The optimal diversity-combining technique is investigated for a multipath Rayleigh fading channel with imperfect channel state information at the receiver. Applying minimum mean-square error channel estimation, the channel state can be decomposed into the channel estimator spanned by channel observation, and the estimation error orthogonal to channel observation. The optimal combining weight is obtained from the first principle of maximum a posteriori detection, taking into consideration the imperfect channel estimation. The bit-error performance using the optimal diversity combining is derived and compared with that of the suboptimal application of maximal ratio combining. Numerical results are presented for specific channel models and estimation methods to illustrate the combined effect of channel estimation and detection on bit-error rate performance.

We consider the channel capacity of an optical intensity-modulated direct-detection (IM/DD) system using multiple-subcarrier modulation (MSM) with fixed bias. The channel is modeled as an additive white Gaussian noise (AWGN) channel with nonnegative input waveform. The mean of the nonnegative input waveform is the average transmitted optical power. The mean of the waveform during a symbol period is called the d.c. bias of the symbol. In this work, a fixed bias is used for all symbols. Therefore, the power used for each symbol is constant and equals the average transmitted power. The main result of this correspondence shows that, because the input waveforms during each symbol period are nonnegative and have fixed mean, their Fourier coefficients must lie inside certain trigonometric moment spaces. These moment spaces are characterized both algebraically and geometrically. Through the geometrical characterization, we determine the volumes of these moment spaces. The channel capacities of quadrature amplitude modulation (QAM) and pulse amplitude modulation (PAM) systems are shown to be upper-bounded by sphere-packing Gaussian noise in the respective moment spaces.

We consider the channel capacity of an optical intensity-modulated direct-detected (IM/DD) system using multiple-subcarrier modulation (MSM) with fixed bias. The channel is modeled as an additive white Gaussian noise (AWGN) channel with non-negative input waveform. The mean of the non-negative input waveform is the average transmitted power. The mean of the waveform during a symbol period is called the DC bias of the symbol and in this work is fixed for all symbols. Thus, the power used for each symbol is constant and equals the average transmitted power. The main result of this paper shows that, because the input waveforms during each symbol period are non-negative, their Fourier coefficients must form positive semi-definite (p.s.d.) sequences. Furthermore, these sequences are constrained inside the moment space of trigonometric functions. The volume of the moment space is calculated for both PAM and QAM cases. The capacity of each channel is shown to be upper-bounded by sphere-packing Gaussian noise in the respective moment space.

We describe two classes of simple, effective techniques for reducing the average optical power requirement in intensity-modulated optical systems using multiple BPSK or QPSK subcarriers. The first class of techniques involves block coding between the information bits to be transmitted and the symbol amplitudes modulated onto the subcarriers in order to increase the minimum value of the multiple-subcarrier electrical waveform. The second class of techniques involves replacing the fixed DC bias by a bias signal that varies on a symbol-by-symbol basis. These two classes of techniques can be applied separately or in tandem. The reduction in power requirement increases with the number of subcarriers and, with eight subcarriers, can be as high as about 3.6 dB and 3.2 dB with BPSK and QPSK, respectively. The techniques described are applicable as long as all subcarriers originate from a single transmitter and are symbol-synchronized.

We describe two classes of simple, effective techniques for reducing the average optical power requirement in intensity-modulated optical systems using multiple BPSK or QPSK subcarriers. The first class of techniques involves block coding between the information bits to be transmitted and the symbol amplitudes modulated onto the subcarriers, in order to increase the minimum value of the multiple-subcarrier electrical waveform. The second class of techniques involves replacing the fixed d.c. bias by a bias signal that varies on a symbol-by-symbol basis. These two classes of techniques can be applied separately or in tandem. The reduction in power requirement increases with the number of subcarriers, and with eight subcarriers, can be as high as about 3.6 dB and 3.2 dB with BPSK and QPSK, respectively. The techniques described are applicable as long as all subcarriers originate from a single transmitter and are symbol-synchronized.