In [14, 15], the Walsh-Hadamard
matrix and the discrete Fourier transform (DFT) operation have been used as precoding matrices to decrease the PAPR of the OFDM signals.
The final resolution (number of points) is bounded by the requirements of the Walsh-Hadamard
Transform  used in the pattern analysis, which requires the number of data points (n) to be of the order of [2.sup.n].
The spatially uncorrelated feature of the transmission signals is produced using Walsh-Hadamard
code sets; then multipath delayed waves are produced for each signal, and finally a different Doppler shift is added for each probe antenna.
For example, with [N.sub.T] = 4, the 4 matrices that are selected are the identity matrix [I.sub.N] corresponding to no transform, the Walsh-Hadamard
transform (WHT) matrix [P.sup.W], the discrete cosine transform (DCT) matrix [P.sup.C], and the discrete Hartley transform (DHT) matrix [P.sup.H].
transform returns sequency values.
transformation, operator to rotate phase and inversion about average transformation were achieved through matrices of zeros and ones available as Matlab commands.
Algazi, "Unified Matrix Treatment of the Fast Walsh-Hadamard
Transform", IEEE Transactions on Computers, vol.
The Walsh functions are row vectors of Walsh-Hadamard
The transformation that applies H to n bits is called the Walsh, or Walsh-Hadamard
, transformation W.
(2) New codebooks for SSK are introduced and their performance is investigated, including the Full-Combination (FC), Walsh-Hadamard
(WH), Quasi-Orthogonal Sequences (QOS), and Orthogonal Array Testing (OAT) codebooks.
An orthogonal code such as Walsh-Hadamard
code is used to achieve minimum multiple access interference (MAI) in the fading channel.