1/5Abstract - We develop an adaptive, low complexity tree-searchreceiver using the T-algorithm for multipath fading ISI channels.Unlike previous research on sequence based detection, a symbolspaced channel is not given a priori, rather the receiver utilizesthe feedforward channel estimation to derive the matched filterand the symbol-spaced statistics. Then, to enhance the efficiencyof theT-algorithm, the use of a mean-square whitening filter (MS-WF) is proposed. We also propose the use of per-survivorprocessing which brings a further SNR advantage and reductionof the average computations required bythe T-algorithm receiver.A substantial SNR benefit over a correct decision feedback DFEis achieved at a moderate increase in complexity.I. INTRODUCTIONThe receiver technique developed in this paper is intended tofacilitate the implementation of a reliable, adaptive and highlybandwidth efficient communication link over time-varyingdispersive channels. The receiver must cope with the unknownchannel exhibiting Doppler spreading, frequency-selectivefading and shadowing. In addition, since the radio spectrum isdear, use of a large signal set modulation is highly desirable. Wetherefore consider system with a large signal set (up to 64 QAM),together with an explicit antenna diversity combining andadaptive equalization. For equalization, we investigate a lowcomplexity sequence search receiver using the T-algorithm foruncoded use, which achieves a performance very close to that ofmaximum likelihood sequence detection (MLSD).A great deal of research has been undertaken to reduce thecomputational complexity required to achieve the performanceof MLSD. Research in this arena includes reduced state sequenceestimation (RSSE), the M-algorithm and the relatively newer T-algorithm [4]. Originally introduced by Simmons [4], the T-algorithm has been shown to exhibit a superior error-rate versusaverage-computational-complexity behavior compared to theRSSE and the M-algorithm. Simmons has applied the T-algorithm to decode trellis coded QAM transmitted over staticISI channels [5]. Other research extends the T-algorithm to thetime-varying dispersive channel environment in [6][7].We develop the optimum diversity combining front-end (FE)filters which provide the symbol-spaced sufficient statistics forthe T-algorithm. They consist of a fractionally-spaced matchedfilter (MF) at each diversity branch and a symbol-spaced mean-squares whitening filter (MS-WF), both adapting to the time-varying channel (See Fig 1. and section II for details). Previousresearch [6,7] uses a symbol-spaced channel model even for anunknown time-varying channel. However, whenever the channelis unknown, the symbol-spaced channel model is imprecise--orpays significant amount of SNR penalty in practical use, since theMF or WMF cannot be identified. In this paper, the unknowntime-varying channel is estimated in a feedforward fashion andtracked using the channel estimation procedure from [1], and theMF and MS-WF are updated from the channel estimates.For the T-algorithm, we propose to include a per-survivorchannel tracking procedure. The per-survivor processing bringsthe additional benefit of lowering the average complexity of theT-algorithm: In a correct path, the channel estimate is enhanced;in a wrong path, the channel estimate quickly degrades,promoting the early elimination of the path from the survivor list.A simple overflow handling routine is suggested to reduce thesize of the maximum allowed survivors.We show for a static channel with a dB null in its foldedspectrum and Rayleigh fading ISI channels that the proposedreceiver achieves detection performance very close to that of theViterbi algorithm (VA), surpassing a correct decision feedbackequalizer’s performance, at a moderate increase in complexity--less than 10 survivors on average with 100 maximum allowedsurvivors for 4-QAM and less than 50 on average with 200maximum for 64-QAM.This paper is organized as follows: The over-sampled discrete-time system model is developed in section II. In section III., wedevelop the optimal diversity combining front-end filters. Insection IV., the reduced search T-algorithm is discussed. SectionV. discusses the simulation results and section VI provides ourconclusion.II. SYSTEM MODELFig.1 defines the baseband equivalent channel model for an L-diversity channel receiver. We denote the cascade of the transmitpulse shaping filter , the base-band equivalent time-varyingchannel and any anti-aliasing filter at the receiver(assumed to be an ideal brick wall filter) by . We assumeis an excess bandwidth pulse, and then the basebandreceived signal at -th diversity branch should be fractionallysampled. We denote the sampling interval as = , whereis the symbol period and . We assume the effective spanof extends over a symbol period, i.e., the delayspread is zero outside of an interval [0, ]. Thesampled noise is assumed to be additive white Gaussian with zero20–gt()clτ t;()hlτ t;()gt()lTsTBNs⁄TBNs2≥h τ •;() Nhh τ •;() NhTAdaptive Sequence Detection using T-algorithm for Multipath Fading ISI ChannelsHeung-No Lee and Gregory J. PottieElectrical Engineering Department, University of California at Los AngelesBox 951594 Los Angeles, CA 90095Email: [email protected]: (310) 825-8150, FAX: (310) 206-84952/5mean and variance . For the -th symbol interval we havediscrete-time samples of which can be described by,for and . We now define the columnvectors for the fractional samples in the -th epoch as:, and.Thus, a [( ) x 1] vector represents the non-zeroportion of the overall channel impulse response, sampled at therate of , i.e., .Then, for the time interval of interest, , thediscrete-time system equation is given by, (1)where ,,,, is the ( ) vector of zeros, andis the transmitted data symbols. The isused in place of the training segments for simplicity.In this paper, we assume continuous transmission of frames,where a frame consists of training and unknown data segments.Then the feedforward channel estimation scheme [1] providesthe estimates of the time-varying channel vectors in . Thefeedforward channel estimation is comprised of two modes--thesnap-shot channel vector estimation during the training segmentand the interpolation on a set of channel estimate vectors tocapture the channel variation between training. The least squareschannel estimator (LSE) [1] is used in this paper. For details onfeedforward channel estimation, readers are