Some challenging problems in wireless communications

In this dissertation, we study three challenging topics in wireless communications: (1) QoS provisioning for single-user wireless systems, (2) reliability-delay tradeoff in wireless ad hoc networks, (3) frequency synchronization for OFDM systems.;We study the performance of a single-user wireless communication system over fading channels. We instigate the maximum transmission data rate over fading channels with both delay and error probability constraints. The system under study consists of (1) a finite-buffer discrete-time queueing system on the link layer, and (2) a rate-adaptive channel coding system on the physical layer. The objective of our work is to analyze the relationship among data rate (R), packet error probability (E), and delay bound (D), under the interaction between the link layer and the physical layer. In our analysis, we consider three types of packet errors, i.e., (1) packet drop due to full buffer, (2) packet error due to delay bound violation, and (3) packet decoding error due to channel noise. We obtain an upper bound on the packet error probability. Furthermore, by minimizing the packet error probability over the transmission rate control policies, we obtain an optimal rate control policy that guarantees the user-specified data rate and delay bound. In the case of constant arrival, the optimal rate control policy results in an RED triplet; then by varying data rate and delay bound, we obtain RED Pareto-optimal surface. Our results provide important insights into optimal rate control policy for joint link layer and physical layer design; the RED Pareto surface represents a major step toward deriving the probabilistic delay-constrained channel capacity of fading channels, which is an unsolved problem in information theory.;Though the relationship between capacity and average delay in wireless ad hoc networks has been intensively studied in the literature, statistical delay guarantee provisioning in large scale ad hoc networks has not received enough attention. A realtime application, e.g., interactive game and realtime video, requires stringent delay (delay bound) but may allow a small probability of outage (deadline violation probability). This motivates us to study the relationship between delay bound and deadline violation probability. In this work, we try to answer the following interesting questions: as the network size scales up, (1) given a delay bound B(n), how does the deadline violation probability scale? (2) does the deadline violation probability go to zeros? (3) if the deadline violation probability goes to zeros, how fast is it? For mobile ad hoc networks, based on a simple i.i.d. mobility model, we shown that tradeoff between deadline violation probability and delay bound is given by is given by Pl ( n) = e--theta( B(n )/n). This tradeoff explicitly indicates the increase of delay one must tolerate for achieving specified decay rate of deadline violation probability. Since the deadline violation probability can be interpreted as a description of the reliability of delay-sensitive communications, our results provide insights into understanding the reliability-delay tradeoff in large scale wireless ad hoc networks.;We switch to PHY layer design in the last part of this dissertation. A recursive maximum likelihood (ML) carrier frequency offset (CFO) estimator is proposed in this work, where redundancy information contained in the cyclic prefix (CP) of multiple consecutive OFDM symbols is exploited in an efficient recursive fashion. Since the estimator is based on multiple OFDM symbols, the time-varying CFO must be considered. We investigate the effect of time-varying CFO on the performance of the estimator and the tradeoff between fast tracking ability and low estimation variance. We show that, without channel noise, the mean squared estimation error (MSE) due to CFO variation increases approximately quadratically with n, where n is the number of OFDM symbols used for CFO estimation (estimation window size), while the MSE due to channel noise decreases proportionally to 1/n (approximately) if the CFO is constant. A closed-form expression of the optimal estimation window size (approximately) is derived by minimizing the MSE caused by both the time-varying CFO and channel noise. For wireless systems with time-varying rate of change for CFO, the proposed estimator can be implemented adaptively. In addition, typical optimal estimation window sizes for WiMAX, DVB-SH and MediaFLO systems are evaluated as an example.