# Energy detector based sensing

In the this paper, A Survey of Spectrum Sensing Algorithms for Cognitive Radio Applications, what is $L_f L_t$ in equations $(8)$ and $(9)$ as shown below?

\begin{align} P_F&=1-\Gamma\left(L_fL_t, \frac{\lambda_E}{\sigma^2_w}\right),\tag{8}\\ P_D&=1-\Gamma\left(L_fL_t, \frac{\lambda_E}{\sigma^2_w + \sigma^2_s}\right),\tag{9} \end{align}

• isn't it defined in reference [41], where that formula is from? Note that it's really bad style of the authors to not introduce all their symbols explicitly, especially in a survey paper, whose primary job is to take the task of reading all the referenced papers of the reader. – Marcus Müller Jun 22 '17 at 19:17
• uses different equations and it's not clear unfortunately <pdfs.semanticscholar.org/847c/…> – sh2017 Jun 22 '17 at 20:55

I looked at [41] and no clue either. The incomplete gamma is related to the exceedance probability of adding $N$ $\chi^2$ random variables. My guess is that $L_f$ $L_t$ would be related to something like the total number of DFT bins over $L_t$ time scans and $L_f$ frequency bins. It appears to be a time bandwidth matched energy detector, if you know what $L_f$ and $L_t$ are. This is the energy detection counterpart to a synchronized matched filer.
This really isn't true for an actual unknown signal. $L_f$ and $L_t$ are unknown.