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We view a hybrid ARQ scheme as an incremental accumulation of redundancy at the receiver. A hybrid ARQ design problem is formulated as a search for the sequence of redundancies maximizing throughput or minimizing delay. The optimization is performed within the framework of a Markov decision process. The state space is defined as the total accumulated redundancy at the receiver. The transition probabilities model the error-correcting capability of the code and properties of the channel. Employing a dynamic programming approach, the optimum sequence of redundancies is characterized. I. SYSTEM MODELThe transmitter encodes a message into a codeword of infinite length and transmits a portion of the codeword to the receiver. The receiver attempts to decode the message. If decoding fails, the receiver requests an additional portion of the codeword. This process continues until the message is successfully decoded. Let Uk denote the redundancy per information bit contained in the kth transmission and s k denote the total redundancy up to and including the kth transmission. The ARQ scheme can be then described by the Markov chain shown in Figure 1. The state of the Markov chain is given by SI, denoting the event that redundancy s k was accumulated at the receiver after the kth transmission and decoding has failed. The transition probability is defined as the conditional probability that decoding fails with redundancy s k + l given that decoding failed with redundancy s k . That is, Pskfllsk = g(Sk,Uk+l), where the function g(.,.) is strictly decreasing in both variables and is strictly less than one. The function g(., .) is implicitly dependent on channel conditions and receiver performance. We assume here that g(., .) is time invariant and based on average link behavior. The absorbing terminal state T represents the event that the packet has been successfully decoded. We note that the expected number of transitions to reach the terminal state is finite based on the stated properties of g(., .). DYNAMIC PROGRAMMING APPROACHOur objective is to derive and characterize the delay-optimum ARQ strategy. The search for the optimum strategy, or equivalently the optimum sequence { u ; }~=~, is formulated as a dynamic programming optimization problem. In particular, each state SI, of the Markov chain is assigned an instantaneous cost Csk which models the delay incurred by an ARQ strategy in leaving that state. This cost is expressed as Csk = p U k + l + 6, 'This work was supported by Motorola Labs. The authors would like to thank Dr. R. Berry for his valuable comments. Figure 1: Continuous state-space, discrete-time Markov model for the ARQ scheme. where p is a proportionality constant and 6 denotes the waiting time for feedback from the receiver. The delay-optimum strategy is then the solution to E c p u k + 6 (1) 1 min { U k } p = o = , : " k E [ U m i n . Uma=l where umin > 0. A throughput-optimum strategy is obtained by solving (1) with 6 = 0. The optimum strategy can be determined from the solution to the infinite horizon Bellm...

Abstract-The problem of initial acquisition of the channel parameters of a wideband CDMA signal received in a multipath fading environment with multiaccess interference is considered. Since the signal is wideband, the fading is frequency selective and the parameters of interest are the (complex) gains and delays in the corresponding tapped delay line model for the channel. The scenario considered is one where a single new user is to be acquired on the reverse link by the base station, and where the channel parameters of the interfering users are known. Following a minimum mean squared error (MMSE) strategy for suppressing the multiaccess interference, the parameter estimation problem is posed in a maximum likelihood framework. To reduce complexity, the solution is implemented in two stages: first, the estimated tap delays are restricted to be at chip spacings; second, the number of taps is reduced by allowing for arbitrary spacing between them. The performance of the proposed techniques is studied through numerical simulations. It is shown that significant gains can be obtained by exploiting the structure of the interference and acquiring the channel parameters jointly.

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