Abstract
Paraunitary (PU) matrices play an important role in various areas of signal processing (such as in the theory of filter banks [1]), especially in complementary sequence design [2]–[6]. A salient feature of PU matrices is the energy balance property that can avoid the noise amplification problem [1]. That is, the output vector y[k] satisfies Ey =Ex , where x[k] is an input vector with finite energy Ex for a normalized PU matrix. A PU matrix is called an antipodal PU (APU) matrix if all of its coefficients are ±1 . In the literature, a number of constructions for APU matrices have been proposed in [7]– [10]. In [9], Wornell had shown that a code division multiple access (CDMA) system with APU spread-signature sets has better error probability performance than the conventional CDMA system. Also, it has been shown in [10] that an orthogonal frequency division multiplexing (OFDM) system with APU precoding matrices achieves better error probability performance than the conventional OFDM. Recently, the precoding application of APU matrices for a multiple-input multiple-output (MIMO) OFDM system has been reported in [11].