Design of Multistage Decimation Filters Using Cyclotomic Polynomials: Optimization and Design Issues

This paper focuses on the design of multiplier-less decimation filters suitable for oversampled digital signals. The aim is twofold. On one hand, it proposes an optimization framework for the design of constituent decimation filters in a general multistage decimation architecture. The basic building blocks embedded in the proposed filters belong, for a simple reason, to the class of cyclotomic polynomials (CPs): the first 104 CPs have a z-transfer function whose coefficients are simply {-1,0,+1}. On the other hand, the paper provides a bunch of useful techniques, most of which stemming from some key properties of CPs, for designing the proposed filters in a variety of architectures. Both recursive and non-recursive architectures are discussed by focusing on a specific decimation filter obtained as a result of the optimization algorithm. Design guidelines are provided with the aim to simplify the design of the constituent decimation filters in the multistage chain.Comment: Submitted to CAS-I, July 07; 11 pages, 5 figures, 3 table

On the Polyphase Decomposition for Design of Generalized Comb Decimation Filters

Generalized comb filters (GCFs) are efficient anti-aliasing decimation filters with improved selectivity and quantization noise (QN) rejection performance around the so called folding bands with respect to classical comb filters. In this paper, we address the design of GCF filters by proposing an efficient partial polyphase architecture with the aim to reduce the data rate as much as possible after the Sigma-Delta A/D conversion. We propose a mathematical framework in order to completely characterize the dependence of the frequency response of GCFs on the quantization of the multipliers embedded in the proposed filter architecture. This analysis paves the way to the design of multiplier-less decimation architectures. We also derive the impulse response of a sample 3rd order GCF filter used as a reference scheme throughout the paper.Comment: Submitted to IEEE TCAS-I, February 2007; 11 double-column pages, 9 figures, 1 tabl

Connection Between System Parameters and Localization Probability in Network of Randomly Distributed Nodes

This article deals with localization probability in a network of randomly distributed communication nodes contained in a bounded domain. A fraction of the nodes denoted as L-nodes are assumed to have localization information while the rest of the nodes denoted as NL nodes do not. The basic model assumes each node has a certain radio coverage within which it can make relative distance measurements. We model both the case radio coverage is fixed and the case radio coverage is determined by signal strength measurements in a Log-Normal Shadowing environment. We apply the probabilistic method to determine the probability of NL-node localization as a function of the coverage area to domain area ratio and the density of L-nodes. We establish analytical expressions for this probability and the transition thresholds with respect to key parameters whereby marked change in the probability behavior is observed. The theoretical results presented in the article are supported by simulations.Comment: To appear on IEEE Transactions on Wireless Communications, November 200

A Model of the IEEE 802.11 DCF in Presence of Non Ideal Transmission Channel and Capture Effects

In this paper, we provide a throughput analysis of the IEEE 802.11 protocol at the data link layer in non-saturated traffic conditions taking into account the impact of both transmission channel and capture effects in Rayleigh fading environment. Impacts of both non-ideal channel and capture become important in terms of the actual observed throughput in typical network conditions whereby traffic is mainly unsaturated, specially in an environment of high interference. We extend the multi-dimensional Markovian state transition model characterizing the behavior at the MAC layer by including transmission states that account for packet transmission failures due to errors caused by propagation through the channel, along with a state characterizing the system when there are no packets to be transmitted in the buffer of a station.Comment: Accepted for oral presentation to IEEE Globecom 2007, Washington D.C., November 200

On The Linear Behaviour of the Throughput of IEEE 802.11 DCF in Non-Saturated Conditions

We propose a linear model of the throughput of the IEEE 802.11 Distributed Coordination Function (DCF) protocol at the data link layer in non-saturated traffic conditions. We show that the throughput is a linear function of the packet arrival rate (PAR) $\lambda$ with a slope depending on both the number of contending stations and the average payload length. We also derive the interval of validity of the proposed model by showing the presence of a critical $\lambda$, above which the station begins operating in saturated traffic conditions. The analysis is based on the multi-dimensional Markovian state transition model proposed by Liaw \textit{et al.} with the aim of describing the behaviour of the MAC layer in unsaturated traffic conditions. Simulation results closely match the theoretical derivations, confirming the effectiveness of the proposed linear model.Comment: To appear on IEEE Communications Letters, November 200

On the Behavior of the Distributed Coordination Function of IEEE 802.11 with Multirate Capability under General Transmission Conditions

The aim of this paper is threefold. First, it presents a multi-dimensional Markovian state transition model characterizing the behavior of the IEEE 802.11 protocol at the Medium Access Control layer which accounts for packet transmission failures due to channel errors modeling both saturated and non-saturated traffic conditions. Second, it provides a throughput analysis of the IEEE 802.11 protocol at the data link layer in both saturated and non-saturated traffic conditions taking into account the impact of both the physical propagation channel and multirate transmission in Rayleigh fading environment. The general traffic model assumed is M/M/1/K. Finally, it shows that the behavior of the throughput in non-saturated traffic conditions is a linear combination of two system parameters; the payload size and the packet rates, $\lambda^{(s)}$, of each contending station. The validity interval of the proposed model is also derived. Simulation results closely match the theoretical derivations, confirming the effectiveness of the proposed models.Comment: Submitted to IEEE Transactions on Wireless Communications, October 21, 200

Saturation Throughput Analysis of IEEE 802.11 in Presence of Non Ideal Transmission Channel and Capture Effects

In this paper, we provide a saturation throughput analysis of the IEEE 802.11 protocol at the data link layer by including the impact of both transmission channel and capture effects in Rayleigh fading environment. Impacts of both non-ideal channel and capture effects, specially in an environment of high interference, become important in terms of the actual observed throughput. As far as the 4-way handshaking mechanism is concerned, we extend the multi-dimensional Markovian state transition model characterizing the behavior at the MAC layer by including transmission states that account for packet transmission failures due to errors caused by propagation through the channel. This way, any channel model characterizing the physical transmission medium can be accommodated, including AWGN and fading channels. We also extend the Markov model in order to consider the behavior of the contention window when employing the basic 2-way handshaking mechanism. Under the usual assumptions regarding the traffic generated per node and independence of packet collisions, we solve for the stationary probabilities of the Markov chain and develop expressions for the saturation throughput as a function of the number of terminals, packet sizes, raw channel error rates, capture probability, and other key system parameters. The theoretical derivations are then compared to simulation results confirming the effectiveness of the proposed models.Comment: To appear on IEEE Transactions on Communications, 200

Unsaturated Throughput Analysis of IEEE 802.11 in Presence of Non Ideal Transmission Channel and Capture Effects

In this paper, we provide a throughput analysis of the IEEE 802.11 protocol at the data link layer in non-saturated traffic conditions taking into account the impact of both transmission channel and capture effects in Rayleigh fading environment. The impact of both non-ideal channel and capture become important in terms of the actual observed throughput in typical network conditions whereby traffic is mainly unsaturated, especially in an environment of high interference. We extend the multi-dimensional Markovian state transition model characterizing the behavior at the MAC layer by including transmission states that account for packet transmission failures due to errors caused by propagation through the channel, along with a state characterizing the system when there are no packets to be transmitted in the buffer of a station. Finally, we derive a linear model of the throughput along with its interval of validity. Simulation results closely match the theoretical derivations confirming the effectiveness of the proposed model.Comment: To appear on IEEE Transactions on Wireless Communications, 200