262 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 55, NO. 2, FEBRUARY 2007 Analysis of the Channel Energy Capture in Ultra-Wideband Transmitted Reference Systems Yanxin Na, Member, IEEE, and Mohammad Saquib, Member, IEEE Abstract—In this letter, we analyze the expected value of the channel energy capture as a function of the integration interval of the correlator in a transmitted reference system. A modified Saleh–Valenzuela channel model is employed. We observe that for the system specifications (such as channel model, data rate, and signal-to-noise ratio) considered here, an integration interval that captures approximately 84%–89% of the expected value of the channel energy provides a bit-error probability close to the min- imum one. Index Terms—Channel energy capture, Saleh–Valenzuela channel model, transmitted reference (TM) systems, ultra-wide- band (UWB). I. INTRODUCTION U LTRA-WIDEBAND (UWB) technology has recently drawn significant interest due to its attractive features of low power, low complexity, and amazing high data transmis- sion rate [1], [2]. UWB transmission can resolve many paths, yielding multipath diversity [3]. Exploitation of this multi- path diversity through a Rake receiver requires UWB channel estimation, which is a challenging task. An alternative ap- proach to exploiting the multipath diversity without estimating channel coefficients explicitly is the transmitted reference (TR) spread-spectrum system [4]. 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 detecting the information symbol. The performance of a UWB system can be measured in terms of energy capture; please see [5], which quantifies the tradeoff between energy capture and diversity level in a Rake receiver using measured received waveforms. 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 [6] and a reference therein. The analysis in [6] is based on the assumption that the correlator template estimate remains a Gaussian vector. Paper approved by D. I. Kim, the Editor for Spread Spectrum Transmission and Access of the IEEE Communications Society. Manuscript received August 6, 2005; revised March 14, 2006 and June 22, 2006. This work was supported in part by Nokia under Grant 525532, and in part by the Erik Jonsson School of Engineering (UT-Dallas) under Grant 529921. The authors are with the Wireless Communications Research Laboratory (WiCoRe), The University of Texas at Dallas, Richardson, TX 75083-0688 USA ( e-mail: yanxin@utdallas.edu; saquib@utdallas.edu). Digital Object Identifier 10.1109/TCOMM.2006.888540 In this letter, we analyze the expected value of the channel en- ergy capture as a function of the integration interval of the corre- lator. We use a measurement-based modified Saleh–Valenzuela UWB channel model [7], [8], in which paths arrive in a cluster, and interarrival 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-normal rather than Rayleigh distributed random vari- able as suggested by [8] and [9]. We observe that analysis of the channel energy capture as a function of integration interval provides a fine insight into the effects of the integration interval on the bit-error probability (BEP). Our numerical study demon- strates that for the considered system specifications [such as channel model, data rate, and signal-to-noise ratio (SNR)], an integration interval that captures approximately 84%–89% of the expected value of the channel energy provides a nearly op- timum BEP. II. SYSTEM MODEL In the system model, we transmit binary phase-shift keying (BPSK) symbols using the normalized pulse . The spectral bandwidth of pulse is in the 3.1–10.6 GHz frequency band, which meets the Federal Communications Commission (FCC)’s requirement. The transmitted signal over a frame duration is (1) where is the pilot symbol transmitted using power , 1 is the th information symbol transmitted using power , is the number of information symbols, is the duration between two sequential information symbols and is the duration of the pilot signal. 2 We consider a multipath fading UWB channel [8], [9] (2) where denotes the cluster number, denotes the path number within cluster . The term is the arrival time of the first path of cluster and denotes the delay of path within cluster rel- ative to the first path arrival time . The arrival time of the first cluster . The interarrival times of clusters and those of paths within a cluster are modeled by independent exponential random variables. Since the sum of independent and identically 1 For simplicity and to keep the system overhead minimum, we deliberately use one pilot symbol. Our system model can be extended to any number of pilot symbols. 2 A typical value of is , which is the multipath spread of the channel. 0090-6778/$25.00 © 2007 IEEE