This thesis presents two original ontributions on orthogonal frequency division multiplexing (OFDM). The first is a thorough investigation of the error performance and channel capacity of asymmetrically clipped optical OFDM (ACO-OFDM). ACO-OFDM is a modulation scheme designed specifically for optical communications. The second concerns the use of multiple-input multiple-output (MIMO) OFDM in radio frequency (RF) systems. A new scheme which uses polynomial cancellation coding (PCC) OFDM with time offsets is proposed. This new scheme is robust to both carrier frequency offset (CFO) and channel estimation errors. OFDM has been used extensively to reduce the effect of dispersion in wired and wireless RF systems. Although dispersion is also a problem in optical wireless systems, OFDM has not until recently been considered for use in these. This is because optical wireless systems use intensity modulation (IM) and so the transmitted signals must be nonnegative and as a result conventional OFDM signals which are bipolar cannot be used directly. ACO-OFDM and DC biased optical OFDM (DCO-OFDM) are two non-negative forms of OFDM developed for optical systems. Both are robust to ISI but ACO-OFDM is in most cases much more power efficient. In this thesis results are presented for the performance of ACO-OFDM, DCO-OFDM and conventional optical modulation schemes such as on-off keying (OOK) and pulse position modulation (PPM) for both dispersive and non-dispersive channels. These show that ACO-OFDM is more tolerant to dispersion and requires less optical power than the other modulation schemes. To investigate the theoretical limits of an ACO-OFDM system, closed form analytical expressions for the channel capacity of ACO-OFDM are derived both for a flat channel and for representative dispersive optical wireless channels. The capacity of ACO-OFDM cannot be compared with the general case of an intensity modulated signal, because no general solution for this has yet been found. Instead the mutual information of an ACO-OFDM signal is calculated and compared with two other signal distributions: an exponential distribution and a clipped-Gaussian distribution. The combination of OFDM and MIMO has been used in several radio standards. However, MIMO OFDM systems like single-input single-output (SISO) OFDM systems are very sensitive to CFO. An improved MIMO PCC OFDM system is proposed in this thesis. In this system, the signals transmitted from different antennae have different time offsets. At the receiver, OFDM symbols are demodulated by using each of these time offsets in a matched detection window. This system shows better performance than a MIMO PCC OFDM system without time offsets in two cases: when there are channel estimation errors and in MIMO systems with more transmit antennae than receive antennae
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