Automatic modulation classification based on high order cumulants and hierarchical polynomial classifiers

In this paper, the performance of a decision-feedback coherent code tracking loop for pilot-symbol-aided (PSA) direct-sequence spread-spectrum systems, considering the effect of both symbol and channel estimation errors, is analyzed. An analytical closed-form expression on the steady-state jitter variance in additive white Gaussian noise (AWGN) environments using the linear analysis model is first derived. Then, the upper and lower bounds of the jitter variance in fading environments are obtained based on the analysis of the loop bandwidth variation according to the input signal level. Finally, a second-order coherent tracking loop is designed, and its performance in both AWGN and fading environments is evaluated, along with verification by computer simulations. It is demonstrated that analytical results are very close to the simulation results in AWGN environments and that the jitter variance in fading environments is located between analytical upper and lower bounds with its position depending on the fading rate.

The paper proposes an automatic modulation recognition scheme based on instantaneous features of intercepted signals. The modulation classifier can discriminate modulations such as Amplitude Modulation (AM), Double Side Band (DSB), Single Side Band (SSB), Frequency Modulation (FM), M-ary Amplitude Shift Keying (M-ASK), M-ary Frequency Shift Keying (M-FSK), M-ary Phase Shift Keying (M-PSK) and M-ary Quadrature Amplitude Modulation (M-QAM) without any prior information. The scheme is with simple structure, computationally simpler, and suitable for real-time processing. And the recognition parameters are anti-noise, and insensitive to frequency offset, phase offset and timing error. To evaluate the performance of the scheme, several experiments with signals in Additive White Gaussian Noise (AWGN) channel were carried out in the MATLAB by varying the values of both the main modulation parameters and the signal-to-noise ratios (SNRs). The results show that the approach can achieve high recognition accuracy even at low SNR.

The paper presents a new algorithm for modulation recognition of digital communication signals based on higher order cumulants (HOCs) and support vector machines (SVM). The fourth and sixth order cumulants of the received signal are used as the input classification feature vector to the SVM. The SVM maps the input vectors nonlinearly into a high dimensional feature space, constructs the optimum separating hyperplane in that space and makes the non-separable data separable. This method is robust to Gaussian noise and constellation rotation due to the initial phase of the signal and avoids the overfitting and local minimum in a neural network. The high performance and robustness of the algorithms are proved by computer simulation.

We show that the concept of correlation detection of deterministic signals in additive Gaussian noise can be extended in a natural manner to the detection of signals that are transmitted through a "Gaussian" random channel besides being corrupted by additive Gaussian noise. Such situations are typical in communication over scatter-multipath channels (with or without a specular component). In the deterministic case, the receiver essentially crosscorrelates the received signal with the signal before the additive noise was introduced. When a random channel is present, however, this latter signal, i.e., the output of the random channel, is not known at the receiver, However, knowing the statistics of the channel and the noise, the receiver can make an estimate of it from the received signal on the hypothesis that a particular signal was transmitted. The optimum receiver then crosscorrelates this estimate with the received signal.

An improved modulation classification algorithm of MPSK signals based on high order cumulants is proposed and analyzed. Under the condition of unknown carrier frequency, first the constant amplitude and delayed complex conjugated multiplication is used to preprocess the original signal, then four order cumulants are exploited to construct the classified character. The unchangeness of classified character is proved in detail, and the robustness of the algorithm is analyzed aiming at short wave channels. Theoretical analysis and practical signal testing justify the effectiveness of the new algorithm.

The optical ZCZ code, which is a set of pairs of binary and biphase sequences with zero correlation zone, can provide code division multiple access (CDMA) communication system without co-channel interference. The M-ary amplitude shift keying spread spectrum (M-ary/ASK-SS) system using this code can detect a desired sequence without interference of undesired sequences. We have proposed the compact construction of a matched filter bank for this code, which is called the compact-type matched filter bank. However, M-ary/ASK-SS system using this filter bank might go down the bit error rate (BER) performance because input-output characteristics of this filter bank for this code with zero correlation zone 4n - 2 are nonlinear characteristics. In this paper, we clarify that BER performance in the M-ary/ASK-SS system over the additive white Gaussian noise (AWGN) channels is not influenced by nonlinear characteristics of this filter bank by the theoretical formula of BER characteristics and the computer simulation. The BER performance in the ASK-SS system using compact-type matched filter under the AWGN environment go down compared to that using direct-type matched filter as expected. But the BER performance in the M-ary/ASK-SS system using this compact-type matched filter bank under the AWGN environment is almost equal compared to that using parallel-type matched filter bank. In fact, this compact-type matched filter bank is effective in the M-ary/ASK-SS system.

Modulation classification (MC) of a signal is one of the major tasks of an intelligent receiver in various civilian and military applications. For mixed signals, it is a big challenge to recognize their modulation types. In this paper, a novel MC algorithm based on independent component analysis (ICA) is proposed. The proposed algorithm can separate mixed signals and identify modulation types for demodulation simultaneously under block fading channel. The design of the algorithm essentially involves two steps, namely, the separation of mixed signals through ICA algorithm and MC for the separated signals. Depending on ICA algorithm chosen in the first step, statistically independent signals are separated in block fading channel. Regarding the second step, higher-order cumulants are chosen as a promising approach for MC of the separated signals. Through the algorithm, the problem of the MC of the mixed signals can be solved and the mixed signals can be demodulated. Furthermore, simulation results are provided to verify the performance and robustness of the algorithm.

The optimum detection of binary antipodal signals in additive white Gaussian noise (AWGN) channels with Gaussian channel estimation error has been studied in prior work. In this paper, we present the optimum detector based on the maximum- likelihood criterion for binary orthogonal signals in the presence of Gaussian distributed channel estimation error and AWGN. It is shown that the optimum detector is a linear combination of the optimum coherent and optimum noncoherent detectors. We derive the exact closed-form expression of the average bit error probability of the proposed optimum detector in Rayleigh fading channels with AWGN. It is found that if the variance of channel estimation error for a given average SNR is greater than a threshold, then orthogonal signalling outperforms antipodal modulation, and the analytical expression of this threshold is derived.

The use of information theory to design waveforms for the measurement of extended radar targets exhibiting resonance phenomena is investigated. The target impulse response is introduced to model target scattering behavior. Two radar waveform design problems with constraints on waveform energy and duration are then solved. In the first, a deterministic target impulse response is used to design waveform/receiver-filter pairs for the optimal detection of extended targets in additive noise. In the second, a random target impulse response is used to design waveforms that maximize the mutual information between a target ensemble and the received signal in additive Gaussian noise. The two solutions are contrasted to show the difference between the characteristics of waveforms for extended target detection and information extraction. The optimal target detection solution places as much energy as possible in the largest target scattering mode under the imposed constraints on waveform duration and energy. The optimal information extraction solution distributes the energy among the target scattering modes in order to maximize the mutual information between the target ensemble and the received radar waveform. >

Optimal detection of a known FSK-modulated binary signal in additive white Gaussian noise using a matched filter receiver requires knowledge of second-order noise statistics. The dependence on noise statistics causes the probability of detection to be sensitive to errors in the noise variance value. This makes the optimal scheme of limited use in situations where the noise statistics are unknown and cannot be estimated reliably. We propose an alternative approach, which has a more easily calculated test statistic than the optimal method and yields a constant false detection rate, regardless of noise statistics. While this approach has sub-optimal detection probability, it is significantly advantageous in applications where a primary interest is to limit false detections strictly. In addition, it allows one to determine easily the required detection length (in symbols) to achieve a desired performance level.

Because of advantageous spectral properties, coherent minimum shift keying (MSK) is attractive for electronic counter-counter measures (ECCM) systems where high data throughput is required. These high rate ECCM systems typically use frequency-hopped (FH) spread-spectrum techniques to enhance antijam capabilities. The performance of MSK signals combined with FH in simultaneous optimized partial-band multitone jamming and additive white Gaussian noise (AWGN) is examined. The signals are assumed to be coherently detected. Performance is evaluated, assuming a worst-case jammer strategy, in terms of the probability of bit error. The analysis is performed for two different frequency-hopping patterns. The results show that the performance of a random hopping pattern exhibits improved performance over a fixed hopping scheme.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Two three‐dimensional (3D) 16‐ary signal constellations having extended lattice structures are presented in this paper. The theoretical symbol error probabilities (SEPs) of the new constellations in additive white Gaussian noise (AWGN) and Rayleigh fading channel are derived. Computer simulation confirms that the closed‐form expressions for average SEPs of the constellations in the AWGN channel are very accurate. The theoretical SEP upper bounds in the Rayleigh fading channel are very tight. Since the presented constellations have larger minimum Euclidean distance (MED) than the conventional one, error performance can be improved up to 0.9 dB in an AWGN environment. Hence, the proposed constellations and their theoretical analysis can be used as a reference for the development of a wireless communication system with 3D signal constellations.

Automatic identification of digitally modulated signal has to be able to identify the digitally modulated signal correctly and accurately. Importance of automatic identification of digitally modulated signals are rising increasingly. In this paper an advanced technique is presented, that automatically identifies the multi-user chirp modulated signals in Additive White Gaussian Noise (AWGN) channel. The proposed technique is implementing high order moments (fourth, sixth, and eighth) of detail coefficients of discrete wavelet transform (DWT) as a feature extraction set. Adaptive Neural-Fuzzy Inference System (ANFIS) is proposed as a classifier. The proposed identification procedure is capable of identifying multi-user chirp modulated signals with high accuracy at 0dB, 5dB, and 10dB Signal to Noise Ratio (SNR), over AWGN channel.

A new block coded modulation (BCM) scheme for a PCM communication system which uses the optimum vector quantizer (VQ) as a source coder is proposed. The proposed BCM scheme minimizes the mean square distortion of the received signal after VQ decoding. First, the paper derives the upper-bound on the mean square distortion of the signal in additive white Gaussian noise (AWGN) and Rayleigh fading channels. Next, the paper proposes a new BCM scheme which is optimized to minimize the upper-bound by the simulated annealing known as the non-linear global optimization algorithm. The paper provides the optimum BCM and shows the mean square distortion performances in the AWGN and Rayleigh fading channels. Computer simulation results show that using the proposed BCM improves the signal-to-noise ratio (S/N) performances of the output signal of the source decoder. Furthermore, the proposed BCM scheme can provide a stepwise graceful degradation in the output S/N performance against the channel S/N.

In this paper, we present a theoretical analysis of non linear quadratic systems using higher order cumulants (HOC). In the one hand, we develop the equations linking the second and third order cumulants with the impulse response of quadratic non linear systems. In the other hand, these relationships are used to develop an extension of linear algorithm based on third order cumulants to non linear algorithm for identification of quadratic systems. The proposed algorithm is tested using different quadratic models for various values of signal to noise ratio (SNR).