A note on least-squares estimates from likelihood ratios

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.

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.

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>

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.

A theoretical result for processing signals that have unknown distributions and priors in white Gaussian noise

Spectrum estimation using an analytic signal representation

A novel algorithm is proposed for frequency estimation of a single complex exponential signal or a real sinusoid signal in additive white Gaussian noise (AWGN). The proposed algorithm consists of a coarse search and a fine search, where the coarse search can be accomplished by maximum likelihood (ML) estimation, while the fine search performs a frequency interpolation via time-domain zero padding before applying discrete Fourier transform (DFT) with a novel residue frequency estimator proposed. Simulation results demonstrate that improved performance can be achieved by our proposed estimator based on zero-padding data sequence.

A method of fuzzy likelihood-ratio hypothesis testing is applied to binary signal integration. Imprecise parameters of the distribution under each hypothesis are modeled as fuzzy numbers. The false alarm rate and detection rate are therefore also imprecise. The effects of parameter imprecision on integration performance are examined using an example; the method is applied to envelope detection and integration of fixed amplitude signals in additive white Gaussian noise. For low parameter imprecision, the integration system produces performance which is nearly crisp. However, as parameter imprecision increases significantly, the performance quickly becomes so imprecise that the system may no longer be of practical use.

The problem of interest is the detection of transient signals in additive white Gaussian noise (AWGN) in the presence of missing signal observations (samples). Specifically, a fusion center aims at detecting the presence of transient signals by collecting measurements from individual sensors through erasure channels. Under the assumption that the fusion center can control the sampling procedure through a feedback channel, a strategy is proposed to adapt the sampling rate in response to sample missing with the goal of achieving accurate and timely decisions with the minimum communication cost measured by sampling rate. The proposed strategy is flexible in that it can be configured to suit different performance requirements. Compared with fixed-rate sampling, the proposed strategy achieves better tradeoff between Quality of Detection (QoD) and communication cost through dynamic adaptation.

In this paper we present two new, reduced complexity algorithms for multistage detection of direct sequence code division multiple access (DS-CDMA) signals in additive white Gaussian noise (AWGN) channels. The selective and successive selective multistage detection algorithms are designed to reduce the amount of computation performed by the conventional multistage detection algorithm while providing roughly the same bit error rate performance. Bit error rate performance of the new algorithms is determined via Monte Carlo simulation.

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.

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

We propose a new technique to estimate the signal-to-noise ratio (SNR) over flat fading time-varying single-input multiple-output (SIMO) channels, for quadrature amplitude modulation (QAM) signals in complex additive white Gaussian noise (AWGN). This technique relies on the use of periodically transmitted pilot symbols in the estimation process. It is a decision directed (DD) procedure since detected data symbols are also used. Performance is assessed via Monte Carlo simulations. Using the normalized root mean square error (NRMSE) as a measure of performance, our new estimator performs well over a wide SNR range.

In this paper, we develop a new method for signal-to-noise ratio (SNR) estimation when multiple antenna elements receive linearly-modulated signals in complex additive white Gaussian noise (AWGN) spatially uncorrelated between the antenna elements. We also derive extensions of other existing moment-based SNR estimators to the single-input multiple-output (SIMO) configuration. The new SIMO SNR estimation technique is non-data-aided (NDA) since it is a moment-based method and does not rely, therefore, on the a priori knowledge or detection of the transmitted symbols; it does not require the a priori knowledge of the modulation type or order. The new method is shown by Monte Carlo simulations to clearly outperform the best NDA moment-based SNR estimation methods in terms of normalized root mean square error (NRMSE) over QAM-modulated transmissions, namely the M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> method and the estimators referred to, in this paper, as the GT and the M <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sub> methods, even when we extend them to the SIMO configuration.