2178 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 56, NO. 12, DECEMBER 2008 UWB Spectrally-Encoded Spread-Time CDMA in the Presence of Multiple Gaussian Interferences: RAKE Receiver and Three-Level Codes Saeed Mashhadi and Jawad A. Salehi, Senior Member, IEEE Abstract—In this paper we study and analyze the performance of the RAKE receiver for a typical Ultrawideband (UWB) Spectrally-Encoded Spread-Time (ST) CDMA in the presence of multiple Gaussian Interference (GI) signals. We demonstrate that by combining useful properties of three-level codes, i.e., codes with values of -1, 0, +1, and RAKE receiver, we can introduce a new strategy in which it can result in superior performance when compared to previous results. In particular, following a discussion on three-level codes we can show that RAKE receiver with optimum multiplicative weights achieves a better performance when compared with simple two-level codes. With the help of an example we show various properties of RAKE receiver as well as three-level codes and relate these properties to a number of simple descriptive parameters of the communication media. Simulation results obtained in this paper indicate the precision with which the analytical results have been obtained in modeling the above system. Index Terms—RAKE receiver, SNR, ST-CDMA, two- and three-level codes, UWB. I. I NTRODUCTION T HE application of spectrally-encoded spread-time (ST) technique in ultrawideband (UWB) communications could result in significant performance improvement and brings about many fundamental and enriching principles and features. The spectrally-encoded ST technique which was first introduced in the context of optical code division multiple- access (CDMA) for femto- and pico-second light pulses [1] (extremely wideband) can be easily extended and applied to UWB nanosecond pulse systems [2]–[6]. The ability in matching the transmitted spectrum with the channel spectrum is one of the attractive features highlighted for spectrally-encoded ST technique. The direct application of spectrally-encoded ST technique to the transmission channels with disjoint or non-continuous frequency band allocation had been highlighted in [5] and [6]. This feature may prove to be an extremely important features in UWB communication systems [10]–[11] especially when it encounters multiple interferences and disjoint spectrum allocation mask, which is typical in most UWB environments [2]–[3], [12]–[13]. So from the above descriptions, it is important to highlight that Paper approved by A. Zanella, the Editor for Wireless Systems of the IEEE Communications Society. Manuscript received July 7, 2006; revised March 17, 2007 and July 30, 2007. This paper is supported in part by the Iran National Science Foundation (INSF). The authors are with the Optical Networks Research Lab (ONRL), De- partment of Electrical Engineering, Sharif University of Technology, Tehran 11365, Iran (e-mail: mashhadi@ee.sharif.edu, jasalehi@sharif.edu). Digital Object Identifier 10.1109/TCOMM.2008.060285 the UWB migration from impulse radio to multiband schemes, due to its spectral efficiency, will remain transparent to UWB spectrally-encoded ST technique. Previously, we have reported on the advantages of applying ST to time-hopping UWB in order to combat the near-far problem while increasing the system rate and its corresponding performance [4]. In this paper we introduce and analyze an UWB spectrally- encoded ST in combating multiple Gaussian interferences while simultaneously offering multiple-access capability [7]. The superior feature in the above proposed technique is that the multiple Gaussian interference cancellation takes place by employing a RAKE detection scheme along with three-level codes, i.e., codes that can take on three values of -1, 0, +1 [8]. This scheme not only enhances the performance of the system but it also avoids having to design various, complex, bandpass filters for multiple Gaussian interferences removal at the receiver. In other words, we have shifted the design criterion from being a hardware oriented to an algorithmically oriented code design which can be easily implemented through software programming. We believe the technique introduced in this paper, namely UWB spectrally-encoded ST, will be- come an important candidate in many and various wireless communication systems. The rest of this paper is organized as follows. In Section II we describe our system model. In Section III, we introduce the structure of RAKE receiver in the context of UWB spectrally-encoded CDMA communication systems. Section IV discusses three-level codes and compares different channel access schemes. In Section V we introduce an important and a practical example through which we show performance differences between two- and three-level codes. Furthermore in this section we present a few figures and discuss both analytical and simulation based numerical results. In fact the simulation results indicate the accuracy with which we have modeled our proposed scheme and systems. Section VI concludes the paper. II. SYSTEM MODEL FOR TWO-LEVEL CODES In a typical ST-CDMA system each user employs a sig- nature sequence to encode and transmit its data bits. Let  ξ (n) l : l =1, 2, ··· ,L  denote the random signature se- quence of the nth user (n =1, 2,...,N ) with length L. For two-level codes the variable ξ (n) l ∈{+1, 1}, and for all values of l and n the variables are mutually independent. For the nth 0090-6778/08$25.00 c  2008 IEEE