  A new unified formulation for seven different orthogonal frequency-division
multiplexing (OFDM) systems is presented. The proposed formulation relies on
six parameters and encompasses conventional OFDM systems, with windowing in the
transmitter and/or in the receiver, and also with a cyclic prefix (CP) or both
a CP and cyclic suffix (CS). A new equivalent channel matrix that is useful for
calculating both the received signal and the intersymbol and intercarrier
interference power is defined and characterized. Unlike previous works, this
new channel matrix formulates the channel convolution with no restrictions on
the length of the channel impulse response. Moreover, it includes the
overlap-and-add procedure performed in the transmitter of windowed OFDM
systems. Furthermore, new theoretical expressions for the intersymbol and
intercarrier interference and also for the signal-to-interference-plus-noise
ratio are derived.
