On the channel energy capture in ultra-wide-band transmitted reference systems

Abstract

Dense multipath fading associated with ultra-wide- band (UWB) channel presents technical challenges for reliable communication. To adapt to this radio environment efficiently, we use low complexity transmitted reference spread spectrum system and analyze the average value of the channel energy capture as a function of the integration interval of the correlator. In our analysis, we use a measurement based UWB channel model. We find that an integration interval that captures approximately 90% of the average value of the channel energy provides a bit error probability (BEP) close to the minimum one. I. INTRODUCTION The ultra-wide-band (UWB) technology has recently drawn significant interest due to its attractive features of low power, low complexity and amazing high data transmission rate. UWB transmission can resolve many paths yielding multipath diversity. Exploitation of this multipath diversity through a Rake receiver requires UWB channel estimation which is a challenging task. An alternative approach to exploit the multipath diversity without estimating channel coefficients explicitly is the transmitted reference (TR) spread spectrum system (1). The original TR system couples the transmission of each information-carrying pulse with a pilot pulse. The received pilot pulse (which is referred to as the reference signal or correlator template) is correlated with the received signal of the information-carrying pulse for demodulating the information symbol. The overhead due to the pilot-pulse transmission in the original TR system was 50%. To overcome this shortcoming, recently, reference (2) introduces a general pilot waveform assisted modulation for TR systems in which transmitter pa- rameters are selected by jointly optimizing channel estimation performance and the information rate. References (3), (4) provide an analytical framework for the TR system based on a sampling expansion approach and use moment generating functions to derive closed-form expressions for the symbol error probability. An important issue in a TR system is that its performance is very sensitive to the length of the integration interval of the correlator. Use of a too short integration interval captures only a small fraction of the desired signal energy, whereas, that of a too long integration interval accumulates unnecessary noise energy at the receiver. Thus, the integration interval in a TR system must be carefully selected and the above phenomena was previously observed in (5) and a reference therein. Analysis of (5) is based on the assumption that the correlator template estimate remains a Gaussian vector. In this paper, we analyze the average value of the channel energy capture as a function of the integration interval of the correlator. We use a measurement based UWB channel model (6), in which path arrives in a cluster and inter- arrival times of clusters as well as those of paths within a cluster are independent and exponentially distributed random variables. The amplitude of the channel coefficient on each path is a log-normally rather than Rayleigh distributed random variable as suggested by (7), (8). Unlike the received signal energy capture, the channel energy capture does not depend on the transmitter signalling scheme. In addition, the latter is a simpler performance measure than the former in terms of analytical and computational complexities. At the same time, we find that the analysis of the channel energy capture as a function of the integration interval provides a fine insight into the effects of the integration interval on the bit error probability (BEP). Deriving the closed form expression of the BEP and analyzing it as a function of the integration interval for the above channel model are challenging and require further investigation. Our analysis shows that conditioned on the channel, the average value of the channel energy capture increases quickly for small values of the integration interval, however, the increase becomes gradual and negligible after some values of the integration interval. We show that an integration interval that captures approximately 90% of the average value of the channel energy provides a BEP, which is nearly optimum. Use of an integration interval close to the optimum one reduces not only the BEP but also the complexity of the integrate-and- dump operation at the correlator compared to the use of the integration interval equal to the multipath spread. It should be noted that a UWB system is expected to support high data rate transmission, thus the problem of inter-symbol interference will be inevitable. Unlike most of the existing research works on UWB transceiver design, we present results taking inter- symbol interference into consideration. This work is based on the single user case. However, one can extend our result to the multiuser case (where one transmitter