# binaryintloss

Loss due to M-of-N binary pulse integration

## Syntax

``LB = binaryintloss(PD,PFA,N)``
``LB = binaryintloss(PD,PFA,N,M)``
``[LB,PDSP,PFASP] = binaryintloss(___)``

## Description

````LB = binaryintloss(PD,PFA,N)` calculates the binary integration loss, `LB`, in dB due to M-of-N pulse integration. The function computes the loss assuming that you are using a square-law detector and a nonfluctuating target. NoteThe number of detections, `M` in the M-of-N integration scheme is set to `M=0.955*N0.8`. This value is close to the optimal value that results in the binary integration loss lower than `1.5` dB for the `N` in the range between `[5,700]`. ```

example

````LB = binaryintloss(PD,PFA,N,M)` calculates the binary integration loss using number of detections `M`.```
````[LB,PDSP,PFASP] = binaryintloss(___)` also calculates single-pulse probabilities of detection, `PDSP`, and single-pulse probabilities of false alarm, `PFASP`, which are required at the input of the binary integrator to achieve the desired `PD` and `PFA`. Specify the input arguments from any of the previous syntax.```

## Examples

collapse all

Calculate binary integration loss for `12` detections from `24` received pulses. Assume a probability of detection of `0.9` and probability of false alarm of `1e-6`

```PD = 0.9; PFA = 1e-6; N = 24; M = 12; binaryintloss(PD,PFA,N,M)```
```ans = 1.0596 ```

## Input Arguments

collapse all

Probability of detection in the range [`0.1,0.999999`], specified as a positive scalar or as a length-J vector with each element in the range [`0.1,0.999999`] .

Probability of false alarm, specified as a positive scalar in the range [`1e-15,1e-3`] or as a length-K vector with each element in the range [`1e-15,1e-3`] .

Number of received pulses, specified as a positive scalar.

Number of detections, specified as positive scalar.

## Output Arguments

collapse all

Binary integration loss, returned as a J-by-K matrix in dB with rows corresponding to the number of elements in `PD` and columns corresponding to the number of elements in `PFA`.

Single-pulse probabilities of the detection, returned as a J-by-K matrix with rows corresponding to the number of elements in `PD` and columns corresponding to the number of elements in `PFA`.

Single-pulse probabilities of the false alarm, returned as a J-by-K matrix with rows corresponding to the number of elements in `PD` and columns corresponding to the number of elements in `PFA`.

## Version History

Introduced in R2021a