Dov Wulich

Reduction of peak factor in orthogonal multicarrier modulation by amplitude limiting and coding

A main disadvantage of orthogonal multicarrier modulation is that it exhibits a high peak-to-average-power ratio (PAPR). Because of this, all circuits between the output of the modulator and the input of the demodulator must be linear within a large dynamic range to avoid distortions and spectral spreading. It is therefore desirable to limit the PAPR of the multicarrier signal. A method based on amplitude limiting and forward error correcting (AL-FEC) coding is proposed for reduction of the PAPR. The performance of the AL-FEC is compared to two methods, based on block coding, specially constructed to reduce the PAPR. The AL-FEC is superior as compared to the existing methods. Moreover, its practical realization is very simple for any number of carriers.

Minimum BER power loading for OFDM in fading channel

A novel approach to power loading for orthogonal frequency-division multiplexing (OFDM) systems is proposed. The corresponding algorithm minimizes the aggregate bit-error rate, but appears to be rather complicated. Consequently, a much simpler, quasi-optimal loading algorithm is developed. The performance of various power loading strategies known in the literature are compared with the proposed quasi-optimal algorithm in the Rayleigh frequency-selective fading channel.

Peak-to-average power ratio in high-order OFDM

The problem of peak-to-average power ratio (PAPR) of high-order orthogonal frequency-division modulation (OFDM) is considered. Using results on level crossing of random processes, an upper bound on the probability that the PAPR of an OFDM signal will exceed a given value is derived. Numerical computations are used to show that this bound is tight for low-pass OFDM systems. The central limit theorem is used to find an asymptotic expression for the bound when the number of carriers N grows to infinity. The central limit theorem is also used to find an asymptotic expression for another bound that is based on the envelope of the OFDM signal, and is tighter for bandpass systems. It is shown that, effectively, the PAPR grows as 2lnN and not linearly with N, and by developing a lower bound on the probability that the PAPR of an OFDM signal will exceed a given value, it is shown that asymptotically most OFDM symbols have a PAPR close to 2lnN. Some approaches to coping with the PAPR problem are discussed in light of the obtained results.

Definition of efficient PAPR in OFDM

A high PAPR is a main drawback of OFDM. There are many methods for reducing the PAPR with an ultimate goal of reducing the PAPR as much as possible. It is shown that if, among other factors, the power efficiency-PAPR relationship of the power amplifier is also taken into account, then there exists a PAPR level for which the BER reaches a minimal value. This PAPR may be used as a definition of an efficient PAPR. The efficient PAPR is not necessary the lowest possible value of PAPR.

Level clipped high-order OFDM

The asymptotic behavior of level clipped orthogonal frequency-division multiplexing when its order N approaches infinity is analyzed. It is shown that if the clipping level approaches infinity faster than /spl radic/lnN, then a zero bit-error rate penalty and arbitrarily large peak to-average power ratio (PAPR) gain are asymptotically obtained. Moreover, the expression for the probability of clipping is found, and using it, the upper bound of the probability of error is derived. This upper bound can be used to analyze the tradeoff between PAPR and probability of error.

Securing OFDM over wireless time-varying channels using subcarrier overloading with joint signal constellations

A method of overloading subcarriers by multiple transmitters to secure OFDM in wireless time-varying channels is proposed and analyzed. The method is based on reverse piloting, superposition modulation, and joint decoding. It makes use of channel randomness, reciprocity, and fast decorrelation in space to secure OFDM with low overheads on encryption, decryption, and key distribution. These properties make it a good alternative to traditional software-based information security algorithms in systems where the costs associated with such algorithms are an implementation obstacle. A necessary and sufficient condition for achieving information theoretic security in accordance with channel and system parameters is derived. Security by complexity is assessed for cases where the condition for information theoretic security is not satisfied. In addition, practical means for implementing the method are derived including generating robust joint constellations, decoding data with low complexity, and mitigating the effects of imperfections due to mobility, power control errors, and synchronization errors.

Comments on the peak factor of sampled and continuous signals

Peak factors of the continuous signal and a corresponding sampled sequence are considered. It is shown, by means of an illustrative example, that in spite of the fact that the peak factor of the sampled signal is bounded, the peak factor of the continuous signal may be arbitrarily large.

Optimal noise suppression in Fresnel incoherent correlation holography (FINCH) configured for maximum imaging resolution

An optimal setup in the sense of imaging resolution for the Fresnel incoherent correlation holography (FINCH) system is proposed and analyzed. Experimental results of the proposed setup in reflection mode suffer from low signal-to-noise ratio (SNR) due to a granular noise. SNR improvement is achieved by two methods that rely on increasing the initial amount of phase-shifted recorded holograms. In the first method, we average over several independent complex-valued digital holograms obtained by recording different sets of three digital phase-shifted holograms. In the second method, the least-squares solution for solving a system of an overdetermined set of linear equations is approximated by utilizing the Moore-Penrose pseudoinverse. These methods improve the resolution of the reconstructed image due to their ability to reveal fine and weak details of the observed object.

Reverse piloting protocol for securing time varying wireless channels

We consider single-tone pilot based burst transmission over slow time varying flat fading wireless channels with no line of sight. We propose a reverse pilot signaling protocol, based on sending the pilot signal from the receiver to the transmitter instead of from the transmitter to the receiver and on channel tracking at the receiver. We show that the channel performs automatic symbol level encryption analogous to a shift cipher. We derive explicit relationships between channel and system parameters which guarantee secure transmission of the entire data burst for given channel conditions, and depict them for Rayleigh fading. The proposed protocol exhibits high key generating rates, and no overheads on key distribution, enciphering and deciphering. Its security strength increases with mobility. These properties make it a good candidate for mobile wireless systems where bandwidth and power resources are scarce, such as mobile wireless sensor networks and mobile ad-hoc networks.

MIMO–OFDM With Nonlinear Power Amplifiers

The influence of nonlinear power amplifiers (PAs) on the performance of multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) systems is investigated. A “full” MIMO scheme with transmitters (TX) precoding and receivers (RX) decoding is considered. It is shown, under assumption of high order OFDM and frequency selective channel, that the ratio between the useful signal and the nonlinear distortions is proportional to the number of TX antennas, i.e., the influence of the nonlinear distortions decreases as the number of TX antennas increases. The distortion reduction factor (DRF) is proposed as a performance metric for MIMO-OFDM systems with nonlinear PAs. A general formula for signal to distortion and noise ratio is obtained for the nonlinear PA with memory, described by the Wiener-Hammerstein (WH) model. Special cases of MIMO, such as maximum ratio transmission (MRT) and maximum ratio combining (MRC), are considered. A full agreement between the theoretical and simulation results is obtained. The main contribution of this paper is in a statement that TX processing reduces the effect of nonlinear distortions. This is obtained by novel approach for analysis of the MIMO-OFDM systems with nonlinear PAs with memory.