1.4 Non-Cooperative Sensing
1.4.3 Summary of Presented Methods and Simulations
Bandwidth 8MHz
Mode 2K
Guard interval 1/4
Channel models Rayleigh/Rician (K=1) Maximum Doppler shift 100Hz
Frequency-flat Single path
Sensing time 1.25ms
Location variability 10dB
TABLE1.1 – The transmitted DVB-T primary user signal parameters
1.4.2.4 Other Blind Sensing Methods
Another blind technique called multi resolution sensing was proposed in [33]. This technique produces a multi resolution PSD estimate using a tunable wavelet filter that can change its cen- ter frequency and its bandwidth [34]. In [35], wavelets are used for detecting PU signals in blind manner. The wavelet based approach is efficiently used for wideband spectrum sensing where a wi- deband signal spectrum is decomposed into elementary building blocks of sub-bands that are well characterized by local irregularities in frequency [35]. The wavelet transform is then employed in order to detect and to estimate the local spectral irregular structure that carries important informa- tion about the frequency location and power spectral densities of the sub-bands. Others methods that exploit a recorded form of the covariance matrix are also derived in the literature [36].
Scenario 1 : OFDM signal in AWGN channel We consider here a DVB-T OFDM signal in an AWGN channel. It is assumed that the detection performance in AWGN will provide a good impression of the performance, but it is necessary to extend the simulations to include signal distortion due to multipath and shadow fading.
Scenario 2 : OFDM signal in Rayleigh multipath fading with shadowing This scenario utilizes the same DVB-T OFDM signal as scenario 1, but to make the simulations more realistic, the signal is subjected to Rayleigh multipath fading and shadowing following a log normal distribution in addition to the AWGN. The maximum Doppler shift of the channel is 100Hz and the standard deviation for the log normal shadowing is 10dB. Since the fading causes the channel to be time variant, it is necessary to apply longer averaging than in scenario 1 to obtain good simulation results. Thus the number of iterations in the Monte Carlo simulation is increased from 500 to 1000.
Scenario 3 : OFDM signal in Rician multipath fading with shadowing The third simulation sce- nario utilizes also a DVB-T OFDM signal in Rician multipath fading with shadowing. The K-factor for the Rician fading is 10, which represents a very strong line of sight component.
The maximum Doppler shift of the channel and the standard deviation for the log normal shadowing are the same as in the second scenario.
Simulations are important in assessing the performance of the presented spectrum sensing algorithms. The three scenarios provide different attributes so that the performance can be asses- sed under different conditions, providing fair conditions before making conclusions. Figure 1.2 presents the detection performances of the presented detectors in the three proposed simulation scenarios. The simulations are split in two main parts. Part one presents the probability of detec- tion versus SNR with a fixedPF A = 0.05. Part two evaluates the algorithms in terms of receiver operating characteristics (ROC). In these simulations, the sensing time is set to1.12ms.
Figures 1.2 (a), (b) and (c) show the PD versus SNR at a constant false alarm rate for the five sensing detectors (CD, AD, ED, MMED and KLD) in the three proposed scenarios. From these figures, we show that the ED has lost its detecting ability when decreasing the SNR. For sufficiently low SNR, robust detection becomes impossible. The same can be observed for the KLD. These results come from the fact that the theoretical analysis for the ED and KLD algorithms assume the noise variance to be known, and the underlying noise to have a perfect stationary Gaussian distribution. This assumption does not hold. In reality, the noise variance will usually not be completely stationary. The assumption about the distribution of the noise is also known to be weak. On the other hand, we find that if knowledge of signal parameters is provided, the CD and AD can still perform a high probability of detection. Since this group of detection algorithms requires a priori knowledge about the received signal, they are not blind and are therefore not directly relevant to the work presented in this thesis. The two proposed detectors in this thesis will be compared with the KLD and MMED as reference algorithms. In the following chapters we will show as well the difference between these detectors and the proposed ones. Results in Figures 1.2 (d), (e) and (f) present the ROC curves. All detectors work at a SNR= −7dB condition. From these curves we show that the CD and AD outperform the others detectors. These results confirm the ones presented in Figures 1.2 (a), (b) and (c).
Complexity of signal detection process is also a great concern for CR other than detection performance. Complexity terminology will be the asymptotic O−notation, which is standard when analyzing algorithms. For readers who are not familiar with this notation, it will be briefly introduced. The notation is used to describe an asymptotic upper bound and is defined as
O(g(n))={f(n) :∃positive constantscandn0such that0≤f(n)≤cg(n) ∀ n≥n0} (1.25)
−150 −10 −5 0 0.1
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
SNR [dB]
PD
CD AD MMED ED KLD
−300 −25 −20 −15 −10 −5 0 5 10
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
SNR [dB]
PD
CD AD MMED ED KLD
(a)PDvs. SNR : Scenario 1 (b)PD vs. SNR : Scenario 2
−400 −30 −20 −10 0 10
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
SNR [dB]
PD
CD AD MMED ED KLD
0 0.2 0.4 0.6 0.8 1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
PFA PD
CD AD MMED ED KLD
(c)PDvs. SNR : Scenario 3 (d) ROC curves : Scenario 1
0 0.2 0.4 0.6 0.8 1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
PFA PD
CD AD MMED ED KLD
0 0.2 0.4 0.6 0.8 1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
PFA PD
CD AD MMED ED KLD
(e) ROC curves : Scenario 2 (f) ROC curves : Scenario 3
FIGURE 1.2 – Monte Carlo simulation results assessing detection performance of a number of spectrum sensing algorithms using an DVB-T OFDM primary user system : Probability of detec- tion versus SNR curves withPF A = 0.05and ROC curves with SNR=−7dB and sensing time
=1.12ms.
68%6
68
68
68
387[ 385[
FIGURE1.3 – Cooperative spectrum sensing in cognitive radio networks : SU 1 is shadowed over the reporting channel and SU 3 is shadowed over the sensing channel.
This definition is taken from [39]. This book is an excellent reference on algorithms and analysis of algorithms.
We summarize the number of multiplications required for each technique in Table 1.2. Note thatprefers to the number of samples andN to the size of the covariance matrix (i.e. number of observations). From this table, we conclude that the CD, AD and MMED detectors are the most complex among all, while ED is the least complex among them. For more information about the complexity study of spectrum sensing methods see [40].