System and method for transmitting and receiving single-carrier OQAM symbols with non-nyquist transmit pulse shaping

An apparatus comprising:

• a processor and memory configured to perform the following steps:
• producing a set of 2K outputs that include K real components and K imaginary components from K complex symbols;
• performing a Fourier transform operation on the 2K outputs to produce 2K Fourier transform outputs;
• pulse shaping the 2K Fourier transform outputs by multiplying each of J of the 2K Fourier transform outputs with a respective one of J non-zero coefficients, wherein the J non-zero coefficients represent a frequency response of a transmit pulse shape of a set of transmit pulse shapes, to produce J pulse shaped outputs, where K≤J<2K for odd K, and K+1≤J<2K for even K;
• performing an inverse Fourier transform operation on the J pulse shaped outputs to produce an inverse Fourier transform output;
• outputting the inverse Fourier transform output;
• and
• transmitting signalling conveying J and K;
• wherein the signaling comprises an index of a value of J from within a set of possible values;
• or an index of a value of K/J from within a set of possible values of K/J.