SpectraMap: Efficiently Constructing a Spatio-temporal RF Spectrum Occupancy Map

Abstract

The RF spectrum is typically monitored from a single, or few, vantage points. A larger spatio-temporal view of spectrum occupancy, such as over a few weeks on a city-wide scale, would be beneficial for several applications, for example, spectrum inventory by regulators or spectrum monitoring by wireless carriers. However, achieving such a view requires a dense deployment of spectrum analyzers, both in space and time, which is prohibitively expensive.

In this paper, we present a novel efficient approach to obtain an accurate extrapolated spatio-temporal view of spectrum occupancy. Our method uses RSSI measurements alone and does not require a-priori information of terrain, transmitter location, transmit power or path-loss model. We present our method as an algorithmic framework, called SpectraMap, which through targeted deployment of both static and mobile spectrum analyzers, gives a view of the spectrum occupancy over both time and space. We contrast SpectraMap’s accuracy with that of Kriging (an accepted well performing method of RSSI spatial extrapolation) through simulations and present RSSI map construction savings achieved through actual deployment on a large university campus. Finally, we draw a theoretical distinction between SpectraMap and relevant contemporary solutions in the fields of space-time RSSI maps and spectrum management.

Appendix

Proof of Theorem 1 (Time Cover bound):

Our aim is to find an upper-bound for $\mathbf {E}[|\mathbb {Z}_{\hat{m}}(t_d+u) - \mathbb {Z}_{\hat{m}}(t_d)|]$.

To that end, consider the following derivation (through arithmetic):

Proof of Theorem 2 (Space Cover bound):

We need to find an upper-bound for $| z_{m'}(t_s) - z_{m}(t_s) |$. It is as follows:

The final approximation can be justified by Markov’s Inequality. Let $\alpha \in [0,1]$. Then, $Pr[ \mathbb {Q}^\varDelta _{m,m'} \ge \alpha \times \rho ^*_s ] \le \frac{\mathbf {E}[\mathbb {Q}^\varDelta _{m,m'}]}{\alpha \times \rho ^*_s} := \kappa$.

Now, the smaller the ‘space-quietness factor’ $(\alpha ,\kappa )$, the more $\rho ^*_s$ dominates $q^\varDelta _{m,m'}(t_d,t_s)$.