Spectrum Sensing Procedure and Algorithm

If we are able to detection the alternating point of the ACK and data packet, we can separately take the two independent observations from different position, both in the dimension of geometry and time. The sensing also performs in different sensing channel. The difference in geographical dimension results in different path loss factor and the sensing channel difference results in independent fading. In fact, we can

formulate the spectrum sensing problem under the intelligent decision framework.

The following table illustrates the formulation:

Intelligent Decision Framework Spectrum Sensing

Event Primary Transmission

Physical quantity 1 PS-Tx transmission data

Physical quantity 2 PS-Rx ACK

Observation 1 Sensing data packet

Observation 2 Sensing ACK

Table 7.1. Formulation under Intelligent decision framework

Fig. 7.8 Spectrum Sensing Procedure

The spectrum sensing scheme follows the following procedures (Fig.7.8):

1. Identifying the timing pattern

We assume CR has the knowledge of the duration of data packet and ACK. We also know that because the signals from PS-Tx and PS-Rx experience different path-loss, their power level is different when they arrive in CR-Tx. In other words, the mean power of receiving signal process is different. The Change Detection algorithms [40,41] applied in signal segmentation or remote can be applied here to detect the

change in the process mean at the alternating point of data packet and ACK.

With the above knowledge, the following procedures are sufficient to identify the timing pattern of the intertwined ACK and data packet:

(1) Start monitoring at

(2) Keep monitoring until a change in mean happened or until . Denote the time of the change point . If the change does not happen until ,

.

(3) If _ACK, stop the monitoring. If _ACK, keep monitoring

until _ACK.

Then we can construct the timing pattern by the following inference:

(1) If _ACK, at the change point the transmission changes from data packet transmission to ACK reply.

(2) If _ACK and a change point is observed at _ACK, at the change point the transmission changes from data packet transmission to ACK reply. Otherwise, at the change point the transmission changes from ACK reply to data packet transmission.

The performance of Change Detection algorithm is better when the process changes significantly. When the process only changes a little, the performance degrades. However, our spectrum sensing scheme has large performance gain when the signal power of ACK and data packet is significantly different, which will be elaborated in the following sections. If the signal power is almost the same, our scheme acts almost like ordinary energy detector. Hence the performance of our spectrum sensing scheme would not be sensitive to the performance of Change Detection because in the region which the performance of Change Detection may degrade, the correct timing of PS transmission would not significantly affect the performance of our spectrum sensing scheme.

2. Derive the test statistics of ACK & data packet

The ACK and data packet detection problem falls back to detect an unknown signal in the fading channel which is a well-studied subject [42]. As mentioned previously, the signal takes the form:

· 7.3 The only difference in signal model between ACK and data packet is the path-loss factor which determines the mean of channel fading factor h.

And the test statistic Y is the integration of the square of the received signal:

1 7.4

T is the duration of sensing time, is the standard deviation of the noise.

Conditioning on SNR , the distribution of Y is:

~

2 7.5 is chi-square distribution with 2u degrees of freedom. is the time-bandwidth product. 2 is chi-square distribution with 2u degrees of freedom and a non-centrality parameter 2 . Because h follows Rayleigh distribution,

follows the distribution:

1exp 7.6

where

T for test statistics of data packet and

R for test statistics of ACK.

3. Fusion center

Traditionally, there are several kinds of combining (fusion) scheme to deal with the problem of detecting signal in the fading channel. The most widely used

combining schemes are weighted combining and selective combining. Equal gain combining is a special case of weighted combining. In fact, the weighted combining scheme is the Ratio Combining scheme and the selective combining is Observation Selection in the intelligent decision framework. Since primary transmission detection is a detection problem, we slightly modified the Ratio Combining and Observation Selection scheme for estimation problem without modifying the underlying structure.

A. Observation Selection

The fusion center selects the observation to make decision according to the geographical separation. In other words, the fusion center selects the observation of ACK if the distance between PS-Rx and CR-Tx is smaller. Otherwise, it selects data packet observation. The validity of this selection rule is justified by that according to our system model, the expectation of SNR is monotonic decreasing function of distance. Then the selected test statistics is compared with a threshold to decide the presence of primary transmission.

B. Ratio Combining

The fusion center combines the test statistics with the weighting coefficient determined by the quality of the observation. The quality of observation can be determined by the detection probability alone because the false alarm probability is the same for the two observations. Hence the weighting coefficient is the ratio of detection probability. Then the test statistic of Ratio Combining, _RC, is the weighted sum of test statistics of data packet and ACK:

RC T

T R T R

T R R 7.7 where _T is the test statistics of data packet, _R is the test statistics of ACK packet. Then the weighted sum of test statistics _RC is compared with a threshold

to decide the presence of primary transmission. The detection probability of energy detection in fading channel has been derived in [42],

T exp probability is a monotonic increasing function of the mean of SNR distribution, _T and _R . And the mean of SNR distribution is a monotonic decreasing function of the distance between the sensing node and the signal source. Hence the weighting coefficient is the decreasing function of distance, which is intuitively true.