Ergodic capacity of the exponentially correlated slotted amplify and forward relay channel

In this paper we analyze the performance degradation of slotted amplify-and-forward protocol in wireless environments with high node density where the number of relays grows asymptotically large. Channel gains between source-destination pairs in such networks can no longer be independent. We analyze the degradation of performance in such wireless environments where channel gains are exponentially correlated by looking at the capacity per channel use. Theoretical results for eigenvalue distribution and the capacity are derived and compared with the simulation results. Both analytical and simulated results show that the capacity given by the asymptotic mutual information decreases with the network density.

Ergodic capacity of the slotted amplify and forward relay channel with finite relays

Abstract—In this paper we investigate the capacity of a general class of the slotted amplify and forward (SAF) relaying protocol where multiple, though a finite number of relays may transmit in a given cooperative slot and the relay terminals being half-duplex have a finite slot memory capacity. We derive an expression for the capacity per channel use of this generalized SAF channel assuming all source to relay, relay to destination and source to destination channel gains are independent and modeled as complex Gaussian. We show through the analysis of eigenvalue distributions that the increase in limiting capacity per channel use is marginal with the increase of relay terminals.

Ergodic capacity and outage performance of amplify-and-forward protocols

This thesis analyses the performance bounds of amplify-and-forward relay channels which are becoming increasingly popular in wireless communication applications. The statistics of cascaded Nakagami-m fading model which is a major obstacle in evaluating the outage of wireless networks is analysed using Mellin transform. Furthermore, the upper and the lower bounds for the ergodic capacity of the slotted amplify-and-forward relay channel, for finite and infinite number of relays are derived using random matrix theory. The results obtained will enable wireless network designers to optimize the network resources, benefiting the consumers.

An effective approach to verbose queries using a limited dependencies language model

Intuitively, any `bag of words' approach in IR should benefit from taking term dependencies into account. Unfortunately, for years the results of exploiting such dependencies have been mixed or inconclusive. To improve the situation, this paper shows how the natural language properties of the target documents can be used to transform and enrich the term dependencies to more useful statistics. This is done in three steps. The term co-occurrence statistics of queries and documents are each represented by a Markov chain. The paper proves that such a chain is ergodic, and therefore its asymptotic behavior is unique, stationary, and independent of the initial state. Next, the stationary distribution is taken to model queries and documents, rather than their initial distri- butions. Finally, ranking is achieved following the customary language modeling paradigm. The main contribution of this paper is to argue why the asymptotic behavior of the document model is a better representation then just the document's initial distribution. A secondary contribution is to investigate the practical application of this representation in case the queries become increasingly verbose. In the experiments (based on Lemur's search engine substrate) the default query model was replaced by the stable distribution of the query. Just modeling the query this way already resulted in significant improvements over a standard language model baseline. The results were on a par or better than more sophisticated algorithms that use fine-tuned parameters or extensive training. Moreover, the more verbose the query, the more effective the approach seems to become.

An effective approach to verbose queries using a limited dependencies language model

Intuitively, any ‘bag of words’ approach in IR should benefit from taking term dependencies into account. Unfortunately, for years the results of exploiting such dependencies have been mixed or inconclusive. To improve the situation, this paper shows how the natural language properties of the target documents can be used to transform and enrich the term dependencies to more useful statistics. This is done in three steps. The term co-occurrence statistics of queries and documents are each represented by a Markov chain. The paper proves that such a chain is ergodic, and therefore its asymptotic behavior is unique, stationary, and independent of the initial state. Next, the stationary distribution is taken to model queries and documents, rather than their initial distributions. Finally, ranking is achieved following the customary language modeling paradigm. The main contribution of this paper is to argue why the asymptotic behavior of the document model is a better representation then just the document’s initial distribution. A secondary contribution is to investigate the practical application of this representation in case the queries become increasingly verbose. In the experiments (based on Lemur’s search engine substrate) the default query model was replaced by the stable distribution of the query. Just modeling the query this way already resulted in significant improvements over a standard language model baseline. The results were on a par or better than more sophisticated algorithms that use fine-tuned parameters or extensive training. Moreover, the more verbose the query, the more effective the approach seems to become.

Time-varying bispectral analysis of visually evoked multi-channel EEG

Theoretical foundations of higher order spectral analysis are revisited to examine the use of time-varying bicoherence on non-stationary signals using a classical short-time Fourier approach. A methodology is developed to apply this to evoked EEG responses where a stimulus-locked time reference is available. Short-time windowed ensembles of the response at the same offset from the reference are considered as ergodic cyclostationary processes within a non-stationary random process. Bicoherence can be estimated reliably with known levels at which it is significantly different from zero and can be tracked as a function of offset from the stimulus. When this methodology is applied to multi-channel EEG, it is possible to obtain information about phase synchronization at different regions of the brain as the neural response develops. The methodology is applied to analyze evoked EEG response to flash visual stimulii to the left and right eye separately. The EEG electrode array is segmented based on bicoherence evolution with time using the mean absolute difference as a measure of dissimilarity. Segment maps confirm the importance of the occipital region in visual processing and demonstrate a link between the frontal and occipital regions during the response. Maps are constructed using bicoherence at bifrequencies that include the alpha band frequency of 8Hz as well as 4 and 20Hz. Differences are observed between responses from the left eye and the right eye, and also between subjects. The methodology shows potential as a neurological functional imaging technique that can be further developed for diagnosis and monitoring using scalp EEG which is less invasive and less expensive than magnetic resonance imaging.