IEEE - Aerospace and Electronic Systems - January 2020 - 34

Feature Article:

DOI. No. 10.1109/MAES.2019.2955586

Radar Doppler Frequency Measurements-Accuracy
Versus SNR in Practical Processors
Nadav Levanon, Department of Electrical Engineering, Systems Tel-Aviv
University, Tel-Aviv, Israel

INTRODUCTION
Doppler shift of a target-return provides the target's rangerate information. In the prevailing low-signal-to-noise
ratio (SNR) scenes, the radar's coherent processing interval (CPI) determines the Doppler measurement resolution.
Clutter joins thermal noise to render most scenes as low
SNR. In low-SNR scenes, Doppler resolution defines also
Doppler accuracy and the SNR value hardly enters the
analysis. The Doppler assigned to a target detected in a
specific range-Doppler cell is the cell's nominal Doppler
value. Processing methods usually shape the Doppler
response to minimize the mainlobe width and reduce sidelobes that can overlap neighboring Doppler cells.
Radar Doppler measurement will be demonstrated
using a coherent train of pulses. The CPI will be long
enough to contain many pulse repetition intervals (PRI).
Furthermore, the Doppler frequency fD of interest will be
small enough to provide adequate number of samples
(pulses) during one Doppler cycle, namely fD PRI ( 1.
The three subplots in Figure 1 show received (noise free)
Doppler-shifted coherent pulses after the intermediate frequency stage (top), the synchronously detected in-phase (I)
samples (middle), and quadrature-phase (Q) (bottom subplot). The nth sample of the complex envelope is given by
un ¼ In þ jQn :

(1)

In a high-SNR scene, the phase of each received pulse
can be measured, relative to the known phase of the transmitted pulse. The resulted phase ramp during one Doppler
Authors' current addresses: Nadav Levanon, Department of Electrical Engineering, Systems Tel-Aviv
University, Tel-Aviv 6997801, Israel. (E-mail:
levanon@tauex.tau.ac.il).
Manuscript received September 2, 2019, revised
November 5, 2019, and ready for publication November
21, 2019.
Review handled by D. W. O'Hagan.
0885-8985/19/$26.00 ß 2019 IEEE
34

cycle (short CPI), or the Doppler cycle count (long CPI),
can yield very accurate Doppler information. In that case,
we will show that the standard deviation (STD) of the
phase measurement error depends on the inverse of the
square root of the SNR, as predicted by the Carmer-Rao
[1], [2] lower bound.
In pulse-compression radar, each pulse is intrapulse
phase coded or frequency modulated. The ensuing analysis will use pulses that are phase coded by a 13 element
binary sequence (Barker 13). For simplicity, the receiver
will not contain a mismatched filter, which is commonly
used to reduce the range sidelobes.

PROCESSING LOW-SNR SCENE-THE "AMBIGUITY
FUNCTION" APPROACH
Figure 2 describes a simple generic range-Doppler processor
that can handle a low-SNR radar scene. Synchronous I&Q
detection and sampling follow the IF amplifier. If the pulse is
phase coded, then, the sampling period ts is equal to or
shorter than the code element duration tb . Tr is the PRI. To
obtain good Doppler resolution M identical pulses are processed coherently, yielding CPI ¼ M Tr . A matched filter
precedes the Doppler processing. It is assumed that the intrapulse phase ramp, caused by Doppler shift, does not seriously
degrade the sidelobe behavior of the delay response.
Doppler processing is handled by the interpulse Doppler compensation, known also as slow-time Doppler compensation. The present matched filter output joins the
previous outputs from M -1 shift registers, each register
produces delay equal to Tr , to create M inputs to an fast
Fourier transform (FFT), all coming from the same delay
(range cell). In some cases, a moving target indicator
(MTI) precedes Doppler processing by the FFT. Its task is
to attenuate very strong reflections from stationary nearclutter that can exceed the dynamic span of the following
processing stages.
When the interpulse weight window is uniform, the M
FFT outputs produce M cuts of the periodic ambiguity

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