# Constant False-Alarm Rate Detection

The constant false-alarm rate (CFAR) detection benchmark is an example of data-dependent processing designed to find targets in an environment of varying background noise. The benchmark subjects a subset of a radar data cube to this algorithm. Assume a data cube consisting of real (as opposed to complex) data whose dimensions are beams, range, and dopplers. During CFAR detection, a local noise estimate is computed from the 2N_{cfar}range gates near the cell C(i,j,k) under test. A number of guard gates G immediately next to the cell under test will not be included in the local noise estimate (this number does not affect the throughput). For each cell C(i,j,k), the value of the noise estimate T(i,j,k) is calculated as

(1)

The range cells involved in calculating the noise estimate for a particular vector are shown in Figure 1. For each cell C(i,j,k), the quantity |C(i,j,k)|

^{2}/T(i,j,k) is calculated: this represents the normalized power in the cell under test. If this normalized power exceeds a threshold µ, the cell is considered to contain a target.

Figure 1: Sliding window in CFAR detection. The example shows
the number of guard cells G = 1 and the number of cells used in computing the estimate N

_{cfar}= 3.An efficient implementation of the CFAR algorithm makes use of the redundancy in the computation of T according to the formula given in Equation (1). Note that the relationship between T(i,j,k) and T(i,j + 1,k) is

Using this relationship, the value of T for a particular set of N

_{rg}range gates can be calculated in O(N

_{rg}) time, that is, independent of the values of G and N

_{cfar}. Note that some variations of this formula and equation (1) occur at the boundary areas. For the most part, these are handled in a straightforward fashion: if a computed index would cause reference to a cell outside the cube's boundaries, we ignore that term in the computation. The parameter sets for the CFAR benchmark are shown in Table 1.

Table 1: Parameter sets for the CFAR Kernel Benchmark.

Name | Description | Set 0 | Set 1 | Set 2 | Set 3 | Units |

Nbm | Number of beams | 16 | 48 | 48 | 16 | beams |

Nrg | Number of range gates | 64 | 3500 | 1909 | 9900 | range gates |

Ndop | Number of doppler bins | 24 | 128 | 64 | 16 | doppler bins |

Ntgts | Number of targets that will be pseudo-randomly distributed in Radar data cube | 30 | 30 | 30 | 30 | targets |

Ncfar | Number of CFAR range gates | 5 | 10 | 10 | 20 | range gates |

G | CFAR guard cells | 4 | 8 | 8 | 16 | range gates |

mu | Detection sensitivity factor | 100 | 100 | 100 | 100 | |

W | Workload | 0.17 | 150 | 41 | 18 | Mflop |