ABSTRACT
A CDMA system distinguishes signals from dierent users with the code sequence of these users and dierent codebooks could make much dierence to the system performance. Within the frame theory, a Grassmannian frame is one that minimizes the maximum correlation among all frame elements, and a frame is called the optimum Grassmannian frame or an equiangular tight frame (ETF) when this correlation meets the Welch bound (WB) [1]. ETFs are widely used in compressive sampling [2,3] and MIMO [4] since the correlation among their frame elements is the lowest and that between any two frame elements is the same. In the same way, ETFs are very suitable when used to construct frequency spread sequences of a CDMA system, which are widely concerned as the optimum Grassmannian sequences or MWBE (maximum Welch bound equality) sequences [5-7]. However, how to construct an ETF is a widely known challenge [8] and an ETF exists only when the dimension m and the number of column vectors are certain given values [9,10]. Each of the few existing construction methods has its own limitations. Conference Matrix, for example, only constructs ETFs at N = 2m provided that N p 1a= + for a real-valued frame or = +N 2a 1 for a Complex-valued frame, where p is an odd prime number and a is a nonnegative integer [11], while Alternating Project Algorithm [12,13] and Genetic Algorithm (GA) [14,15] are positioned to construct low-dimension Grassmannian frames only. In tthis paper, a real-valued ETF construction method
based on best antipodal spherical codes (BASC) and a binary ETF construction method based on simulated annealing genetic algorithm (SAGA) are proposed. Numerical simulation indicates that, compared with some of the existing construction methods, andboth the two new methods proposed have better dimensional fitness and higher convergence rate.
