In CR networks, cooperative spectrum sensing is more favorable than local spectrum sensing due to its improved sensitivity and the effectiveness in avoiding the hidden terminal problem. However, the performance of cooperative sensing is subject to sev- eral realistic restrictions. For example, it is difficult for the SUs to acquire perfect knowledge of the primary signal space and the CSI of the entire network. Further- more, the fading of the sensing and reporting channels can deteriorate the sensing performance. Hence, we have investigated effective spectrum sensing methods aim- ing at tackling the aforementioned challenges.
The spectrum sensing problems with limited a priori knowledge can be modeled as binary hypothesis testing problems with unknown parameters. In this chapter, we have applied the GLRT principle to two realistic sensing examples. Firstly, assuming an unknown structure of the primary signal space at the SUs, we exploited the rank information to extract its structure. The GLRT-based sensing methods were then de- signed corresponding to two scenarios, i.e., unknown or known noise variances. The resulting algorithms also generalize some special cases in the literature. Secondly, we considered the influence of the fading sensing and reporting channels on cooperative sensing. The SUs are assumed to only have partial CSI of the channels but without knowing the structure of the primary signal space. We derived the sensing algorithms under two scenarios, i.e., the noise variances of the sensing channels are unknown or known. Overall, the proposed GLRT-based algorithms effectively utilize the avail- able information at the SUs in countering the performance degradation caused by environment uncertainties, e.g., fading effects and noise uncertainty.
Power Allocation with Partial Primary
CSI
The underlay paradigm allows for the simultaneous transmission of PUs and SUs. Due to the hierarchical usage of the resources, the main goal is to design the secondary transceiver strategies in order to constrain the performance degradation caused to the PUs below some tolerable limit.
Power allocation is an effective way for interference mitigation. Several works [8, 33, 37, 64, 120] have considered the design of power control strategies using the conventional metric to evaluate the performance degradation of the PU, i.e., the IT constraint denoting the received interference power at the PR. Alternatively, limiting the primary capacity loss is the ultimate goal in regulating the secondary transmis- sion. To this end, the authors in [65, 149] demonstrated that a gain on the secondary rate is achieved by further exploiting the primary CSI instead of considering solely the IT constraint during the system design.
In practice, the SUs can only acquire partial CSI of the entire network, especially regarding the CSI related to the PUs. Two kinds of partial CSI models were considered in the literature: outdated CSI [73, 89, 94, 110, 121] and statistical CSI [12, 28, 80, 116]. On the one hand, outdated CSI is obtained on a real-time basis subject to the delay caused in channel feedback or estimation. The works [73, 89] found that the low correlation between the outdated and the actual CSI yields a large performance loss of the secondary transmission. On the other hand, statistical CSI changes on a time scale that is much larger than the channel coherence time. Given such CSI, the performance loss of the PUs can be limited in an average or a probability-constrained manner.
Given the power control strategies, it is desirable to obtain insights on the achiev- able performance of the SUs at the expense of the performance degradation to the PUs. Such performance analysis can be used for a performance assessment and to provide guidelines in selecting system parameters for power adaptation strategies. However, the optimal power strategy is usually not given in closed form. Thus, it brings in mathematical challenges in the performance analysis. An alternative way is to develop a near-optimal strategy. If the corresponding analytical performance is obtained, it can be a good approximation of the optimal achievable performance.
In this chapter, power allocation strategies for the secondary transmission are investigated subject to different QoS constraints on the primary link under Rayleigh fading channels assuming only partial CSI related to the PR is available at the ST. After introducing the system model in Section 4.1, we study the power allocation in Section 4.2 subject to an average IT constraint and a transmit power constraint on the ST. Motivated by the benefit of exploiting the primary CSI [149], the power allocation
Figure 4.1: Spectrum sharing system with a primary and a secondary link.
strategies are designed in Section 4.3 using the statistical CSI of the primary link subject to an outage probability constraint on the PU instead of an IT constraint. We aim at not only deriving the optimal power allocation strategies but also designing the low-complexity near-optimal strategies with the corresponding performance analysis. The results presented in this chapter have been published in part by the author in [40, 41, 47–49]1.
4.1
System Model
Figure 4.1 depicts the considered cross-interfering spectrum sharing system in which a secondary link coexists with a primary link. We assume that a single antenna is equipped at the ST, the SR, the PT, and the PR, respectively. The transmit symbols of the PT and the ST at the kth time instant are given by x1[k] ∼ CN (0, 1) and x2[k] ∼
CN (0, 1), respectively. We assume that the PT uses non-adaptive power transmission with the power denoted by P1, while the ST optimizes the power P2[k]according to the CSI at the kth time instant. We remark that similar to [37, 69], here the term “power” refers to the instantaneous power averaged over the transmit symbols.
All channels are assumed to be stationary, ergodic, and mutually independent Rayleigh flat fading channels in a slow-fading scenario. Instantaneous CSI of the PT- PR link, the PT-SR link, the ST-PR link, and the ST-SR link is given by h11[k], h12[k], h21[k], and h22[k], respectively. The noise of the primary and the secondary link is given by np[k] ∼ CN (0, σP2) and ns[k] ∼ CN (0, σS2), respectively, with positive and 1In reference to IEEE copyrighted material which is used with permission in this thesis, the IEEE
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finite σP2 and σS2. Consequently, the received signals at the PR and the SR at the kth time instant are denoted by y1[k]and y2[k], respectively:
y1[k] = p P1h11[k]x1[k] + q P2[k]h21[k]x2[k] +np[k] (4.1) y2[k] = q P2[k]h22[k]x2[k] + p P1h12[k]x1[k] +ns[k]. (4.2) The channel power gain is denoted by
gij[k] = hij[k] 2 , i, j =1, 2 (4.3)
which is exponentially distributed with the PDF
fgij(x) =
(
lije−lijx, x ≥0
0, x <0 i, j=1, 2 (4.4) with lij indicating the rate parameter. In practice, the instantaneous CSI g11[k] and g21[k] is difficult to obtain at the ST due to limited cooperation between the SU and the PU. However, we assume statistical parameters l11 and l21 to be available at the ST due to the exploitation of side information [61]. For the PT-SR link, either statistical CSI parameter l12 or the the instantaneous CSI g12[k] is available at the ST, depending on the scenario whether the ST can obtain statistical parameters by the location infor- mation or obtain the instantaneous CSI via estimation or feedback. Additionally, we assume both the ST and the SR know perfect instantaneous CSI of the secondary link g22[k] and the SR additionally knows the instantaneous CSI of the PT-SR link g12[k]. For the remainder of the chapter, we omit the time argument k for simplicity.
We consider two kinds of QoS constraints to restrict the performance degradation of the primary transmission: average IT constraint and outage probability constraints. Besides, the peak power of the ST is limited. The power control strategies aiming at maximizing the achievable rate of the secondary link subject to aforementioned constraints are investigated in the remainder of this chapter.