Shuangchi He

Many-server diffusion limits for G/Ph/n+GI queues

This paper studies many-server limits for multi-server queues that have a phasetype service time distribution and allow for customer abandonment. The rst set of limit theorems is for critically loaded G=Ph=n + GI queues, where the patience times are independent, identically distributed following a general distribution. The next limit theorem is for overloaded G=Ph=n + M queues, where the patience time distribution is restricted to be exponential. We prove that a pair of diusion-scaled total-customer-count and server-allocation processes, properly centered, converges in distribution to a continuous Markov process as the number of servers n goes to innity. In the overloaded case, the limit is a multi-dimensional diusion process, and in the critically loaded case, the limit is a simple transformation of a diusion process. When

On Superimposed Training for MIMO Channel Estimation and Symbol Detection

Channel estimation for multiple-input multiple-output (MIMO) time-invariant channels using superimposed training is considered. A user-specific periodic (nonrandom) training sequence is arithmetically added (superimposed) at a low power to each users information sequence at the transmitter before modulation and transmission. Two versions of a two-step approach are adopted where in the first step we estimate the channel using only the first-order statistics of the data. Using the estimated channel from the first step, a linear minimum mean-square error (MMSE) equalizer and hard decisions, or a Viterbi detector, are used to estimate the information sequence. In the second step of the two-step approach a deterministic maximum-likelihood (DML) approach based on a Viterbi detector or a linear MMSE equalizer-based approach is used to iteratively estimate the MIMO channel and the information sequences sequentially. We also present a performance analysis of the first-order statistics-based approach to obtain a closed-form expression for the channel estimation variance. We then address the issue of superimposed training power allocation for complex Gaussian random (Rayleigh) channels for MIMO systems arising from spatial multiplexing of a single-user signal. Illustrative simulation examples are provided

Customer Abandonment in Many-Server Queues

We study G/G/n + GI queues in which customer patience times are independent, identically distributed following a general distribution. When a customers waiting time in queue exceeds his patience time, the customer abandons the system without service. For the performance of such a system, we focus on the abandonment process and the queue length process. We prove that under some conditions, a deterministic relationship between the two stochastic processes holds asymptotically under the diffusion scaling when the number of servers n goes to infinity. These conditions include a minor assumption on the arrival processes that can be time-nonhomogeneous and a key assumption that the sequence of diffusion-scaled queue length processes, indexed by n, is stochastically bounded. We also establish a comparison result that allows one to verify the stochastic boundedness by studying a corresponding sequence of systems without customer abandonment.

Doubly Selective Channel Estimation Using Exponential Basis Models and Subblock Tracking

Three versions of a novel adaptive channel estimation approach, exploiting the over-sampled complex exponential basis expansion model (CE-BEM), is presented for doubly selective channels, where we track the BEM coefficients rather than the channel tap gains. Since the time-varying nature of the channel is well captured in the CE-BEM by the known exponential basis functions, the time variations of the (unknown) BEM coefficients are likely much slower than those of the channel, and thus more convenient to track. We propose a ?subblockwise? tracking scheme for the BEM coefficients using time-multiplexed (TM) periodically transmitted training symbols. Three adaptive algorithms, including a Kalman filtering scheme based on an assumed autoregressive (AR) model of the BEM coefficients, and two recursive least-squares (RLS) schemes not requiring any model for the BEM coefficients, are investigated for BEM coefficient tracking. Simulation examples illustrate the superior performance of our approach over several existing doubly selective channel estimators.

On Doubly Selective Channel Estimation Using Superimposed Training and Discrete Prolate Spheroidal Sequences

Channel estimation and data detection for frequency-selective time-varying channels are considered using superimposed training. We employ a discrete prolate spheroidal basis expansion model (DPS-BEM) to describe the time-varying channel. A periodic (nonrandom) training sequence is arithmetically added (superimposed) at low power to the information sequence at the transmitter before modulation and transmission; therefore, there is no loss in data transmission rate compared to time-multiplexed (TM) training. We first estimate the channel using DPS-BEM and only the first-order statistics of the observations. In this estimator the unknown information sequence acts as interference resulting in a poor signal-to-noise-and-interference ratio (SNIR) for channel estimation. We then apply a data-dependent superimposed training sequence, to either totally or partially cancel out the effects of the unknown information sequence at the receiver on channel estimation. In total cancellation, at certain frequencies, the information-bearing components are nulled. To compensate for this information loss, we investigate a partially-data-dependent (PDD) superimposed training scheme where a tradeoff is made between interference cancellation and frequency integrity. Design of certain parameters for PDD superimposed training is also investigated. Finally, a deterministic maximum likelihood (DML) approach is used iteratively to enhance channel estimation and data detection. Computer simulation examples show that the proposed approaches are competitive with the conventional TM training without incurring data-rate loss.

Iterative Joint Channel Estimation and Data Detection Using Superimposed Training: Algorithms and Performance Analysis

Channel estimation for single-input multiple-output time-invariant channels is considered using superimposed training. A periodic (nonrandom) training sequence is arithmetically added (superimposed) at low power to the information sequence at the transmitter before modulation and transmission. We extend a recently proposed first-order statistics-based channel estimation approach (IEEE Commun. Lett., vol. 7, p. 413, 2003) to iterative joint channel estimation and data detection using a conditional maximum likelihood approach where the information sequence is exploited to enhance performance instead of being viewed as interference. An approximate performance analysis of the iterative channel estimation method is also presented under certain simplifying assumptions. Illustrative computer simulation examples are presented.

Doubly-Selective Channel Estimation Using Exponential Basis Models and Subblock Tracking

Three versions of a novel adaptive channel estimation approach, exploiting the over-sampled complex exponential basis expansion model (CE-BEM), is presented for doubly selective channels, where we track the BEM coefficients rather than the channel tap gains. Since the time-varying nature of the channel is well captured in the CE-BEM by the known exponential basis functions, the time variations of the (unknown) BEM coefficients are likely much slower than those of the channel, and thus more convenient to track. We propose a ¿subblockwise¿ tracking scheme for the BEM coefficients using time-multiplexed (TM) periodically transmitted training symbols. Three adaptive algorithms, including a Kalman filtering scheme based on an assumed autoregressive (AR) model of the BEM coefficients, and two recursive least-squares (RLS) schemes not requiring any model for the BEM coefficients, are investigated for BEM coefficient tracking. Simulation examples illustrate the superior performance of our approach over several existing doubly selective channel estimators.

Doubly-Selective Channel Estimation Using Data-Dependent Superimposed Training and Exponential Basis Models

Channel estimation for single-user frequency- selective time-varying channels is considered using superimposed training. The time-varying channel is assumed to be well- approximated by a complex exponential basis expansion model (CE-BEM). A periodic (non-random) training sequence is arithmetically added (superimposed) at low power to the information sequence at the transmitter before modulation and transmission. In existing first-order statistics-based channel estimators, the information sequence acts as interference resulting in a poor signal-to-noise ratio (SNR). In this paper a data-dependent superimposed training sequence is used to cancel out the effects of the unknown information sequence at the receiver on channel estimation. A performance analysis is presented. We also consider the issue of superimposed training power allocation. Several illustrative computer simulation examples are presented.

Many-server Queues with Customer Abandonment: Numerical Analysis of their Diffusion Model

We use a multidimensional diffusion process to approximate the dynamics of a queue served by many parallel servers. Waiting customers in this queue may abandon the system without service. To analyze the diffusion model, we develop a numerical algorithm for computing its stationary distribution. A crucial part of the algorithm is choosing an appropriate reference density. Using a conjecture on the tail behavior of the limit queue length process, we propose a systematic approach to constructing a reference density. With the proposed reference density, the algorithm is shown to converge quickly in numerical experiments. These experiments demonstrate that the diffusion model is a satisfactory approximation for many-server queues, sometimes for queues with as few as twenty servers.

Multiuser/MIMO Doubly Selective Fading Channel Estimation Using Superimposed Training and Slepian Sequences

We consider doubly selective multiuser/multiple-input-multiple-output (MIMO) channel estimation and data detection using superimposed training. The time- and frequency-selective fading channel is assumed to be well described by a discrete prolate spheroidal basis expansion model (DPS-BEM) using Slepian sequences as basis functions. A user-specific periodic (nonrandom) training sequence is arithmetically added (superimposed) at low power to each users information sequence at the transmitter before modulation and transmission. A two-step approach is adopted, where, in the first step, we estimate the channel using only the first-order statistics of the observations. In this step, however, the unknown information sequence acts as interference, resulting in a poor signal-to-noise ratio (SNR). We then iteratively reduce the interference in the second step by employing an iterative channel-estimation and data-detection approach, where, by utilizing the detected symbols from the previous iteration, we sequentially improve the multiuser/MIMO channel estimation and symbol detection. Simulation examples demonstrate that, without incurring any transmission data rate loss, the proposed approach is superior to the conventional time-multiplexed (TM) training for uncoordinated users, where the multiuser interference in channel estimation cannot be eliminated and is competitive with the TM training for coordinated users, where the TM training design allows for multiuser-interference-free channel estimation.