In Stage I, the data transmission time is adaptively adjusted subject to the interference time constraint. Here, we assume that the SU Tx know the statistical information of the PU's activity, including the mean, the variance and the PDF of PU's ON and OFF periods.
4.1 Adaptive algorithm for adjusting the transmission time in Stage I
The aim of the adaptive algorithm is to limit the interference time generated in the scenario where the licensed channel switches from OFF state to ON state while SU Tx is transmitting data on the channel.
Given that the channel is in OFF state at t
, the conditional probability that the channel keeps being in OFF state during is
where denotes that the channel is in OFF state at time t, and denotes that the channel is in ON state at time t. Then, the probability that the channel turns from OFF state to ON state at the time of ti+1is
Similarly, the probability that the channel switches from OFF state to ON state in the middle of the i th transmission is
where 0 < s < . The PDF of the residual time s of channel's OFF state is the derivative of (4) with respect to s:
Then, the average interference time is calculated as follows:
where c1 = t
- tsp1 is the time interval starting from the most recent channel switch point tsp1 to the i th SU transmission.
It can be seen from (6) that the interference time is related to the transmission time interval and the time interval c1. While the second variable c1 can't be controlled, the interference time is limited by adjusting the transmission time interval . It is noticed that the interference time is a monotonically increasing function of , because the derivative of (6) with respect to is positive, that is to say
Let α represents the prescribed interference parameter, considering is a monotonically increasing function of , the optimal transmission time interval satisfying the interference limit is
What is worth mentioning is that larger α results in larger interference time , larger transmission time and hence larger throughput of secondary system. Therefore, α can be seen as a tradeoff parameter between the interference time and the throughput of secondary system.
Equation (8) shows that is a function of c1, and declines dramatically to a very small value with the increase of c1. However, in reality every system has a minimum transmission time interval T1, min. Besides, the maximum transmission time interval T1, max is given to further limit the interference. Here, we suggest setting T1, max to be max
f0(x). Therefore, the adaptive transmission time is set to be
4.2 Algorithm for estimation of tsp1
It is clear from (6), (8), and (9) that the calculation of the adaptive transmission time depends on the information of the switch point time tsp1. Thus, it is very important to estimate tsp1 for the proposed ICASST algorithm. Denote and as the old channel switch point and the estimated new channel switch point, respectively, and the real value of the new switch point is tsp1 = t
In this article, minimum mean square error (MMSE) principle is adopted to estimate the new channel switch point tsp1. Given that the channel state is ON at ti+1and is OFF at t
, the conditional probability density function of the residual time s of channel's OFF state is:
Then the mean squared estimation error ε between the estimated value and real value tsp1 is
where is the time interval between the old channel switch point and the i th transmission.
The optimal estimate of the new channel switch point is the one which minimizes the mean squared estimation error ε, and the expression of is