## 2 Model
### Centralized Eigenvalue-based Spectrum Sensing
The choice of this architecture was made based on the consensus that DCR is the one that is promised to be adopted for cognitive radio applications in the majority of situations [15]. The analog radiofrequency front-end is made up of a wideband antenna, a wideband band-pass filter (BPF), a low-noise amplifier (LNA), and quadrature local oscillators (LO) and mixers responsible for non-coherent direct conversion of the target channel to in-phase and quadrature (I&Q) baseband signals. These signals are amplified using an AGC, which is responsible for maintaining its output signal within the dynamic range of the analog-to-digital converters (ADC) in the I&Q signal paths. I&Q channel low-pass filters (LPF) select the desired bandwidth to be sampled and avoid aliasing. A noise-whitening process takes place to guarantee that noise components are kept uncorrelated when the received signal matrix is built at the fusion center. This is done because the detection techniques considered here assume, for optimum operation, that the noise samples are uncorrelated. Remembering that the samples are quantized at the ADC with \(N_{\text{q}}\) quantization levels, the \(\log_{2}N_{\text{q}}\) bits per sample at both I and Q after whitening can then be forwarded to the fusion center by a given digital modulation scheme. At this stage, bit errors in the transmission may cause further impairments at the available samples. This is however not the subject of this study. It is well known that the DC offset is one of the most relevant problems in a direct-conversion receiver [16, 17, 18]. It corresponds to a DC value at the mixer output produced by the self-mixing of the LO signal, which is originated from the non-ideal isolation between the mixer ports and substrate leakage in integrated receivers. DC offset can also be generated by a strong in-band interferer, second-order distortion in the signal path, and LO reradiation. This DC level, which can be constant or time-varying, can saturate subsequent amplifiers or reduce the ADC dynamic range, causing severe performance degradation. DC-blocking via capacitive coupling is the simplest way of cancelling the DC offset, but can produce performance degradation due to the time-slotted nature of the spectrum sensing process: higher capacitances produces low signal distortion, but increases the sensing settling time and hinder receiver integration; lower capacitances reduces the settling time, but causes more signal distortion. Additionally, DC blocking works only if the DC offset is constant. For these reasons, capacitive DC blocking is not well suited for DC offset cancellation in CR receivers with spectrum sensing capabilities. Fortunately, a number of DC offset compensation techniques have been proposed, some of them capable of almost eliminating the DC offset, maintaining low settling time, see [19, 20] and references therein. In this paper we do not consider the DC offset problem, assuming that it was completely removed by some appropriate technique at the receiver. In [8], where the model considered here was proposed, the influence of imperfect DC offset removal on the spectrum sensing performance is addressed.