The problem of optimal carrier recovery and detection of digitally phase modulated signals on fading channels by using a nonstructured approach is presented, i.e. no constraint is placed on the receiver structure. First, the optimal receiver is derived for digitally phase-modulated signals when transmitted over a frequency-nonselective fading channel with memory. The memory results from the fact that usually the coherence time of the channel is larger than the symbol period. Symbols adjacent in time cannot be detected independently and therefore the well-known quadratic receiver is not optimal in this case. A maximum a posteriori (MAP) detector is derived and explicitly utilizes the channel memory for carrier recovery. The derivation shows that the optimal carrier recovery is, under certain conditions, a Kalman filter. Some attractive properties of this carrier recovery unit (including the absence of hang up) are discussed. Then the error rate of several digital modulation schemes is calculated taking the performance of the filter into account. The differences in susceptibility of the modulation schemes to carrier phase jitter are specified. >

A systematic approach to carrier recovery and detection of digitally phase modulated signals of fading channels

The bit-error rate (BER) of bandlimited binary phase-shift keying in a fading and cochannel interference (CCI) environment is derived for the case of perfect coherent detection. The fading-and-interference model assumed is general and of interest for microcellular system studies. The model allows both desired signal and interfering signals to experience arbitrary amounts of fading severity. A precise BER expression is derived using a characteristic function method. Using this accurate analytical result, the impact of the interfering users' fading severity on the desired user-error rate is examined. The BERs obtained under perfect coherent detection are also valid as lower performance bounds for practical realizable receivers where ideal coherent detection is difficult to implement. The error-rate performance of a novel bandwidth-efficient pulse shape is determined for the general fading and CCI environment. Analysis and numerical results show that the new pulse can provide better BER performance than the widely used raised-cosine pulse.

Precise error-rate analysis of bandwidth-efficient BPSK in Nakagami fading and cochannel interference

The performances of QPSK in the presence of cochannel interference in both nonfading and fading environments are analyzed. Three approaches for representing the cochannel interference are investigated. These are a precise error probability method, a sum of sinusoids (sinusoidal) model, and a Gaussian interference model. In addition to determining precise results for the performance of QPSK in cochannel interference, we examine the validity of these two interference models in both additive white Gaussian noise (AWGN) environments and in different flat fading environments; Rayleigh, Ricean, and Nakagami. Nyquist pulse shaping is considered and the effects of cross channel ISI produced by the cochannel interference are accounted for in the precise interference model. Also accounted for are the random symbol and carrier timing offsets of the interfering signals. Two performance criteria are considered. These are the average bit error rate and the interference penalty. The latter is defined as the increase in signal-to-noise power ratio (SNR) required by a system with cochannel interference in order to maintain the same BER as a system without interference. Attention is given, in particular, to the outdoor microcellular fading environment. In this environment, the fading experienced by the interfering signals may be represented by a Rayleigh-fading model while the fading experienced by the desired signal may be represented by a Ricean or a Nakagami-fading model. >

Bandwidth efficient QPSK in cochannel interference and fading

The bit error rate (BER) performance of pi /4-differential quadrature phase shift keying (DQPSK) modems in cellular mobile communication systems is derived and analyzed. The system is modeled as a frequency-selective fast Rayleigh fading channel corrupted by additive white Gaussian noise (AWGN) and co-channel interference (CCI). The probability density function of the phase difference between two consecutive symbols of M-ary differential phase shift keying (DPSK) signals is first derived. In M-ary DPSK systems, the information is completely contained in this phase difference. For pi /4-DQPSK, the BER is derived in a closed form and calculated directly. Numerical results show that for the 24 kBd (48 kb/s) pi /4-DQPSK operated at a carrier frequency of 850 MHz and C/I >

Bit error rate performance of pi /4-DQPSK in a frequency-selective fast Rayleigh fading channel

We developed a hybrid integrated optical module for 1.3/1.55-/spl mu/m wavelength-division multiplexing (WDM) full-duplex operation. The optical circuit was designed to suppress the optical and electrical crosstalk using a wavelength division multiplexing filter, and an optical crosstalk of -43 dB and an electrical crosstalk of -105 dB were achieved with a separation between the transmitter laser diode and the receiver photodiode of more than 9 mm. We used the optical circuit design to fabricate an optical module with a bare chip preamplifier in a package. This module exhibited a full duplex operation of 156 Mbit/s with a minimum sensitivity of -35.2 dBm at a bit error rate of 10/sup -10/.

A 1.3/1.55-/spl mu/m wavelength-division multiplexing optical module using a planar lightwave circuit for full duplex operation

The error rate performance of several digital modulation methods in a fading environment and in the presence of one cochannel interference and AWG noise is analyzed. A unique formula emerges for different PSK systems. It is shown how this information can be used in determining acceptable degradation caused by cochannel interference in the case of a digital mobile communication system.

Digital Modulation in Rayleigh Fading in the Presence of Cochannel Interference and Noise

Receiver sensitivity degradation caused by Rayleigh backscattering and coupler reflections is investigated for bidirectional digital transmission systems. Experimental values for APD receiver sensitivity degradation in a system operating at a bit rate of 10 Mbits/s and at a wavelength of 830 nm were found to be within 2 to 3 dB (optical) of the values predicted by a simple theoretical model.

R. Maciejko

Papers

Digital Modulation in Rayleigh Fading in the Presence of Cochannel Interference and Noise

Digital Optical Receiver Sensitivity Degradation Caused by Crosstalk in Bidirectional Fiber Optic Systems