beat2range

Convert beat frequency to range

Syntax

r = beat2range(fb,slope)

r = beat2range(fb,slope,c)

Description

r = beat2range(fb,slope) converts the beat frequency of a dechirped linear FMCW signal to its corresponding range. slope is the slope of the FMCW sweep.

r = beat2range(fb,slope,c) specifies the signal propagation speed.

Examples

Range of Target in FMCW Radar System

An FMCW waveform sweeps a band of 30 MHz (BW) in 2 ms (T). The dechirped target return has a beat frequency (freqb) of 1 kHz. Compute the target range in meters.

BW = 30e6;
T = 2e-3;
slope = BW/T;
freqb = 1e3;
r = beat2range(freqb,slope)

r = 
9.9931

Input Arguments

fb — Beat frequency of dechirped signal

M-by-1 vector | M-by-2 matrix

Beat frequency of dechirped signal, specified as an M-by-1 vector or M-by-2 matrix in hertz. If the FMCW signal performs an upsweep or downsweep, fb is a vector of beat frequencies.

If the FMCW signal has a triangular sweep, fb is an M-by-2 matrix in which each row represents a pair of beat frequencies. Each row has the form [UpSweepBeatFrequency,DownSweepBeatFrequency].

Data Types: single | double

slope — Sweep slope

nonzero scalar

Slope of FMCW sweep, specified as a nonzero scalar in hertz per second. If the FMCW signal has a triangular sweep, slope is the sweep slope of the up-sweep half. In this case, slope must be positive and the down-sweep half is assumed to have a slope of -slope.

Data Types: single | double

c — Signal propagation speed

speed of light (default) | positive scalar

Signal propagation speed, specified as a positive scalar in meters per second.

Data Types: single | double

Output Arguments

r — Range

M-by-1 column vector

Range, returned as an M-by-1 column vector in meters. Each row of r is the range corresponding to the beat frequency in a row of fb.

Data Types: single | double

More About

Beat Frequency

For an up-sweep or down-sweep FMCW signal, the beat frequency is F_t – F_r. In this expression, F_t is the transmitted signal’s carrier frequency, and F_r is the received signal’s carrier frequency.

For an FMCW signal with triangular sweep, the upsweep and downsweep have separate beat frequencies.

Algorithms

If fb is a vector, the function computes c*fb/(2*slope).

If fb is an M-by-2 matrix with a row [UpSweepBeatFrequency,DownSweepBeatFrequency], the corresponding row in r is c*((UpSweepBeatFrequency - DownSweepBeatFrequency)/2)/(2*slope).

This function supports single and double precision for input data and arguments.

References

[1] Pace, Phillip. Detecting and Classifying Low Probability of Intercept Radar. Artech House, Boston, 2009.

[2] Skolnik, M.I. Introduction to Radar Systems. New York: McGraw-Hill, 1980.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

• Usage notes and limitations:

• Does not support variable-size inputs.

• This function supports single and double precision for input data and arguments.

Version History

Introduced in R2012b