Range Imaging
Range and cross-range imaging is performed using
backprojection algorithm described in [10]. Simple fast-time
correlation of received signal samples with the ideal transmit
signal was performed on a pulse-to-pulse basis to achieve
range profile construction. Conventional short-pulse UWB
radars attain high range resolution by employing impulses
resultant in very narrow peak of autocorrelation function
(ACF). Realistic UWB-OFDM signal’s duration is at least one
hundred times longer than a typical 1 nanosecond UWB pulse
– and, in our study, it is 256 nanoseconds long. However,
wide bandwidth of UWB-OFDM pulse still results in fairly
narrow ACF peaks, although with somewhat higher sidelobes
than with Gaussian pulses. An illustration contrasting between
256 nanosecond UWB-OFDM and Gaussian pulse with 1
GHz centre frequency and 0.5 fractional bandwidth, generated
in MATLAB using gauspuls(tt,1e9,.5), is shown in
Fig. 1. UWB-OFDM pulse was generated randomly and
average of 100 pulses was computed. Based on the appearance
of plots we can expect satisfactory performance of range
reconstruction algorithm using matched filtering and if better
sidelobe characteristics are desired, we can employ more
sophisticated OFDM sub-carrier compositions.
The time limit of sampling window for received signal is
dictated by the original number of sub-carriers – and, thus,
time samples – in the transmit signal. In order to recover each
sub-carrier’s amplitude and phase accurately, we need to
make sure we collect at least 256 samples of the incoming
signal. In the communication system configuration, the
number of samples is even more critical, as our goal is to map
the received signal’s sub-carrier composition to the
transmitted data vector and thus need to perform a 256-point
IFFT on the incoming sample array. The upper limit on the
number of collected samples is, therefore, dependent on how
many 256-sample vectors we would like to collect at each
transmit/receive cycle. In our study we set this limit to one
block of 256-sample data to be collected for each range profile.
This translates into a range swath of 38.4 meters when
sampling at 1 Gs/s as shown by (2). Using the radar equation
and parameters given earlier the maximum recoverable target
distance purely based on signal power was approximately 150
meters.
In simulation it was determined that 46 samples (equivalent to
the point target being 30 meters into the range swath) were
enough to recover range information. Minimum radar range
was assumed to be 120 meters thus making range swath 30
meters, or entire range profile to be [120 … 150] meters. Fig.
2 shows examples of realistic range profile recoveries based
on incomplete signal sampling. It is apparent that even with
incomplete return signals the range recovery of point targets is
feasible. Noise performance will be studied separately,
although white noise is expected to affect the results of
matched filtering very similarly to how it affects other UWB
signals, due to inherently wide signal bandwidth.