Non-orthogonal Signals Research Articles

Noncoherent versus coherent MIMO radar: Performance and simplicity analysis

MIMO radar with properly placed antennas that employs a coherent processing approach can provide superior MSE performance, as indicated by recent work. This paper demonstrates that the magnitude of these gains decreases with an increase in the product of the number of transmit and receive antennas if the antennas for the noncoherent system are also suitably placed, using a placement which is generally different from the one for the coherent processing approach. Initially, we study the systems without constraining the complexity and energy, where each added transmit antenna employs a fixed energy so that the total transmitted energy is allowed to increase as we increase the number of transmit antennas. Later we also look at constrained systems, where adding a transmit antenna splits the total system energy and the total number of antennas employed is restricted. A rigorous theorem is presented for the case of orthogonal signals in temporally and spatially white clutter-plus-noise, but numerical results for nonorthogonal signals and colored clutter-plus-noise follow a similar pattern.

The Effect of Signaling Rate on Information Rate for Single Carrier Linear Transmission Systems

We consider the effect of signaling rate (baud rate) on the information rate of single carrier linear transmission systems with Gaussian inputs. Several different communication scenarios are investigated: correlated or uncorrelated symbols, a fixed modulation pulse or a modulation pulse varying with the signaling rate and frequency selective or flat channels. For uncorrelated symbols, we show that the information rate grows monotonically with signaling rate for some cases while it can in fact decrease in other cases. Sufficient conditions on the modulation pulse and the channel impulse response are derived so that the information rate is increasing with increased signaling rate. Especially, these conditions give criterias for when non-orthogonal signaling is beneficial compared to orthogonal signaling in the case of flat fading. For modulation pulses varying with the signaling rate, it is shown that there are pulses for which the information rate is non-decreasing with increasing signaling rate. When correlation between symbols is allowed, we show that one can guarantee increasing information rate with increased signaling rate, no matter the pulse-channel shape (except for some hypothetical special cases), by signaling with an SNR above a certain finite threshold.

Orthogonal Multirate Modulation

In this letter, the orthogonal multirate (MR) modulation signal is constructed by the orthogonal multiplexing of block-precoded component modulation waveforms occupying the Nyquist bandwidth and shown to outperform the conventional nonorthogonal MR modulation signal in error performance, while giving the same bandwidth efficiency.

Ground Clutter Reduction from GPR Data for Identification of Shallowly Buried Landmines

A method for reducing ground clutter contribution from ground penetrating radar (GPR) data is proposed for discrimination of landmines located in shallow depth. The algorithm of this method is based on the Matching Pursuit (MP) that is a technique for non-orthogonal signal decomposition using dictionary of functions. As the dictionary of function, a wave-based dictionary constructed by taking account of scattering mechanisms of electromagnetic (EM) wave by rough surfaces is employed. Through numerical simulations, performance of ground clutter reduction is evaluated. The results show that the proposed method has good performance and is effective for GPR data preprocessing for discrimination of shallowly buried landmines.

Enhancement of throughput and fairness in 4G wireless access systems by non-orthogonal signaling

Enhancement of throughput and fairness in 4G wireless access systems by non-orthogonal signaling

Optimum detection of non-orthogonal QAM signals with spectral overlapping

The authors evaluate and propose two approaches for the detection of two non-orthogonal m-QAM signals with spectral overlapping through an AWGN channel. Some previously reported works are revisited and alternative solutions in order to permit their application in practical communication systems are proposed. The subject method is proved to be relevant because it does not obey the Riesz basis condition for performing signal separation. The optimum maximum-likelihood receiver for this detection problem is also derived and the performance analysis is presented, including some analytical and Monte Carlo simulation results.

Nonorthogonal Transmission and Noncoherent Fusion of Censored Decisions

In this paper, we consider the binary-distributed hypothesis testing problem, where a wireless sensor network (WSN) is used to determine the true state of nature. We propose a novel signaling scheme where signature vectors (SVs) are used to transmit censored sensor decisions to the fusion center (FC). In particular, the length of the SVs is chosen to be smaller than the number of sensors, resulting in nonorthogonal sensor channels and allowing a desirable tradeoff between bandwidth and power efficiency in WSNs. We consider deterministic SVs that are assumed to be known to the FC and random SVs that are unknown to the FC. For both cases, the optimum noncoherent fusion rules are derived, assuming independent Ricean fading sensor-FC channels. Since the complexity of these optimum fusion rules is prohibitively large, even for WSNs of moderate size, we also consider a low-complexity suboptimum energy-based fusion rule and show that it is equivalent to the optimum fusion rules under certain conditions. Furthermore, we calculate the system probabilities of detection and false alarm for the energy-based fusion rule for both deterministic and random SVs. Numerical and simulation results show that with the proposed nonorthogonal signaling scheme, significant improvements in bandwidth efficiency are possible at the expense of only a small loss in power efficiency.

Testing quantum devices: Practical entanglement verification in bipartite optical systems

We present a method to test quantum behavior of quantum information processing devices, such as quantum memories, teleportation devices, channels, and quantum key distribution protocols. The test of quantum behavior can be phrased as the verification of effective entanglement. Necessary separability criteria are formulated in terms of a matrix of expectation values in conjunction with the partial transposition map. Our method is designed to reduce the resources for entanglement verification. A particular protocol based on coherent states and homodyne detection is used to illustrate the method. A possible test for the quantum nature of memories using two nonorthogonal signal states arises naturally. Furthermore, closer inspection of the measurement process in terms of the Stokes operators reveals a security threat for quantum key distribution involving phase reference beams.

Polarisation control schemes for fibre-optics quantum communications using polarisation encoding

Real-time polarisation control schemes employing two multiplexed non-orthogonal reference signals are shown to provide complete control of multiple polarisation states for polarisation encoded quantum communications with negligible added noise in the quantum channel. The robustness of the control schemes to polarisation mode dispersion and induced penalties are simulated and discussed.

Multiple-Access Capability of Synchronous FHSS Wireless Networks: An Analysis of the Effects of the Spacing Between Hopping Carriers

This paper presents a new analytical performance analysis of slow frequency-hopped synchronous spread-spectrum multiple-access (FHSS-MA) networks employing nonorthogonal binary frequency-shift keying (BFSK) and having arbitrary spacing between the hopping carriers. Taking into account the crosstalk due to the nonorthogonality of both hopping carriers and BFSK tones, and based on an accurate interference analysis, we derive new expressions for the average probability of error of a reference signal subjected to a number of similar signals in the additive white Gaussian noise Rayleigh-faded channel. These are used to investigate the effect of carrier and tone spacing on the spectral efficiency of an FHSS-MA network. It is shown that the spectral efficiency depends primarily on the shape of the employed pulses, in addition to both carrier and tone spacing. Numerical results show that rectangular pulses give higher spectral efficiency as compared with the half-sine pulses. Furthermore, orthogonal tone spacing is shown to be more efficient in the case of rectangular pulses, whereas half-sine pulses become more efficient with the nonorthogonal signaling

Reduction of Non-Orthogonal Interference in OFDM Receivers by Optimized Windowing

For conventional orthogonal frequencydivision multiplexing (OFDM) systems, the guard interval is disregarded in the receiver and rectangular shaped windows are used implicitly due to the discrete Fourier transform (DFT). We consider a Nyquistshaped window in the receiver, so that the transmit signal does not need to be modified, and optimize the window shape in order to suppress interference from non-orthogonal single carrier interferer signals. For the window coefficients, a closed form solution is derived. This type of interference occurs for example in OFDM radio systems like Digital Radio Mondiale (DRM) that are operating in low frequency bands. (Disturbance is given for instance by harmonics of switched-mode power supplies.) Further for multiple interferers, the receiver with optimized window outperforms the conventional receiver.

Blind source separation of positive and partially correlated data

Blind source separation (BSS) consists of processing a set of observed mixed signals to separate them into a set of unobservable original components. Various approaches have been employed to solve BSS problems using the strong assumption focusing on mutually uncorrelated (or orthogonal) source signals. However, in many real-life problems, signal orthogonality is not guaranteed. This paper introduces a new approach to BSS that can be applied to nonorthogonal signals. The orthogonality requirement is replaced by a partial orthogonality and a nonnegativity constraint which are well-suited for many real-world signals. An algebraic property is then exploited to express BSS problems in terms of constrained optimization. An efficient algorithm implementing the approach is reported and applied to examples from nuclear magnetic resonance spectroscopy. Résumé La séparation aveugle de sources consiste à traiter un ensemble de signaux en mélange pour en extraire les composantes inobservables d’origine. Diverses approches utilisent l’hypothèse très restrictive de non-corrélation mutuelle des signaux sources, c’est-a-dire d’orthogonalité. Cependant, dans nombreuses situations réelles, la validité de l’hypothèse n’est pas garantie. Cet article propose une approche originale de la séparation de sources applicable à des sources non-orthogonales. La condition de non-corrélation est remplacée par une hypothèse de positivité, adaptée à de nombreux problèmes réels. Une propriété algébrique permet de transposer le problème en termes d’optimisation sous contrainte. Un algorithme efficace mettant en œuvre cette approche est appliqué à la spectroscopie de résonance magnétique nucléaire.

Noncoherent Multiuser Communications: Multistage Detection and Selective Filtering

We consider noncoherent multiuser-detection techniques for a system employing nonlinear modulation of nonorthogonal signals. Our aim is to investigate near-optimum noncoherent multiuser-detection techniques that utilize the received signal structure while retaining reasonable complexity. Near-optimum approximations of the maximum-likelihood detector are investigated where the signal structure is reflected in the approximation techniques explored. Several implementations of noncoherent soft-interference cancellers are proposed and investigated, each of which exploits the signal structure in a specific way. We propose a class of detectors that employ selective filtering, a technique that exploits the a priori information that each user selects one of M signals for transmission. We show that selective filtering offers improved performance over the noncoherent counterparts of the existing near-optimum multiuser detectors. Both deterministic and blind adaptive implementations of selective filtering are considered. Numerical comparisons are provided to demonstrate the near-optimum performance of the proposed detectors.

Polarisation diversity reception of nonorthogonal multipulse signals in multiuser Rayleigh fading channels

The use of polarisation diversity techniques in conjunction with nonorthogonal multipulse modulation is considered for a multiuser communication system operating on a single-path Rayleigh fading channel. Indeed, in mobile environments multiple reflections and scattering phenomena introduce polarisation rotation of the transmitted power, and polarisation diversity is a suitable means of taking advantage of this effect. Several different two-stage receiving structures, each one relying on different amounts of a priori information on the channel status, are introduced. The performance of the proposed detectors is analysed through Monte Carlo counting techniques. It is seen that these receivers yield a remarkable performance improvement with respect to those not exploiting polarisation diversity.

Diversity reception of nonorthogonal multipulse signals in multiuser Nakagami fading channels

We consider the problem of multiantenna reception of nonorthogonal multipulse signals in a multiuser system operating over a flat-flat Nakagami fading channel, wherein each user sends an M-ary information symbol by transmitting one out of M available waveforms. The receiver first-stage is a decorrelative filter, which gets rid of the MAI, and whose output, is then properly processed in order to decode the information symbols from the user of interest. In particular, we derive both the optimum noncoherent and the GLRT detectors, and show that the latter receiver not only is simpler to implement, but also achieves a performance level very similar to that of the former receiver.

On the relative error probabilities of linear multiuser detectors

The relative error probability performance of three linear multiuser detectors-the minimum mean-square error (MMSE) detector, the decorrelator, and the conventional matched filter (MF) detector-is investigated under nonorthogonal signaling and additive white Gaussian noise conditions. It is shown that, contrary to the general belief, the MMSE detector does not uniformly outperform the other two detectors. In fact, even for the two-user case, one can find counterexamples where the matched filter is significantly better.

Generic error probabilities

This paper presents new forms for an error probability associated, with the phase angle between two vectors perturbed by Gaussian noise. An interesting consequence of the underlying generic form is a new expression for the symbol error rate in MDPSK that is very similar to its counterpart for MPSK. The generic error probability is further shown to contain as special cases MPSK, MDPSK, CPFSK, and digital FM; and to give a new expression for the Marcum Q-function. The generic error probability also simplifies the error probability expressions in other situations such as nonorthogonal signaling, maximum likelihood differential detection of DPSK with block-by-block detection, and Gray coding of MDPSK.

A new formula for MDPSK symbol error probability

This article presents an extremely compact new formula for the symbol error probability in M-ary differential phase shift keying (MDPSK) that is extraordinarily similar to its counterpart for M-ary phase shift keying (MPSK). This result follows from a new form for a generic error probability associated with the phase angle between two vectors perturbed by Gaussian noise. The new form also leads to a new expression for the Marcum Q-function. As special cases, the generic error probability is noted to also contain MPSK, CPFSK, and digital FM. Finally, it is pointed out that the generic error probability simplifies the error probability expressions in other situations such as nonorthogonal signaling, maximum-likelihood differential detection of DPSK with block-by-block detection, and Gray coding of MDPSK.

Probability of error in MMSE multiuser detection

The performance analysis of the minimum-mean-square-error (MMSE) linear multiuser detector is considered in an environment of nonorthogonal signaling and additive white Gaussian noise. In particular, the behavior of the multiple-access interference (MAI) at the output of the MMSE detector is examined under various asymptotic conditions, including: large signal-to-noise ratio; large near-far ratios; and large numbers of users. These results suggest that the MAI-plus-noise contending with the demodulation of a desired user is approximately Gaussian in many cases of interest. For the particular case of two users, it is shown that the maximum divergence between the output MAI-plus-noise and a Gaussian distribution having the same mean and variance is quite small in most cases of interest. It is further proved in this two-user case that the probability of error of the MMSE detector is better than that of the decorrelating linear detector for all values of normalized crosscorrelations not greater than 1/2 /spl radic/(2+/spl radic/3)/spl cong/0.9659.

Nonorthogonal signal representation by Gaussians and Gabor functions

This paper describes a novel approach for nonorthogonal representation of signals using Gaussians and an extension of this method for Gabor representation of signals, based on the equivalence of Gabor expansion to Gaussian expansion in the frequency domain. The Gaussian expansion scheme yields an efficient representation of signals for low number of bits per pixel and is better than the corresponding Discrete Cosine Transform (DCT) representation for very low bit rates. This advantage diminishes gracefully for higher bit rates where the residual approximation error signal to be represented is more random and less structured. It is proved in this paper that a finite number of Gaussians can theoretically approximate sinusoids in a bounded region with arbitrarily small error, and therefore any finite support L/sup 2/(R) signal as well. Two methods for Gaussian representation of signals are outlined. The first, called the Max-Energy paradigm, involves successive extraction of the highest energy Gaussian that best "fits" the signal. The second is a parallel approach and uses an adaptive projection algorithm to first derive the Gaussian basis set to be used in parallel, and then optimizes the coefficients for minimum squared error.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>