for Self-Organizing Network in the Presence of Time-Variant Multipath Flat Fading Channels and Unknown Noise Variance

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Abstract

Cognitive radio, as an important means of implementing spectrum-awareness and dynamic sharing, is of great significance to the future deployment of self-organizing networks. Given its practical application, cognitive radio technology may operate in various adverse self-organizing networks environments. For example, in wireless mobile communication, the multipath propagation with time-varying fading coefficients and unknown noise variance becomes inevitable. Unfortunately, most existing spectrum sensing methods could hardly acquire good performance in this adverse situation. To overcome this difficulty, in this paper we present a novel spectrum sensing algorithm in realistic cognitive radio applications. Firstly, we establish a dynamic state-space model which gives full consideration to the evolution characteristics of primary user’s state and time-variant multipath flat fading channel, while the received signal processed by matched filtering is viewed as the observation. On this basis, spectrum sensing is realized by estimating the primary user’s state, multipath channel impulse response and noise variance jointly and iteratively. This formulated problem is solved based on maximum a posteriori probability criterion and marginal particle filtering technology. Simulations demonstrate that the sensing performance achieved by proposed algorithm is satisfactory and at the same time, the channel response and noise variance are estimated accurately.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (61379016, 61471061) and Postgraduate Innovation Fund of SICE, BUPT, 2015.

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Authors and Affiliations

  1. Beijing University of Posts and Telecommunications (BUPT), Beijing, 100876, China

    Mengwei Sun, Bin Li & Chenglin Zhao

  2. Shanghai Jiao Tong University, Shanghai, 200240, China

    Shenghong Li

Authors
  1. Mengwei Sun
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  2. Shenghong Li
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  3. Bin Li
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  4. Chenglin Zhao
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Corresponding author

Correspondence to Bin Li.

Appendix 1. Posterior probability of TVMFF channel gain

Appendix 1. Posterior probability of TVMFF channel gain

On the condition that the result of coarse detection is in active state and the proposed accumulative modification mechanism, the posterior probability of h n could be represented as:

$$ {\widehat{\mathbf{h}}}_n= \arg \underset{h_{n,l}\in {\mathbf{A}}_l}{ \max}\left[p\left({\mathbf{h}}_n|{\widehat{\sigma}}_{n-1}^2,{\widehat{\mathbf{h}}}_{0:n-1},{\widehat{\mathbf{x}}}_{0:n-1},{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{Y}_n,{L}_n\right)\right] $$
(1-A)

Based on the conditional probability p(B|A)=p(AB)/p(A), we could rewrite (1-A) as:

$$ p\left({\mathbf{h}}_n|{\widehat{\sigma}}_{n-1}^2,{\widehat{\mathbf{h}}}_{0:n-1},{\widehat{\mathbf{x}}}_{0:n-1},{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{Y}_n,{L}_n\right)=\frac{p\left({\mathbf{h}}_n,{\widehat{\sigma}}_{n-1}^2,{\widehat{\mathbf{h}}}_{0:n-1},{\widehat{\mathbf{x}}}_{0:n-1},{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{Y}_n,{L}_n\right)}{p\left({\widehat{\sigma}}_{n-1}^2,{\widehat{\mathbf{h}}}_{0:n-1},{\widehat{\mathbf{x}}}_{0:n-1},{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{Y}_n,{L}_n\right)}=\frac{p\left({Y}_n|{\mathbf{h}}_n,{\widehat{\sigma}}_{n-1}^2,{\widehat{\mathbf{h}}}_{0:n-1},{\widehat{\mathbf{x}}}_{0:n-1},{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{L}_n\right)p\left({\mathbf{h}}_n,{\widehat{\sigma}}_{n-1}^2,{\widehat{\mathbf{h}}}_{0:n-1},{\widehat{\mathbf{x}}}_{0:n-1},{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{L}_n\right)}{p\left({\widehat{\sigma}}_{n-1}^2,{\widehat{\mathbf{h}}}_{0:n-1},{\widehat{\mathbf{x}}}_{0:n-1},{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{Y}_n,{L}_n\right)}=p\left({Y}_n|{\mathbf{h}}_n,{\widehat{\sigma}}_{n-1}^2,{\widehat{\mathbf{h}}}_{0:n-1},{\widehat{\mathbf{x}}}_{0:n-1},{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{L}_n\right)p\left({\mathbf{h}}_n|{\widehat{\sigma}}_{n-1}^2,{\widehat{\mathbf{h}}}_{0:n-1},{\widehat{\mathbf{x}}}_{0:n-1},{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{L}_n\right)\times \frac{p\left({\widehat{\sigma}}_{n-1}^2,{\widehat{\mathbf{h}}}_{0:n-1},{\widehat{\mathbf{x}}}_{0:n-1},{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{L}_n\right)}{p\left({Y}_n|{\widehat{\sigma}}_{n-1}^2,{\widehat{\mathbf{h}}}_{0:n-1},{\widehat{\mathbf{x}}}_{0:n-1},{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{L}_n\right)p\left({\widehat{\sigma}}_{n-1}^2,{\widehat{\mathbf{h}}}_{0:n-1},{\widehat{\mathbf{x}}}_{0:n-1},{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{L}_n\right)}=\frac{p\left({Y}_n|{\mathbf{h}}_n,{\widehat{\sigma}}_{n-1}^2,{\widehat{\mathbf{h}}}_{0:n-1},{\widehat{\mathbf{x}}}_{0:n-1},{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{L}_n\right)p\left({\mathbf{h}}_n|{\widehat{\sigma}}_{n-1}^2,{\widehat{\mathbf{h}}}_{0:n-1},{\widehat{\mathbf{x}}}_{0:n-1},{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{L}_n\right)}{p\left({Y}_n|{\widehat{\sigma}}_{n-1}^2,{\widehat{\mathbf{h}}}_{0:n-1},{\widehat{\mathbf{x}}}_{0:n-1},{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{L}_n\right)} $$
(2-A)

The observation Y n is only associated with the channel gain, the PU state in n-th sensing slot and the L n , thus, the simplification could be performed as:

$$ p\left({\mathbf{h}}_n|{\widehat{\sigma}}_{n-1}^2,{\widehat{\mathbf{h}}}_{0:n-1},{\widehat{\mathbf{x}}}_{0:n-1},{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{Y}_n,{L}_n\right)=\frac{p\left({Y}_n|{\mathbf{h}}_n,{\widehat{\sigma}}_{n-1}^2,{\widehat{\mathbf{h}}}_{0:n-1},{\widehat{\mathbf{x}}}_{0:n-1},{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{L}_n\right)p\left({\mathbf{h}}_n|{\widehat{\sigma}}_{n-1}^2,{\widehat{\mathbf{h}}}_{0:n-1},{\widehat{\mathbf{x}}}_{0:n-1},{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{L}_n\right)}{p\left({Y}_n|{\widehat{\sigma}}_{n-1}^2,{\widehat{\mathbf{h}}}_{0:n-1},{\widehat{\mathbf{x}}}_{0:n-1},{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{L}_n\right)}=\frac{p\left({Y}_n|{\mathbf{h}}_n,{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{L}_n\right)p\left({\mathbf{h}}_n|{\widehat{\sigma}}_{n-1}^2,{\widehat{\mathbf{h}}}_{0:n-1},{\widehat{\mathbf{x}}}_{0:n-1},{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{L}_n\right)}{{\displaystyle \sum_{{\mathbf{h}}_n}p\left({Y}_n|{\mathbf{h}}_n,{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{L}_n\right)p\left({\mathbf{h}}_n|{\widehat{\sigma}}_{n-1}^2,{\widehat{\mathbf{h}}}_{0:n-1},{\widehat{\mathbf{x}}}_{0:n-1},{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{L}_n\right)}}\propto \kern0.5em p\left({Y}_n|{\mathbf{h}}_n,{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{L}_n\right)p\left({\mathbf{h}}_n|{\widehat{\sigma}}_{n-1}^2,{\widehat{\mathbf{h}}}_{0:n-1},{\widehat{\mathbf{x}}}_{0:n-1},{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{L}_n\right) $$
(3-A)

Furthermore, the channel gain and the PU state are independent with each other, thus:

$$ p\left({\mathbf{h}}_n|{\widehat{\sigma}}_{n-1}^2,{\widehat{\mathbf{h}}}_{0:n-1},{\widehat{\mathbf{x}}}_{0:n-1},{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{L}_n\right)=p\left({\mathbf{h}}_n|{\widehat{\mathbf{h}}}_{pre}\right) $$
(4-A)

In combination, the Eq. (2-A) could be simplified as:

$$ \begin{array}{l}p\left({\mathbf{h}}_n|{\widehat{\sigma}}_{n-1}^2,{\widehat{\mathbf{h}}}_{0:n-1},{\widehat{\mathbf{x}}}_{0:n-1},{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{Y}_n,{L}_n\right)\\ {}\propto p\left({Y}_n|{\widehat{\sigma}}_{n-1}^2,{\mathbf{h}}_n,{\mathbf{x}}_n^{\dagger }={\mathbf{s}}_c,{L}_n\right)p\left({\mathbf{h}}_n|{\widehat{\mathbf{h}}}_{pre}\right)\end{array} $$
(5-A)

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Sun, M., Li, S., Li, B. et al. Spectrum Sensing for Self-Organizing Network in the Presence of Time-Variant Multipath Flat Fading Channels and Unknown Noise Variance. Mobile Netw Appl 20, 435–448 (2015). https://doi.org/10.1007/s11036-015-0638-8

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