Decomposition tables for experiments. II. Two--one randomizations

We investigate structure for pairs of randomizations that do not follow each other in a chain. These are unrandomized-inclusive, independent, coincident or double randomizations. This involves taking several structures that satisfy particular relations and combining them to form the appropriate orthogonal decomposition of the data space for the experiment. We show how to establish the decomposition table giving the sources of variation, their relationships and their degrees of freedom, so that competing designs can be evaluated. This leads to recommendations for when the different types of multiple randomization should be used.Comment: Published in at http://dx.doi.org/10.1214/09-AOS785 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A generalization of sum composition: Self orthogonal Latin square design with sub self orthogonal Latin square designs

AbstractA generalization of the theory of sum composition of Latin square designs is given. Via this generalized theory it is shown that a self orthogonal Latin square design of order (3pα − 1)2 with a subself orthogonal Latin square design of order (pα − 1)2 can be constructed for any prime p > 2 and any positive integer α as long as p ≠ 3, 5, 7 and 13 if α = 1. Additional results concerning sets of orthogonal Latin square designs are also provided

CROSSLAYER OPTIMIZATION IN AN LTE NETWORK TO REDUCE THE EFFECT OF CO-CHANNEL INTERFERENCE

In this thesis, synergy between the physical layer and the Medium Access Control (MAC) layer of a Long Term Evolution (LTE) network is exploited to reduce the co-channel interference in both the forward and reverse channels. By doing such cross-layer optimization analysis, physical and MAC layer control decisions reach their full potential when they are designed in an integrated manner. The proposed solution focuses on the integration of the concepts of orthogonal frequency-division multiple access (OFDMA), sectorization, and Latin Square to improve the signal-to-interference ratio (SIR) with the most effective resource utilization. Sectorization in the physical layer alone is able to improve the SIR, however, by also implementing OFDMA and Latin Square techniques to reduce the effect of co-channel interference, better SIR can be achieved. There is some impact on resource utilization, however. The solution seeks to achieve an optimum point of tradeoff between improvement in the SIR and the acceptable amount of the unutilized resources.Civilian, Defence Science and Technology Agency, SingaporeApproved for public release; distribution is unlimited

The design and analysis of factorial experiments

Factorial experiments are experiments which include all combinations of several different sets of treatments or "factors." Information is thus simultaneously obtained on the responses to the different factors, and also on the effects of changes in the level of each factor on the responses to the others. This Technical Communication has not been written with the object of convincing experimenters of the need for employing factorial designs, but rather for those who, while fully conscious of the advantages of such designs, find difficulty in laying them out and in analysing the results. It is,_ in fact, an attempt to give a comprehensive survey oi the simpler types of design at present available, and a description of the appropriate methods of analysis. The reader who has not done so is advised to first read Prof. R. A. Fisher's Design of Experiments, where he will find a full account of the logical basis of the whole technique of modern experimental design

Some Implications on Amorphic Association Schemes

AMS classifications: 05E30, 05B20;