On the combined effect of directional antennas and imperfect spectrum sensing upon ergodic capacity of cognitive radio systems

Abstract

We consider a cognitive radio system, consisting of a primary transmitter (PUtx), a primary receiver (PUrx), a secondary transmitter (SUtx), and a secondary receiver (SUrx). The secondary users (SUs) are equipped with steerable directional antennas. We assume the SUs and primary users (PUs) coexist and the SUtx knows the geometry of network. We find the ergodic capacity of the channel between SUtx and SUrx, and study how spectrum sensing errors affect the capacity. In our system, the SUtx first senses the spectrum and then transmits data at two power levels, according to the result of sensing. The optimal SUtx transmit power levels and the optimal directions of SUtx transmit antenna and SUrx receive antenna are obtained by maximizing the ergodic capacity, subject to average transmit power and average interference power constraints. To study the effect of fading channel, we considered three scenarios: 1) when SUtx knows fading channels between SUtx and PUrx, PUtx and SUrx, SUtx and SUrx, 2) when SUtx knows only the channel between SUtx and SUrx, and statistics of the other two channels, and, 3) when SUtx only knows the statistics of these three fading channels. For each scenario, we explore the optimal SUtx transmit power levels and the optimal directions of SUtx and SUrx antennas, such that the ergodic capacity is maximized, while the power constraints are satisfied.

Source Localization and Tracking for Dynamic Radio Cartography using Directional Antennas

“…In the case that N B > M after M time slots the null space will be empty and w(M + 1) can not be selected from the null space. In this case we can not employ 3 In the case of N B ≤ M the optimum beams will be orthogonal and otherwise we can just optimize them to be uncorrelated. Algorithm 1 Centralized spectrum sensing and beamforming.…”

On Optimal Sensing and Capacity Trade-off in Cognitive Radio Systems with Directional Antennas

“…With the same argument we can show that Dα 0 is a concave functions with respect to τ for ξ > σ 2 n . Taking the first derivative of C with respect to τ , we get (11). solve ∂C/∂φ r = 0 and obtain φ r .…”

“…The optimal φ t and τ can be obtained by using searching methods like bisection method. We consider an initial value for φ t which satisfies (10a) and τ ∈ (0, T ), and obtain P opt using (11). Then, the optimal φ r can be found by solving ∂C/∂φ r = 0, subject to the constraint (10b).…”

“…In those works, spectrum sensing seeks spectrum holes in the time domain so that SUs exploit them for transmitting their data. Different from the bulk of the literature, in this paper we assume the SUs are equipped with steerable directional antennas which allow them to use spatial spectrum holes [8]- [11] to increase spectrum utilization, specially in cognitive satellite networks [12]. The directional antennas can identify and enable transmission and reception across spatial domain and further enhance spectrum utilization, compared with omni-directional antennas.…”

Achievable Rates of Opportunistic Cognitive Radio Systems Using Reconfigurable Antennas with Imperfect Sensing and Channel Estimation

“…In opportunistic CR systems, spectrum sensing is necessary for detecting PUs' activities and protecting the PUs against harmful interference. In general, any spectrum sensing (signal in noise detection) technique is prone to errors, that can be described as mis-detection or false alarm probability [11], [12]. On the other hand, imperfect CSI of SU tx -SU rx link due to channel estimation error (even under perfect spectrum sensing) has negative influence on the link capacity.…”