Unified Complex Hadamard Transform Research Articles

Quaternary DS-SSMA Communications Employing Generalized Detector over Rayleigh Fading Channels

This paper deals with an employment of the complex modulators and generalized receivers constructed based on the generalized approach to signal processing (GASP) in noise in quaternary direct-sequence spread-spectrum multiple-access (DS-SSMA) communication systems with complex signature sequences in flat Rayleigh fading. Owing to availability of large sets of complex spreading sequences possessing perfect correlation characteristics, the interest to use the complex spreading sequences in DS-SSMA communication systems has increased. The complex spreading sequences investigated in the present paper are based on the recently introduced orthogonal unified complex Hadamard transform (UCHN) sequences. In the present paper, the complex processing in modulators and generalized receivers is also employed with the purpose to take advantage of the correlation properties of complex signature sequences. We derive the average bit error rate (BER) for quarternary synchronous communications system based on the generalized approach to signal processing in noise first, and then the BER for quaternary asynchronous ones is evaluated using the characteristic function approach. We presented some results based on the Gaussian approximation method for asynchronous communication systems constructed on the basis of the generalized approach to signal processing in noise Computer modeling results demonstrate that the communication systems using UCHT spreading sequences perform generally better than the GOLD sequences and the 4-phase family A sequences. Comparative analysis between the asynchronous communication systems constructed on the basis of the generalized approach to signal processing in noise demonstrates superiority over the asynchronous communication systems employing the correlation receiver.

Sequency-Ordered Complex Hadamard Transform: Properties, Computational Complexity and Applications

In this paper, the generation of sequency-ordered complex Hadamard transform (SCHT) based on the complex Rademacher matrices is presented. The exponential form of SCHT is also derived, and the proof for the unitary property of SCHT is given. Using the sparse matrix factorization, the fast and efficient algorithm to compute the SCHT transform is developed, and its computation load is described. Certain properties of the SCHT matrices are derived and analyzed with the discussion of SCHT applications in spectrum analysis and image watermarking. Relations of SCHT with fast Fourier transform (FFT) and unified complex Hadamard transform (UCHT) are discussed.

Performance of DS-CDMA Downlink Systems With Orthogonal UCHT Complex Sequences

This letter investigates a transmitted signaling technique using orthogonal unified complex Hadamard transform (UCHT) spreading sequences and the coherent RAKE receiver in direct-sequence code-division multiple-access (DS-CDMA) downlinks to maintain the orthogonality between users and reduce the effect of multipath fading and interference from other users. A general multipath-fading channel model is assumed. System performance is evaluated by means of signal-to-interference-plus-noise ratio (SINR) at the RAKE receiver. It is shown that the SINR of the system employing UCHT complex sequences is independent of the phase offsets between different paths, while the SINR of the system using Walsh-Hadamard (WH) sequences is related to the squared cosine of path phase offsets. As a result, the bit-error ratio performance of the DS-CDMA downlink system employing UCHT complex sequences is better than that of the system with WH sequences at high SINRs

Performance evaluation for quaternary DS-SSMA communications with complex signature sequences over Rayleigh-fading channels

Performance of quaternary direct-sequence spread-spectrum multiple-access (DS-SSMA) systems with complex signature sequences and complex modulators and receivers in flat Rayleigh fading is investigated in this paper. Due to the availability of potentially large sets of complex sequences with good correlation characteristics, the interest of using complex spreading sequences in DS-SSMA has increased dramatically. The complex spreading sequences investigated in this paper include the recently introduced orthogonal unified complex Hadamard transform (UCHT) sequences. In this paper, complex processing in modulators and receivers is also employed in order to take advantage of the correlation properties of complex signature sequences. The average bit error rate (BER) for quaternary synchronous systems is obtained first, and then the BER for quaternary asynchronous systems is evaluated using characteristic function approach. Result based on Gaussian approximation method is also presented for asynchronous systems. The numerical examples illustrate that the systems based on UCHT spreading sequences perform generally better than the Gold sequences and the 4-phase family A-sequences.

Complex composite spectra of Unified Complex Hadamard transform for logic functions

A method to evaluate the Unified Complex Hadamard spectra of AND, OR, and XOR for Boolean functions, directly from the spectra of the functions, is presented. The results are given using a general coding scheme, and different possible codings of Boolean functions are also discussed. A new definition of the convolution operation called complex convolution is derived. Different properties of such a convolution are presented. A theorem giving final formulas for the composite Unified Complex Hadamard spectra of Boolean functions is stated in terms of the complex convolution. Efficient representations of the spectra in the form of decision diagrams are presented. An application of Unified Complex Hadamard Transform in image watermarking is also discussed.