UWB Receiver Design

UWB 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 below).

    Figure 1: Transmit (left) and receive (right) pulse. Channel distortion is severe.

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 below).

Figure 2: 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.

Figure 3: Perfect Matched Filter Performance: all the energy is captured

Theoretical expressions for the simple and matched filter BER performance were derived at MPRG. Equations are included in the presentation (link at bottom of page).

Rake Receivers

UWB Research has mainly concentrated on the analysis of Rake receivers. However, Rake receivers applied to UWB systems suffer from two major drawbacks:

•  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 ([1],[2])

• Second, each 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 ([3]).

Figure 4: Typical MRC-based F finger Rake Receiver

An analysis of a Rake receiver using MRC combining and PPM modulation can be found in [4] and [5]. However, these two works make the assumption that the Rake receiver is able to completely resolve the L strongest channel paths. A study of the effect of imperfect channel estimation can be found in [6].

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 page).

Figure 5 below compares the theoretical and simulated performance of a UWB Rake 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

Pilot-based Receivers

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 latter.

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 synchronization problems. 

TR systems were first proposed in the 1920s ([4]). 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 [7]. 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 ([8] and [9]).

An analytical characterization of the performance of an UWB autocorrelation TR system can be found in [10].

Experimental results comparing the TR receiver with Rake receiver structures can be found in [4].

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.[11] introduce a general pilot waveform assisted modulation (PWAM) scheme, which subsumes TR as a special case. The values of the system’s parameters are derived to minimize the channel’s MSE and maximize the average capacity. The circumstances under which the UWB autocorrelation-TR system is optimal are also analyzed. In [12], 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 [13], 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

A theoretical 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.

References

[1] Win, M.Z.; Scholtz, R.A.; "Characterization of ultra-wide bandwidth wireless indoor channels: a communication-theoretic view," IEEE Journal on Selected Areas in Communications Volume: 20 , Issue: 9 , Dec. 2002 Pages:1613 - 1627

[2] Win, M.Z.; Scholtz, R.A.; "On the energy capture of ultrawide bandwidth signals in dense multipath environments,"
 IEEE Communications Letters. Volume: 2 , Issue: 9 , Sept. 1998 Pages:245 - 247

[3] Win, M.Z.; Scholtz, R.A.; "Energy capture vs. correlator resources in ultra-wide bandwidth indoor wireless communications channels," MILCOM 97 Proceedings. Volume: 3 , 2-5 Nov. 1997 Pages:1277 - 1281 vol.3

[4] Choi, J.D.; Stark, W.E.; "Performance of ultra-wideband communications with suboptimal receivers in multipath channels," IEEE Journal on Selected Areas in Communications. Volume: 20 , Issue: 9 , Dec. 2002 Pages:1754 - 1766

[5] Choi, J.D.; Stark, W.E.; "Performance analysis of Rake receivers for ultra-wideband communications with PPM and OOK in multipath channels," IEEE International Conference on Communications, 2002. ICC 2002.  Volume: 3 , 28 April-2 May 2002 Pages:1969 - 1973 vol.3

[6] Huaning Niu; Ritcey, J.A.; Hui Liu; "Performance of UWB Rake receivers with imperfect tap weights," Proceedings of the 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing. Volume: 4 , 6-10 April 2003 Pages:IV - 125-8 vol.4

[7] M.K Simon, J.K. Omura, R. A. Sholtz, B.K Levitt; "Spread Spectrum Communications, Volume I," Computer Science Press. 1985

[8] Hoctor, R.; Tomlinson, H.; "Delay-hopped transmitted-reference RF communications," 2002 IEEE Conference on Ultra Wideband Systems and Technologies, 2002. Digest of Papers. 21-23 May 2002 Pages:265 - 269

[9] van Stralen, N.; Dentinger, A.; Welles, K., II; Gaus, R., Jr.; Hoctor, R.; Tomlinson, H.;  "Delay hopped transmitted reference experimental results," 2002 IEEE Conference on Ultra Wideband Systems and Technologies, 2002. Digest of Papers. 21-23 May 2002 Pages:93 - 98

[10] Choi, J.D.; Stark, W.E.; "Performance of autocorrelation receivers for ultra-wideband communications with PPM in multipath channels," 2002 IEEE Conference on Ultra Wideband Systems and Technologies, Digest of Papers. 21-23 May 2002 Pages:213 - 217

[11] Liuqunig Yang; Giannakis, G.B.; "Optimal pilot waveform assisted modulation for ultra-wideband communications," Conference Record of the Thirty-Sixth Asilomar Conference on Signals, Systems and Computers, 2002. 3-6 Nov. 2002 Volume: 1 , Pages:733 - 737

[12] Yi-Ling Chao; Scholtz, R.A.; "Optimal and suboptimal receivers for ultra-wideband transmitted reference systems," IEEE Global Telecommunications Conference, 2003. GLOBECOM '03. Volume: 2 , 1-5 Dec.2003 Pages:759 - 763

[13] Franz, S.; Mitra, U.; "On Optimal Data Detection for UWB Transmitted Reference Systems," IEEE Global Telecommunications Conference, 2003. GLOBECOM '03. Volume: 2 , 1-5 Dec.2003 Pages:744 - 748