Patent ID: 7433418

Claim:
A method comprising: selecting a set of one or more original ordered sequences the set of ordered sequences having at least one desired property; creating a set of extended sequences, each based on an original ordered sequence of the set of ordered sequences by beginning with an element of the original ordered sequence of the set of ordered sequences, cyclically appending elements of the original ordered sequence of the set of ordered sequences in order to obtain a desired extended sequence length comprising at least one subsequence, and modifying each extended sequence using a corresponding modifying sequence by multiplying each element of each extended sequence by a corresponding element of the modifying sequence, the modifying sequence comprising a sequence of pairs of equal complex numbers, such that each complex number pair is equal to the previous complex number pair multiplied by exp(2π/M), wherein M is a positive integer greater than 1; such that a training sequence can be generated from any one of the modified extended sequences by beginning with a first element of a subsequence of the any one modified extended sequence and taking each element of the subsequence in order to obtain the training sequence, the modifying sequence being selected so that the obtained training sequence when modulated by a π/M−MPSK modulation format has the at least one desired property of the corresponding original ordered sequence.