1. A method for compressing channel state information (CSI) of a wireless channel, the method comprising: receiving, at a receiver of a wireless communication system, an orthogonal frequency division multiplexing (OFDM) wireless signal over a wireless channel comprising one or more antenna pair; measuring, at a receiver of a wireless communication system, a channel state information (CSI) vector of the wireless channel from the received OFDM wireless signal for each antenna pair, wherein the CSI vector is an N by 1 vector of complex numbers and wherein each complex number represents an amplitude and a phase of one of N orthogonal frequency division multiplexing (OFDM) subcarriers of the wireless channel; accessing a plurality of configurations stored at the receiver, wherein each of the plurality of configurations “u”, identifies a set of P u base sinusoid vectors on constant frequencies and wherein P u is the order of the configuration and is equal to the number of complex numbers of the compressed CSI if configuration u is selected; calculating, for each of the plurality of configurations, a dot product of the N by 1 CSI vector and a conjugate of each P u base sinusoid vector identified by the selected configuration to generate a P u by 1 projection vector; calculating, for each of the plurality of configurations, a product of a constant P u by P u matrix stored at the receiver and the P u by 1 projection vector to generate a P u by 1 coefficient vector; calculating, for each of the plurality of configurations, a minimum squared error (MSE) fit with the P u by 1 coefficient vector on L evenly-spaced locations, where L is smaller than N, by multiplying each of the P u base sinusoids with the corresponding coefficient in the coefficient vector and taking the summation, at each of the L evenly-spaced locations; selecting configuration u and use its P u by 1 coefficient vector as the compressed CSI, if the total fit residual of the MSE fit of configuration u is below a predetermined threshold times the minimum fit residual among all configurations, and u is such a configuration with the lowest order; transmitting the compressed CSI to a transmitter of the wireless communication system; decompressing the CSI at the transmitter by computing a linear combination of the base sinusoids, using the compressed CSI as the coefficients of the base sinusoids, and adjusting the transmission characteristics of one or more wireless signals transmitted by the transmitter based upon the decompressed CSI.