Degree of polarization detection: a dual‐polarized antenna based spectrum sensing algorithm for cognitive radio

A new spectrum sensing algorithm‐degree of polarization (DoP) sensing algorithm is proposed in this paper. By exploiting a pair of dual‐polarized antenna at the receiver, DoP of the received vector signal is estimated and utilized to detect the presence of primary users based on the polarization characteristics of electromagnetic waves. The dual‐polarized narrowband and broadband systems are both considered for DoP detection. In theoretical analysis, we derive the probability of detection, the probability of false and detection threshold of the proposed algorithm. It is shown that our algorithm overcomes the noise uncertainty problem. Considering the polarization‐sensitive channel impairments, the impact of polarization mode dispersion on DoP detector is discussed. This method can be utilized for various signal detection applications without requiring the knowledge of signal, transmission channel, and noise power. In simulations based on wireless microphone signals, by applying polarization information signal carries, DoP achieves a better detection performance than arithmetic‐to‐geometric mean detector, the maximum‐to‐minimum ratio eigenvalue detector, and energy detector with noise uncertainty. The simulations based on digital video broadcasting‐terrestrial signals are also presented, which may show the detection performance of the proposed method may be affected by polarization mode dispersion. Copyright © 2013 John Wiley & Sons, Ltd.     

An adaptive detector for deterministic signals in noise of unknownspectra using the Rao test

An adaptive detector for a known deterministic signal of unknown amplitude in Gaussian noise of unknown spectra is described. The detector is based on the Rao test, which is asymptotically equivalent to the generalized likelihood ratio. The detector achieves constant false alarm probability in the presence of large changes in input noise bandwidth and variance while providing optimum detection performance. The results are supported by simulation     

Locally optimum rank detection of correlated random signals inadditive noise

Nonparametric detection of a zero-mean random signal in additive noise is considered. The locally optimum detector based on signs and ranks of observations is derived, for good weak-signal detection performance under any specified noise probability density function. This detector is shown to have interesting similarities to the locally optimum detector for random signals. It may also be viewed as a generalization of the locally optimum rank detector for known signals. Examples of the test statistic of the detector are given for some specific noise probability density functions. Asymptotic and finite sample-size performance of the locally optimum rank detector is also considered     

Robust detection using extreme-value theory

The use of extreme-value theory (EVT) in the detection of a binary signal in additive, but statistically unknown, noise is considered. It is shown that the optimum threshold and the probability of error of the system can be accurately estimated by using EVT to obtain properties of the initial probability density functions on their "tails." Both constant signals and slowly fading signals are considered. In the case of a fading signal, the detector becomes adaptive. Detection of the constant signal, both with and without an initial learning period, is studied by computer simulation.     

Error probability analysis for continuous phase modulation withViterbi detection on a Gaussian channel with multiple signalinterference

The effects are studied on the symbol error probability of the Viterbi detector for continuous phase modulations with constant amplitude, when the desired signal is received in multiple interfering signals and white Gaussian noise. The detection is assumed to be coherent and, furthermore, perfect timing in the detector is also assumed. An upper bound on the symbol error probability is derived for the Viterbi detector. The bound is based on the union bound technique, and it is shown to be tight for small error probability levels. It is found that the smoothed binary and all quaternary modulations sustain much larger interference power in adjacent channel interference than minimum-shift keying (MSK) does and, thus, the adjacent channels can be spaced closer in frequency for these modulations, In particular, the smoothed quaternary modulations seem to be significantly more efficient than MSK. In cochannel interference the difference in error performance between the schemes is relatively small     

Optimum detection of Gaussian signal fields in the multipath-anisotropic noise environment and numerical evaluation of detection probabilities

The optimum detector of Gaussian signal fields in the multipath-anisotropic noise environment is derived. The optimum detector consists of a series of matched quadratic filters and a decisionmaker. The filters are spatially and temporally matched to the eigenwaves of the signal-to-noise covariance, and the decisionmaker compares a quadratic form with a preassigned threshold. The optimum detector for single-path signals in isotropic white noise is the well-known delay-and-sum beamformer, which is widely used because of its simple structure. In the case of multipath signals in anisotropic noise, a substantial improvement in detection performance is possible over the beamformer. This is shown by numerically comparing the detection probability of the beamformer with that of the optimum detector for this case. In addition, we numerically evaluate the sensitivity of such an improvement to accurate knowledge of the signal and noise parameters that are required by the optimum detector. We also show the possibility of further improvement by the addition of a vertical segment to the commonly used horizontal linear array to provide sensitivity to the elevation angles of multipath signals.     

A CFAR adaptive subspace detector for second-order Gaussian signals

We study the problem of detecting subspace signals described by the Second-Order Gaussian (SOG) model in the presence of noise whose covariance structure and level are both unknown. Such a detection problem is often called Gauss-Gauss problem in that both the signal and the noise are assumed to have Gaussian distributions. We propose adaptive detectors for the SOG model signals based on a single observation and multiple observations. With a single observation, the detector can be derived in a manner similar to that of the generalized likelihood ratio test (GLRT), but the unknown covariance structure is replaced by sample covariance matrix based on training data. The proposed detectors are constant false alarm rate (CFAR) detectors. As a comparison, we also derive adaptive detectors for the First-Order Gaussian (FOG) model based on multiple observations under the same noise condition as for the SOG model. With a single observation, the seemingly ad hoc CFAR detector for the SOG model is a true GLRT in that it has the same form as the GLRT CFAR detector for the FOG model. We give an approximate closed form of the probability of detection and false alarm in this case. Furthermore, we study the proposed CFAR detectors and compute the performance curves.     

On Optimum and Suboptimum Coherent Detection of Continuous Phase Modulation on a Two-Ray Multipath Fading Channel

In this paper, the performance of continuous phase modulation (CPM) transmitted on a two-ray fading channel and received in white Gaussian noise is studied. The optimum coherent maximum likelihood (ML) detector and approximations thereof and their performance are studied by means of minimum Euclidean distance and simulated symbol error probability. A linear detector optimum at large signal-to-noise ratios is also studied and the performance is given by means of error probability. It is assumed that measurements on the channel provide information about the channel parameters. It is found that the loss in signal power due to the channel is small when an ML detector or an approximation thereof is used for binary schemes with modulation indexh =1/2. The loss for these schemes with a linear detector becomes significantly larger, especially when MSK is transmitted. The performance for this linear detector can, however, be improved significantly by using decision feedback, but still, the performance of the ML detector is superior.     

Improved energy detector for random signals in gaussian noise

New and improved energy detector for random signals in Gaussian noise is proposed by replacing the squaring operation of the signal amplitude in the conventional energy detector with an arbitrary positive power operation. Numerical results show that the best power operation depends on the probability of false alarm, the probability of detection, the average signal-to-noise ratio or the sample size. By choosing the optimum power operation according to different system settings, new energy detectors with better detection performances can be derived. These results give useful guidance on how to improve the performances of current wireless systems using the energy detector. It also confirms that the conventional energy detector based on the generalized likelihood ratio test using the generalized likelihood function is not optimum in terms of the detection performance.     

Binary orthogonal signaling over the Gaussian channel with unknownphase/fading: new results and interpretations

The problem of binary orthogonal signaling over a Gaussian noise channel with unknown phase/fading is considered. By viewing the problem in a rotated coordinate system, the orthogonal signal structure is considered as the combination of an antipodal signal set and a pilot tone for channel measurement. For data detection the optimum matched-filter envelope-detector is shown to be identical to a novel detector-estimator receiver in which the detector performs partially coherent detection, using an absolute coherent reference generated by the estimator from the channel measurement provided by the pilot-tone component of the orthogonal signal structure. This detector-estimator interpretation shows that it is incorrect to refer to the optimum receiver as a noncoherent receiver. It also leads to the development of new approaches for analyzing the error probability of the receiver. An exponential Chernoff upper bound is obtained for the Rician channel     

Cyclostationarity-based signal detection and source location innon-Gaussian noise

The paper deals with two-sensor interception of cyclostationary signals in the presence of additive non-Gaussian noise. The locally optimum approach is considered as a starting point to derive cyclostationarity-exploiting receiver structures for detecting a weak signal and locating its emission source through time-difference-of-arrival (TDOA) measurements. To obtain analytical information about the detection performance of the proposed receivers, the deflection in both constant and variable noise-level environments is evaluated. Monte Carlo simulations, aimed at evaluating the detection performance in terms of detection probability and false-alarm probability, and the TDOA estimation accuracy, have been carried out. The results show that the cyclostationarity-exploiting receivers can significantly outperform the radiometric receivers in both signal detection and source location, when the noise level is unknown or variable and/or strong interfering signals are present     

Performance of energy detector in the presence of noise uncertainty in cognitive radio networks

Energy detector is simple in structure and easy to implement. Therefore, it is a promising candidate for spectrum sensing in cognitive radio networks. However, its detection performance is typically challenged by the noise uncertainty. Thus, the detection performance of energy detector in the presence of noise uncertainty needs to be evaluated. In this paper, we derive the decision rules for the energy detector in the presence of noise uncertainty by employing a widely used model. Firstly, we derive the decision rule for unknown deterministic signal when the noise power is uncertain. Second, we derive the decision rule for random Gaussian distributed signal when there is noise uncertainty. Then, we analyze the detection performance of the energy detector in the presence of noise uncertainty for both unknown deterministic signal and random Gaussian distributed signal. Both theoretical analyses and simulation results show that in the presence of noise uncertainty, our derived decision rules provide precise sensing thresholds for the energy detector. Furthermore, compared with the conventional decision rule obtained by overestimating the noise power, our decision rules provide performance gains in terms of signal to noise ratio.     

Transmitted-reference techniques for random or unknown channels

In this paper, a particular approach to the problem of communicating in certain random or unknown channels is considered. A particular set of signals is chosen, each member of which is partitioned into a known reference or sounding signal and a message signal. The channel is assumed to be linear, and is divided into a multiplicative and an additive portion. The multiplicative portion is assumed to have the same response to both message and reference components, while the additive noises associated with these components are assumed to be independent. The channel outputs and the additive noises are further assumed to be Gaussian. Under these circumstances, the optimum receiver is shown to cross-correlate the message portion of the received signal with a filtered version of the posterior mean of the channel output, which is merely a filtered combination of the prior mean and the perturbed reference signal. This is an interesting extension of the optimum receiver for known signals in additive Gaussian noise. Several special cases are considered which yield additional insight into the operation of the optimum receiver.     

Detection of harmonic sets

We examine the detection problem of signals with narrowband, harmonically related components received by a passive sensor array. We investigate detector structures based on the Fourier method. The harmonic detector estimates the total signal power by combining the DFT coefficients from harmonic frequency bins. This power estimate is normalized by the estimated background noise power and then compared to a threshold. We investigate two harmonic detector structures: one that operates with coherent, correlated signals and the other with uncorrelated harmonic signals. We derive statistical laws governing both detector structures that facilitate setting a power threshold for a given probability of false alarm; and present upper- and lower-bounds for the probability of detection. The results developed and presented demonstrate the inherent advantage of the harmonic detector. At operating conditions characterized by low signal-to-noise power ratio values the harmonic detector exhibits enhanced detection performance by combining the estimated signal power from harmonic frequency bins. We generalize results from single-bin and harmonic detector structures and present them as special cases of a unifying framework     

Suboptimum detection for the two-wave Rayleigh-fading channel

Indoor wireless communication in the 20-60 GHz band requires schemes that are biased toward power efficiency rather than bandwidth efficiency and use simple, robust detectors. Using the two-wave Rayleigh-fading channel as a model for the indoor wireless channel, the optimum detector structure is derived, and a simple suboptimum detector is developed. This suboptimum detector is a straightforward extension of the optimum detector for the single-wave Rayleigh-fading channel. The suboptimum detector is optimum for the channel when the delay of the second wave is known, and whenever the equal energy signals have a normalized complex autocorrelation of either zero or unity at that delay. The performance of this suboptimum detector on the two-wave Rayleigh-fading channel with known delay is studied. An exact expression for the probability of error is derived for uniformly orthogonal, equal energy, binary signals. This expression, which is in terms of the average signal-to-noise ratios in the waves and the complex autocorrelation of the signals, explicitly exhibits the presence of a diversity-like effect when the delay between the waves is non zero, and is an approximation for the probability of error when the complex cross-correlation is small. When the suboptimum detector is used, wideband signals, such as chirp signals and variants, perform well on this channel, enhancing the diversity-like effect. Such signals are also shown to make the suboptimum detector nearly optimal in structure     

On the design of signals for sequential and nonsequential detection systems with feedback

The design of signals for binary communication systems employing feedback has previously been considered by Turin. A delayless, infinite-bandwidth forward channel disturbed by additive, white, Gaussian noise is assumed. At each instant of time, the log likelihood ratio of the two possible signals is fed back to the transmitter via a noiseless and delayless feedback channel. The forward-channel signals are said to be optimally designed when the feedback information is so utilized that the average (for sequential detection) or fixed (for nonsequential detection) transmission time is minimized, subject to a specified probability of error. Average and peak power constraints are also placed on the signals. Turin has solved the signal design problem for extreme values (i.e., very large or equal to one) of the peak-to-average power constraint ratio. These results are extended in this paper to arbitrary values of the power constraint ratio, for both sequential and nonsequential detection.     

Detection of weak signals in non-Gaussian noise

A locally optimum detector structure is derived for the detection of weak signals in non-Gaussian environments. Optimum performance is obtained by employing a zero-memory nonlinearity prior to the matched filter that would be optimum for detecting the signal were the noise Gaussian. The asymptotic detection performance of the locally optimum detector under non-Gaussian conditions is derived and compared with that for the corresponding detector optimized for operations in Gaussian noise. Numerical results for the asymptotic detection performance are shown for signal detection in noise environments of practical interest.     

Performance analysis and optimization of a space-time selective PIC for CDMA systems

This paper deals with an efficient receiver for applications in direct sequence-code-division multiple access wireless communication systems. This receiver combines a modified scheme of a parallel interference cancellation detector with antenna arrays with optimum beamforming and is used at the base station for the detection of asynchronous user signals. Each user's transmission channel is assumed to be a multipath frequency-selective independent Rayleigh fading channel. The receiver operates by dividing the signals into reliable and unreliable sets following space-time combining. The reliable signals are detected and canceled from the whole signal received at each sensor. Unreliable signals are then detected to improve the decision reliability. The receiver performance in terms of bit-error probability is analytically derived and optimized. According to the analytical and simulation results, this receiver outperforms previously proposed schemes and, thanks to its low implementation complexity, real-time operation is achieved.     

Simulation Results for the Decision-Directed MAP Receiver for M-ary Signals in Mulitiplicative and Additive Gaussian Noise

Simulation results are presented for the error-rate performance of the recursive digital maximum a posteriori probability (MAP) detector for knownM-ary signals in multiplicative and additive Gaussian noise. The structure of the digital simulation of the optimum detector is generally described, with specific results obtained for a quaternary signal and 2500 digit per second transmission rate. The simulation is focused on the aeronautical multipath communication problem. Plots of detection error rate versus additive signal-to-noise ratio are given, with the power ratio of multiplicative process to desired signal as a parameter. Results are presented for the cases where the detector has perfect knowledge of the first- and second-order statistics of the multiplicative and additive processes and also where these statistics are estimated in near real time. For comparison, the error rates of conventional coherent and noncoherent digital MAP detectors are also obtained. It is shown that with nonzero multiplicative noise, the error rates of the conventional detectors saturate at a level that is irreducible for increasing additive signal-to-noise ratio. The error rate of the optimum detector having perfect statistical knowledge continues to decrease rapidly with increasing additive signal-to-noise ratio. In the absence of multiplicative noise, the conventional coherent detector and the optimum detector are shown to exhibit identical performance. Suboptimum detectors, having less than perfect statistical knowledge, yield error rates bounded below by the optimum detector rates and bounded above by the conventional detector rates.     

机载静默射频噪声掩护技术研究

为了规避敌方雷达对于己方战机的探测,该文提出一种战机发射射频掩护信号的方法。针对采用恒虚警类检测器(CFAR)算法的敌方雷达,己方目标发射的一定包络的掩护信号可以提升敌方噪声估计电平,达到使己方战机针对该雷达隐身的效果的同时,避免射频掩护电磁信号被敌方电子侦察设备截获,具体包括敌方雷达信号抵达目标时间估计,敌方探测能力评估,掩护噪声包络功率设计等步骤。基于单元平均恒虚警检测器(CA-CFRA),该文利用数值仿真分析了射频掩护包络和功率对掩护信号被截获概率及目标被探测概率的关系,表明该方法需要恰当的设计掩护包络和平衡信号功率达到更好的射频掩护效果。