Analysis of an LMS linear equalizer for fading channels in decision directed mode

We consider a time varying wireless fading channel, equalized by an LMS linear equalizer in decision directed mode (DD-LMS-LE). We study how well this equalizer tracks the optimal Wiener equalizer. Initially we study a fixed channel.For a fixed channel, we obtain the existence of DD attractors near the Wiener filter at high SNRs using an ODE (Ordinary Differential Equation) approximating the DD-LMS-LE. We also show, via examples, that the DD attractors may not be close to the Wiener filters at low SNRs. Next we study a time varying fading channel modeled by an Auto-regressive (AR) process of order 2. The DD-LMS equalizer and the AR process are jointly approximated by the solution of a system of ODEs. We show via examples that the LMS equalizer ODE show tracks the ODE corresponding to the instantaneous Wiener filter when the SNR is high. This may not happen at low SNRs.

Tracking performance of an LMS-Linear Equalizer for fading channels

We consider a time varying wireless fading channel, equalized by an LMS linear equalizer. We study how well this equalizer tracks the optimal Wiener equalizer. We model the channel by an Auto-regressive (AR) process. Then the LMS equalizer and the AR process are jointly approximated by the solution of a system of ODEs (ordinary differential equations). Using these ODEs, the error between the LMS equalizer and the instantaneous Wiener filter is shown to decay exponentially/polynomially to zero unless the channel is marginally stable in which case the convergence may not hold.Using the same ODEs, we also show that the corresponding Mean Square Error (MSE) converges towards minimum MSE(MMSE) at the same rate for a stable channel. We further show that the difference between the MSE and the MMSE does not explode with time even when the channel is unstable. Finally we obtain an optimum step size for the linear equalizer in terms of the AR parameters, whenever the error decay is exponential.

Modulation Diversity in Fading Channels with a Quantized Receiver

In this paper, we address the design of codes which achieve modulation diversity in block fading single-input single-output (SISO) channels with signal quantization at the receiver. With an unquantized receiver, coding based on algebraic rotations is known to achieve maximum modulation coding diversity. On the other hand, with a quantized receiver, algebraic rotations may not guarantee gains in diversity. Through analysis, we propose specific rotations which result in the codewords having equidistant component-wise projections. We show that the proposed coding scheme achieves maximum modulation diversity with a low-complexity minimum distance decoder and perfect channel knowledge. Relaxing the perfect channel knowledge assumption we propose a novel channel training/estimation technique to estimate the channel. We show that our coding/training/estimation scheme and minimum distance decoding achieves an error probability performance similar to that achieved with perfect channel knowledge.

Performance analysis of UDP with energy efficient link layer on Markov fading channels

In this paper, we analyze the throughput and energy efficiency performance of user datagram protocol (UDP) using linear, binary exponential, and geometric backoff algorithms at the link layer (LL) on point-to-point wireless fading links. Using a first-order Markov chain representation of the packet success/failure process on fading channels, we derive analytical expressions for throughput and energy efficiency of UDP/LL with and without LL backoff. The analytical results are verified through simulations. We also evaluate the mean delay and delay variation of voice packets and energy efficiency performance over a wireless link that uses UDP for transport of voice packets and the proposed backoff algorithms at the LL. We show that the proposed LL backoff algorithms achieve energy efficiency improvement of the order of 2-3 dB compared to LL with no backoff, without compromising much on the throughput and delay performance at the UDP layer. Such energy savings through protocol means will improve the battery life in wireless mobile terminals.

Scheduling for Fading Channels Under Partial Channel Information

We consider a scheduler for the downlink of a wireless channel when only partial channel-state information is available at the scheduler. We characterize the network stability region and provide two throughput-optimal scheduling policies. We also derive a deterministic bound on the mean packet delay in the network. Finally, we provide a throughput-optimal policy for the network under QoS constraints when real-time and rate-guaranteed data traffic may be present.

Is the assumption of perfect channel-state information in fading channels a good assumption?

Fading channels, which are used as a model for wireless communication, are often analyzed by assuming that the receiver is aware of the realization of the channel. This is commonly justified by saying that the channel varies typically slowly with time, and the receiver is thus able to estimate it. However, this assumption is optimistic, since it is prima facie not clear whether the channel can be estimated perfectly. This paper investigates the quality of this assumption by means of the channel capacity. In particular, results on the channel capacity of fading channels are presented, both when the receiver is aware of the realization of the channel and when it is aware only of its statistics. A comparison of these results demonstrates that information- theoretic analyses of fading channels that are based on the assumption that the receiver is aware of the channel's realization can yield helpful insights, but have to be taken with a pinch of salt. ©2009 IEEE.

Opportunistic Control Over Shared Wireless Channels

© 2015 IEEE.We consider a wireless control architecture with multiple control loops over a shared wireless medium. A scheduler observes the random channel conditions that each control system experiences over the shared medium and opportunistically selects systems to transmit at a set of non-overlapping frequencies. The transmit power of each system also adapts to channel conditions and determines the probability of successfully receiving and closing the loop. We formulate the optimal design of channel-aware scheduling and power allocation that minimize the total power consumption while meeting control performance requirements for all systems. In particular, it is required that for each control system a given Lyapunov function decreases at a specified rate in expectation over the random channel conditions. We develop an offline algorithm to find the optimal communication design, as well as an online protocol which selects scheduling and power variables based on a random observed channel sequence and converges almost surely to the optimal operating point. Simulations illustrate the power savings of our approach compared to other non-channel-aware schemes.