Pre-Equalized and Spectrally Precoded OFDM

Abstract

When the channel state information is available, frequency-domain precoding is studied for rectangularly-pulsed orthogonal frequency-division multiplexing (OFDM) using cyclic prefix over dispersive channels to provide extremely compact signal spectrum, enhanced achievable data rate (ADR), and reduced peak-to-average power ratio (PAPR) jointly. With a precoding rate not larger than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1-2I/N$</tex-math></inline-formula> , a general precoder form is first developed for the transmitted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> -subcarrier OFDM signal to provide extremely small baseband power spectral sidelobes decaying asymptotically as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$f^{-2I-2}$</tex-math></inline-formula> or faster, with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$f$</tex-math></inline-formula> being the frequency, and thus achieve high spectrum compactness while yielding reduced PAPR. Incorporating the channel response, a particular spectral precoder following the general form is then designed to maximize the ADR under a fixed transmitted power. When a small out-of-band power proportion is required to guarantee spectrum compactness, the proposed pre-equalized and spectrally-precoded OFDM system can provide much higher ADR per unit bandwidth than pre-equalized OFDM, spectrally-precoded OFDM, and nonprecoded OFDM. When the low-complexity receiver is mandatory, a systematically pre-equalized and spectrally precoded OFDM system is also developed to achieve enhanced ADR, extremely high spectrum compactness, and low-complexity receiver operation by trading transmission power on cancellation subcarriers.