UWB Receiver Design
Communications involves the transmission of ultra-short pulses with a large
fractional bandwidth. Because of the fine time-resolution, UWB
transmissions can resolve many paths, and are thus rich in multipath diversity.
However, the communications channel is extremely frequency-selective because of
the large bandwidth, which results in a significant number of resolvable multipath components. The transmit pulse is therefore extremely distorted (see
Figure 1: Transmit (left) and receive (right) pulse. Channel distortion is
Because of the
distortion caused by the channel, it is inefficient to use a simple
matched filter receiver where the template is matched to the transmit pulse
(including the effect of the transmit and receive antennas). The energy capture
of such a receiver is very low, and performance is unacceptable (see Figure
Simple Matched Filter Performance is highly suboptimal
The template of the optimal UWB correlator should be matched to the
distorted received pulse, rather than the "clean" LOS pulse. If such a template
is readily available, 100% energy capture is possible (see Figure below).
Unfortunately, such a template is hard to generate, and the need arises for a
receiver structure tailored to achieve maximum energy capture.
Perfect Matched Filter Performance: all the energy is captured
expressions for the simple and matched filter BER performance were derived at
MPRG. Equations are included in the presentation (link at bottom of page).
UWB Research has mainly concentrated on the analysis of
Rake receivers. However, Rake receivers applied to UWB systems suffer from two
First, the energy capture is relatively low for a moderate
number of fingers when Gaussian pulses are used. It has been shown that a
typical NLOS channel may have up to 50 resolvable dominant specular compoenents. Even if
a Rake receiver with so many fingers is realizable, it would only be able to
capture part of the signal energy (,)
multipath undergoes a different channel, which causes distortion in the received
pulse shape, and makes the use of a single line of sight path signal as a
template sub-optimal ().
Typical MRC-based F finger Rake Receiver
An analysis of a Rake receiver using MRC
combining and PPM modulation can be found in  and . However, these two works make the assumption that the
receiver is able to completely resolve the L strongest channel paths. A study of
the effect of imperfect channel estimation can be found in .
A theoretical expression for the Rake receiver using MRC combining was developed in MPRG, both
for biphase and PPM modulation. Traditional derivations for an F finger Rake
receiver assume that the strongest F channel paths are selected.
Realistic expressions that better model the finger selection process, were
derived. the effect of noise and path correlations was taken into account.
Equations can be found in the attached presentation (follow link at end of
Figure 5 below compares the theoretical and simulated performance of a UWB
receiver. Notice that the theoretical expression holds well. Also, note that,
even when 50 fingers are used, performance is about 2 dB off the lower bound.
Figure 5: Rake receiver
performance for 25 fingers (left) and 50 fingers (right). Even with 50 fingers,
performance degradation is close to 2 dB
We also look at a receiver where the matched filter template
is obtained by averaging N received pilot signals. This system can be thought of as a generalization of an autocorrelation,
or transmitted-reference (TR) receiver.
In a typical TR system, a pair of unmodulated and
modulated signals is transmitted, and the former is employed to demodulate the
This receiver can capture the entire signal energy for a
slowly varying channel without requiring channel estimation. However, it suffers from the use of noisy received signals
as a template for demodulation (the noise on noise term). Another potentially
attractive feature of UWB autocorrelation receivers is their relative robustness to
TR systems were first proposed in
the 1920s ().
However, fundamental system weaknesses, such as bandwidth inefficiency and high
noise vulnerability, coupled with the advent of stored reference
and matched filter implementations in the 1950s and 1960s largely diminished
research interest in TR schemes . Nonetheless, research in UWB
autocorrelation receivers has been relatively active in the last two years:
A delay-hopped, TR Communications system was recently
built by the research and development center in GE. Experiments show the
viability of such a system in an indoor multipath environment ( and ).
An analytical characterization of the performance of an UWB
autocorrelation TR system can be found in .
Experimental results comparing the TR
receiver with Rake receiver structures can be found in .
It is shown that the TR receiver performs slightly better
than a single finger Rake receiver with maximum ratio combining (MRC). The
effect of the noise on noise term is also illustrated.
Giannakis et al. introduce a general
pilot waveform assisted modulation (PWAM) scheme, which subsumes TR as a special
case. The values of the systemís parameters are derived to
minimize the channelís MSE and maximize the average capacity. The circumstances under which the UWB autocorrelation-TR
system is optimal are also analyzed. In , the performance of a TR
system is derived with and without averaging many pilot signals. A differential
TR system is also proposed. However, it is difficult to average many signals
when differential modulation is used. In , an improved TR template is
introduced, where both pilot and data symbols are used to reconstruct the
template. This method is especially attractive when the number of pilots is restricted.
Figure 6: Pilot-based Receiver
expression for an N pilot-based receiver (Figure 6) was developed in MPRG, both
for biphase and PPM modulation (please follow link to presentation below).
Figure 7 displays the performance of a pilot-based receiver. Note that the BER
curve gets arbitrary closer to the lower bound as the number of pilots and the
integration time increase.
Figure 8 shows that, given enough system resources, the pilot based receiver
outperforms the Rake receiver. However, such a receiver would be extremely
complex and power-hungry.
Figure 7: Pilot-Assisted receiver Performance. Performance improves for
higher integration time and training elements.
Figure 8: Pilot-Assisted receiver vs. Rake Receiver. As
the number of available pilots increases, pilot-assisted receiver outperforms
Rake, even for large number of fingers.
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