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Title:  Low Correlation Sequences Over AMPSK And QAM Constellations 
Authors:  Anand, M 
Advisors:  Vijay Kumar, P 
Keywords:  LowCorrelation Sequences Correlation Code Division Multiple Access (CDMA) Phase Shift Keying VariableRate Signalling DirectSequence Code Division Multiple Access (DSCDMA) AMPSK QAM Constellation 16QAM Sequences Low Periodic Correlation 
Submitted Date:  Apr2007 
Series/Report no.:  G20918 
Abstract:  DirectSequence Code Division Multiple Access (DSCDMA), over the last few years, has become a popular technique and ﬁnds a place in many modern communication systems. The performance of this technique is closely linked to the signature (or spreading) sequences employed in the system. In the past, there have been many successful attempts by research groups to construct families of signature sequences that oﬀer the potential gains promised by theoretical bounds. In this thesis, we present constructions of families of signature sequences over the AMPSK and QAM alphabet with low correlation.
In this thesis, we construct a family of sequences over the 8ary AMPSK constella
tion, Family AOpt(16) that is asymptotically optimal with respect to the Welch bound on maximum magnitude of correlation for complex sequences. The maximum magnitude of correlation for this family, θmax, is upper bounded by √N , where N is the period of the sequences. The 8ary AMPSK constellation is a subset of the 16QAM constellation. We also construct two families of sequences over 16QAM, Family A16A, and Family A16,B , with the maximum magnitude of correlation upper bounded by √2√N .
We construct a family, A(M 2), of sequences over the 2m+1ary AMPSK constellation of period N = 2r 1 and family size (N + 1)/2m1 . The 2m+1ary AMPSK constellation is a subset of the M 2QAM constellation with M =2m . The maximum nontrivial normalized correlation parameter is bounded above by θmax < a √N where a ranges from
1.34 in the case of M 2 = 16 to √5 for large m. Apart from low correlation values, the family possesses several interesting and useful features. In Family A(M 2), users have the ability to transmit 2m bits of data per period of the spreading sequence. The sequences in Family A(M 2) are balanced; all points from the 2m+1ary AMPSK constellation occur approximately equally often in sequences of long period. The Euclidean distance between the signals assigned to a particular user in A(M 2), corresponding to diﬀerent data symbols, is larger than the corresponding value for the case when 2m+1PSK modulation and spreading is used. Perhaps most interestingly, Family A(M 2) permits users on the reverse link of a CDMA system to communicate asynchronously at varying data rates by switching between diﬀerent QAM constellations.
Family A(M 2) is compatible with QPSK sequence families S(p) in the sense that the maximum correlation magnitude is increased only slightly if one adds sequences from (p) S(p)\ S(0) to Family A(M 2).
We also construct families of sequences over AMPSK that tradeoﬀ data rate per sequence period and θmax for a given family size.
We have extended the construction of sequences over AMPSK constellation to construct sequences over the M 2QAM constellation for M =2m . The QAM sequence families, Families (AM 2), have size, data rate and minimum squared Euclidean distance same as the corresponding AMPSK construction but have higher values of θmax. Also included in the thesis are constructions for large families of sequences over the M 2QAM alphabet. 
URI:  http://hdl.handle.net/2005/591 
Appears in Collections:  Electrical Communication Engineering (ece)

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