It is well known that head-of-line (HOL) blocking

Absrract-At each instant of time we are required to sample a fixed number rn 2 1 out of N i.i.d. processes whose distributions belong to a family suitably parameterized by a real number 8. The objective is to maximize the long run total expected value of the samples. Following Lai and Robbins, the learning loss of a sampling scheme corresponding to a configuration of parameters C = (e,, . . a , e,\,) is quantified by the regret R n ( o . This is the difference between the maximum expected reward at time n that could be achieved if C were known and the expected reward actually obtained by the sampling scheme. We provide a lower bound for the regret associated with any uniformly good scheme, and construct a scheme which attains the lower bound for every configuration C. The lower bound is given explicitly in terms of the Kullback-Liebler number between pairs of distributions. Part I1 of this paper considers the same problem when the reward processes are Markovian. I. INTRODUCTTONI N this paper we study a version of the multiarmed bandit problem with multiple plays. We are given a one-parameter family of reward distributions with densities f ( x , 8 ) with respect to some measure v on R . 8 is a real valued parameter. There are N arms Xj, j = 1, -e , N with parameter configuration C = (el, --, When armj is played, it gives a reward with distribution f ( x , Oj)dv(x). Successive plays of armjproduce i.i.d. rewards. At each stage we are required to play a fixed number, m, of the arms, 1 I r n 5 N .Suppose we know the distributions of the individual rewards. To maximize the total expected reward up to any stage, one must play the arms with the rn highest means. However, if the parameters 8, are unknown, we are forced to play the poorer arms in order to learn about their means from the observations. The aim is to minimize, in some sense, the total expected loss incurred in the process of learning for eve9 possible parameter configuration.For single plays, i.e., m = 1, this problem was studied by Lai and Robbins [3]-[5]. The techniques used here closely parallel their approach. However, the final results are somewhat more general even in the single play case. For multiple plays, i.e., rn > 1, we report the first general results. In Part II of this paper we study the same problem when the reward statistics of the arms are Markovian with finite state space instead of i.i.d.

The sum capacity of a multiuser synchronous CDMA system is completely characterized in the general case of asymmetric user power constraints-this solves the open problem posed in [7] which had solved the equal power constraint case. We identify the signature sequences with real components that achieve sum capacity and indicate a simple recursive algorithm to construct them.

Abstract-There has been intense effort in the past decade to develop multiuser receiver structures which mitigate interference between users in spread-spectrum systems. While much of this research is performed at the physical layer, the appropriate power control and choice of signature sequences in conjunction with multiuser receivers and the resulting network user capacity is not well understood. In this paper we will focus on a single cell and consider both the uplink and downlink scenarios and assume a synchronous CDMA (S-CDMA) system. We characterize the user capacity of a single cell with the optimal linear receiver (MMSE receiver). The user capacity of the system is the maximum number of users per unit processing gain admissible in the system such that each user has its quality-of-service (QoS) requirement (expressed in terms of its desired signal-to-interference ratio) met. Our characterization allows us to describe the user capacity through a simple effective bandwidth characterization: Users are allowed in the system if and only if the sum of their effective bandwidths is less than the processing gain of the system. The effective bandwidth of each user is a simple monotonic function of its QoS requirement. We identify the optimal signature sequences and power control strategies so that the users meet their QoS requirement. The optimality is in the sense of minimizing the sum of allocated powers. It turns out that with this optimal allocation of signature sequences and powers, the linear MMSE receiver is just the corresponding matched filter for each user. We also characterize the effect of transmit power constraints on the user capacity.