Showing papers on "Signal-to-noise ratio published in 2016"

Convolutional Radio Modulation Recognition Networks

Abstract: We study the adaptation of convolutional neural networks to the complex-valued temporal radio signal domain. We compare the efficacy of radio modulation classification using naively learned features against using expert feature based methods which are widely used today and e show significant performance improvements. We show that blind temporal learning on large and densely encoded time series using deep convolutional neural networks is viable and a strong candidate approach for this task especially at low signal to noise ratio.

On Probabilistic Shaping of Quadrature Amplitude Modulation for the Nonlinear Fiber Channel

Abstract: Different aspects of probabilistic shaping for a multispan optical communication system are studied. First, a numerical analysis of the additive white Gaussian noise (AWGN) channel investigates the effect of using a small number of input probability mass functions (PMFs) for a range of signal-to-noise ratios (SNRs), instead of optimizing the constellation shaping for each SNR. It is shown that if a small penalty of at most 0.1 dB SNR to the full shaping gain is acceptable, just two shaped PMFs are required per quadrature amplitude modulation (QAM) over a large SNR range. For a multispan wavelength division multiplexing optical fiber system with 64QAM input, it is shown that just one PMF is required to achieve large gains over uniform input for distances from 1400 to 3000 km. Using recently developed theoretical models that extend the Gaussian noise (GN) model and full-field split-step simulations, we illustrate the ramifications of probabilistic shaping on the effective SNR after fiber propagation. Our results show that, for a fixed average optical launch power, a shaping gain is obtained for the noise contributions from fiber amplifiers and modulation-independent nonlinear interference (NLI), whereas shaping simultaneously causes a penalty as it leads to an increased NLI. However, this nonlinear shaping loss is found to have a relatively minor impact, and optimizing the shaped PMF with a modulation-dependent GN model confirms that the PMF found for AWGN is also a good choice for a multi-span fiber system.

Convolutional Radio Modulation Recognition Networks

Abstract: We study the adaptation of convolutional neural networks to the complex temporal radio signal domain. We compare the efficacy of radio modulation classification using naively learned features against using expert features which are widely used in the field today and we show significant performance improvements. We show that blind temporal learning on large and densely encoded time series using deep convolutional neural networks is viable and a strong candidate approach for this task especially at low signal to noise ratio.

Beam tracking for mobile millimeter wave communication systems

Abstract: Millimeter wave (mmWave) is an attractive option for high data rate applications. Enabling mmWave communications requires appropriate beamforming, which is conventionally realized by a lengthy beam training process. Such beam training will be a challenge for applying mmWave to mobile environments. As a solution, a beam tracking method requiring to train only one beam pair to track a path in the analog beamforming architecture is developed. Considering its low complexity which is suitable for mobile settings, the extended Kalman filter is chosen as the tracking filter. Several effects impacting the performance of the proposed tracking algorithm, such as the signal-to-noise ratio (SNR) and array size, are investigated. It is found that at the same SNR, narrower beams, which are more sensitive to angular changes, can provide more accurate estimate. Too narrow beams, however, degrade tracking performance because beam misalignment could happen during the measurement. Finally, a comparison to prior work is given where it is shown that our approach is more suitable for fast-changing environments thanks to the low measurement overhead.

Design of Massive-MIMO-NOMA With Limited Feedback

Abstract: In this letter, a low-feedback nonorthogonal multiple access (NOMA) scheme using massive multiple-input multiple-output (MIMO) transmission is proposed. In particular, the proposed scheme can decompose a massive-MIMO-NOMA system into multiple separated single-input single-output (SISO) NOMA channels, and analytical results are developed to evaluate the performance of the proposed scheme for two scenarios, with perfect user ordering and with one-bit feedback, respectively.

Characterizing and quantifying noise in PMU data

Abstract: Data recorded by Phasor Measurement Units (PMUs) contains noise. This paper characterizes and quantifies this noise for voltage, current and frequency data recorded at three different voltage levels. The probability distribution of the measurement noise and its typical power are identified. The PMU noise quantification can help in generation of experimental PMU data in close conformity with field PMU data, bad data removal, missing data prediction, and effective design of statistical filters for noise rejection.

Improving the signal-to-noise ratio of single-pixel imaging using digital microscanning

Abstract: Single-pixel cameras provide a means to perform imaging at wavelengths where pixelated detector arrays are expensive or limited. The image is reconstructed from measurements of the correlation between the scene and a series of masks. Although there has been much research in the field in recent years, the fact that the signal-to-noise ratio (SNR) scales poorly with increasing resolution has been one of the main limitations prohibiting the uptake of such systems. Microscanning is a technique that provides a final higher resolution image by combining multiple images of a lower resolution. Each of these low resolution images is subject to a sub-pixel sized lateral displacement. In this work we apply a digital microscanning approach to an infrared single-pixel camera. Our approach requires no additional hardware, but is achieved simply by using a modified set of masks. Compared to the conventional Hadamard based single-pixel imaging scheme, our proposed framework improves the SNR of reconstructed images by ∼ 50 % for the same acquisition time. In addition, this strategy also provides access to a stream of low-resolution ‘preview’ images throughout each high-resolution acquisition.

Lévy noise induced stochastic resonance in an FHN model

Abstract: This paper aims to investigate the stochastic resonance (SR) in an FitzHugh-Nagumo (FHN) model with an additive Levy noise numerically. The non-Gaussian Levy noise is a kind of general random noise which is different from the usual Gaussian noise, and it has small fluctuations with the unpredictable jumps to describe the random fluctuations in an FHN model. SR is determined by the signal-to-noise ratio (SNR), and the numerical simulation results show the occurrence of the SR phenomena in the given FHN system. The influence of various parameters of the Levy noise and the FHN model on the SR will be examined, and some mechanisms of the Levy noise-induced SR are presented which are different from those of the Gaussian noise.

Modulation Format Identification in Coherent Receivers Using Deep Machine Learning

Abstract: We propose a novel technique for modulation format identification (MFI) in digital coherent receivers by applying deep neural network (DNN) based pattern recognition on signals’ amplitude histograms obtained after constant modulus algorithm (CMA) equalization. Experimental results for three commonly-used modulation formats demonstrate MFI with an accuracy of 100% over a wide optical signal-to-noise ratio (OSNR) range. The effects of fiber nonlinearity on the performance of MFI technique are also investigated. The proposed technique is non-data-aided (NDA) and avoids any additional hardware on top of standard digital coherent receiver. Therefore, it is ideal for simple and cost-effective MFI in future heterogeneous optical networks.

Mixed-ADC Massive MIMO Detectors: Performance Analysis and Design Optimization

Abstract: The hardware cost and power consumption of a massive multiple-input multiple-output (MIMO) system can be remarkably reduced by using a very low-resolution analog-to-digital converter (ADC) unit in each antenna. However, such a pure low-resolution ADC architecture complicates parameter estimation problems. These issues can be resolved and the potential of a pure low-resolution ADC architecture can be achieved by applying a mixed ADC architecture, whose antennas are equipped with low-precision ADCs, while few antennas are composed of high-precision ADCs. In this paper, a unified framework is presented to develop a family of detectors on a massive MIMO uplink system through probabilistic Bayesian inference. Our basic setup comprises an optimal detector, which is developed to provide a minimum mean-squared-error estimate on data symbols. Considering that highly nonlinear steps are involved in quantization, we also investigate the potential for complexity reduction on an optimal detector by postulating a common pseudo-quantization noise model. We provide asymptotic performance expressions, including mean squared error and bit error rate for optimal and suboptimal MIMO detectors. These expressions can be evaluated rapidly and efficiently. Thus, they can be used for system design optimization.

Optimal Transceiver Design for SWIPT in $K$ -User MIMO Interference Channels

Abstract: This paper investigates simultaneous wireless information and power transfer (SWIPT) in $K$ -user multiple-input multiple-output (MIMO) interference channels. In particular, the power splitting (PS) technique is leveraged at each receiver to divide the received signal into two flows, for information decoding (ID) and energy harvesting (EH), respectively. As a whole system, our objective is to minimize the total transmit power of all transmitters by jointly designing transmit beamformers, power splitters, and receive filters, subject to the signal-to-interference-plus-noise ratio (SINR) constraint for ID and the harvested power constraint for EH at each receiver. Due to the coupling nature of all variables, the formulated joint transceiver design problem is nonconvex, and has not yet been well addressed in the literature. In this paper, we first propose a semidefinite relaxation-based alternating optimization (SDRAO) solution to approach the optimal solution of the problem. Then, we semidecouple the joint optimization by the derived diversity interference alignment (DIA) technique, and obtain a solution of lower complexity. Finally, a closed-form solution is further developed relying on the transmitter-side zero-forcing (TZF), which can be implemented in a distributed manner, with the lowest computational complexity and CSI exchanging overhead.

Robust Synthesis Scheme for Secure Multi-Beam Directional Modulation in Broadcasting Systems

Abstract: Recently, directional modulation has become an active research area in wireless communications due to its security. Unlike existing research work, we consider a multi-beam directional modulation (MBDM) scenario with imperfect desired direction knowledge. In such a setting, a robust synthesis scheme is proposed for MBDM in broadcasting systems. In order to implement the secure transmission of a confidential message, the beamforming vector of the confidential message is designed to preserve its power as possible in the desired directions by minimizing its leakage to the eavesdropper directions while the projection matrix of artificial noise (AN) is to minimize the effect on the desired directions and force AN to the eavesdropper directions by maximizing the average receive signal-to-artificial-noise ratio at desired receivers. Simulation results show that compared with conventional methods, the proposed robust scheme achieves much better bit error rate performance along desired directions for a given signal-to-noise ratio (SNR). From the secrecy-rate aspect, the proposed scheme performs better than conventional methods for almost all SNR regions. In particular, in the medium and high SNR regions, the rate improvement of the proposed scheme over conventional methods is significant.

Delay-multiply-and-sum-based synthetic aperture focusing in photoacoustic microscopy.

Abstract: We propose an improved version of a synthetic aperture focusing technique (SAFT) based on a delay-multiply-and-sum algorithm for acoustic-resolution photoacoustic microscopy (AR-PAM). In this method, the photoacoustic (PA) signals from multiple scan-lines are combinatorially coupled, multiplied, and then summed. This process can be considered a correlation operation of the PA signals in each scan-line, so the spatial coherent information between the PA signals can be efficiently extracted. By applying this method in conventional AR-PAM, lateral resolution and signal-to-noise ratio in out-of-focus regions are much improved compared with those estimated from the previously developed SAFT, respectively, thereby achieving the extension of the imaging focal region. Our phantom and in vivo imaging experiments prove the validity of our proposed method.

Adaptive digital fringe projection technique for high dynamic range three-dimensional shape measurement

Abstract: It is a challenge for any optical method to measure objects with a large range of reflectivity variation across the surface. Image saturation results in incorrect intensities in captured fringe pattern images, leading to phase and measurement errors. This paper presents a new adaptive digital fringe projection technique which avoids image saturation and has a high signal to noise ratio (SNR) in the three-dimensional (3-D) shape measurement of objects that has a large range of reflectivity variation across the surface. Compared to previous high dynamic range 3-D scan methods using many exposures and fringe pattern projections, which consumes a lot of time, the proposed technique uses only two preliminary steps of fringe pattern projection and image capture to generate the adapted fringe patterns, by adaptively adjusting the pixel-wise intensity of the projected fringe patterns based on the saturated pixels in the captured images of the surface being measured. For the bright regions due to high surface reflectivity and high illumination by the ambient light and surfaces interreflections, the projected intensity is reduced just to be low enough to avoid image saturation. Simultaneously, the maximum intensity of 255 is used for those dark regions with low surface reflectivity to maintain high SNR. Our experiments demonstrate that the proposed technique can achieve higher 3-D measurement accuracy across a surface with a large range of reflectivity variation.

Pseudo-Random High-Frequency Square-Wave Voltage Injection Based Sensorless Control of IPMSM Drives for Audible Noise Reduction

Abstract: High frequency (HF) signal injection is an effective sensorless control scheme for interior permanent-magnet synchronous motor (IPMSM) drives to achieve low and zero speed operation. However, the audible noise produced by the injected HF signal is often very shrill and harsh to hear, which restricts the actual application. In order to reduce the audible noise, a novel pseudo-random HF square-wave voltage injection scheme is proposed in this paper. The HF voltages with two different frequencies are randomly injected into the estimated rotor reference frame cycle by cycle, and a corresponding signal demodulation method for extracting the rotor position information is presented. Based on the principle analysis of this random frequency injection scheme, the digital time-delay effect in HF signal is considered and a compensation method for signal demodulation is proposed, which is effective in reducing position estimation error. Then, the power spectra density (PSD) in fixed frequency and pseudo-random frequency injection schemes are compared both theoretically and experimentally. The distribution of HF voltage and current PSD is extended by using the proposed injection scheme. Finally, this sensorless control method is verified by simulation and experiment on a 2.2-kW IPMSM drive platform.

GNSS multipath detection using three-frequency signal-to-noise measurements

Abstract: A new technique for detecting GNSS multipath interference by comparing signal-to-noise (SNR) measurements on three frequencies is presented. Depending on the phase lag of the reflected signal with respect to the direct signal, multipath interference can be either constructive or destructive, with a commensurate effect on the measured SNR. However, as the phase lag is frequency dependent, the SNR is perturbed differently on each frequency. Thus, by differencing SNR measurements on different frequencies and comparing the result with that obtained in a low-multipath environment, multipath can be detected. Using three frequencies makes the process more robust. A three-frequency SNR-based multipath detector has been developed and calibrated using measurements from GPS Block IIF satellites in a low-multipath environment. The new detector has been tested in a range of urban environments and its multipath detection capability verified by showing that the MP observables oscillate when the new detection statistic is above a threshold value determined using data collected in a low-multipath environment. The new detector is also sensitive to diffraction.

Systems and methods for imaging

Abstract: An imaging device has a light field imager and a processor The light field imager includes a microlens array, and a light field sensor positioned proximate to the microlens array, having a plurality of pixels and recording light field data of an optical target from light passing through the microlens array The processor is configured to: receive the light field data of the optical target from the light field sensor, estimate signal to noise ratio and depth of the optical target in the light field data, select a subset of sub-aperture images based on the signal to noise ratio and depth, combine the selected subset of sub-aperture images, and perform image analysis on the combined subset of sub-aperture images

Interference Alignment Based on Antenna Selection With Imperfect Channel State Information in Cognitive Radio Networks

Abstract: Interference alignment (IA) is a promising technique that can eliminate interference in wireless networks effectively and has been applied to spectrum sharing in cognitive radio (CR) networks. However, most existing IA schemes neglect the quality of the desired signal, which may lead to poor performance, particularly at poor channel status. In this paper, we analyze the problem of the decrease in the signal-to-interference-plus-noise ratio (SINR) of the desired signal and propose a novel IA scheme based on antenna selection (AS) to improve the received SINR of each user in IA-based CR networks. In the proposed scheme, multiple antennas are equipped at each secondary receiver, and some of them are chosen to achieve optimal performance. Furthermore, the condition of imperfect channel state information (CSI) is also considered, which can impact the performance of IA-AS. To face this problem, a scheme called CSI filtering is proposed to weaken the influence of the imperfect CSI. Moreover, considering the considerable computational complexity brought by the selection among mass of antenna combinations, an efficient IA-AS algorithm based on discrete stochastic optimization (DSO) is thus proposed, which can converge quickly to the optimum with low computational complexity. To further improve the tracking performance of the algorithm under a time-varying channel environment, we propose an adaptive DSO scheme with window CSI filtering for IA-AS to give the algorithm a good tracking capability. Simulation results are presented to show that the proposed schemes can significantly improve the performance of IA-based CR networks.

Linear Massive MIMO Precoders in the Presence of Phase Noise—A Large-Scale Analysis

Abstract: We study the impact of phase noise on the downlink performance of a multiuser multiple-input–multiple-output (MIMO) system, where the base station (BS) employs a large number of transmit antennas $M$ . We consider a setup where the BS employs $M_{\mathrm{osc}}$ free-running oscillators, and $M/M_{\mathrm{osc}}$ antennas are connected to each oscillator. For this configuration, we analyze the impact of phase noise on the performance of zero forcing (ZF), regularized ZF, and matched filter precoders when $M$ and the number of users $K$ are asymptotically large, whereas the ratio $M/K=\beta$ is fixed. We analytically show that the impact of phase noise on the signal-to-interference-plus-noise ratio (SINR) can be quantified as an effective reduction in the quality of the channel state information (CSI) available at the BS when compared with a system without phase noise. As a consequence, we observe that as $M_{\mathrm{osc}}$ increases, the SINR performance of all considered precoders degrades. On the other hand, the variance of the random phase variations caused by the BS oscillators reduces with increasing $M_{\mathrm{osc}}$ . Through Monte Carlo simulations, we verify our analytical results and compare the performance of the precoders for different phase noise and channel noise variances. For all considered precoders, we show that when $\beta$ is small, the performance of the setup where all BS antennas are connected to a single oscillator is superior to that of the setup where each BS antenna has its own oscillator. However, the opposite is true when $\beta$ is large and the signal-to-noise ratio (SNR) at the users is low.

Segmented CRC-Aided SC List Polar Decoding

Abstract: Because of the existence of channel noise, channel coding serves as an indispensable part of mobile communication system and the essential guarantee for the reliable, accurate, and effective transmission of information. As one of the most competitive channel code candidates for the 5th generation (5G) mobile communication, polar codes are the first codes which can provably achieve the symmetric capacity of binary-input discrete memoryless channels (B-DMCs). In this paper, the segmented CRC- aided successive cancellation list (SCA-SCL) polar decoding scheme is proposed for better tradeoff of performance and complexity. Numerical results on binary-input additive white Gaussian noise channel (BI-AWGNC) have shown that, at SNR of 0.5 dB, this approach successfully provides as high as 41.65% complexity reduction and similar decoding performance compared to state-of-the-art ones.

Energy-Efficient Symbol-Level Precoding in Multiuser MISO Based on Relaxed Detection Region

Abstract: This paper addresses the problem of exploiting interference among simultaneous multiuser transmissions in the downlink of multiple-antenna systems. Using symbol-level precoding, a new approach toward addressing the multiuser interference is discussed through jointly utilizing the channel state information (CSI) and data information (DI). The interference among the data streams is transformed under certain conditions to a useful signal that can improve the signal-to-interference noise ratio (SINR) of the downlink transmissions and as a result the system’s energy efficiency. In this context, new constructive interference precoding techniques that tackle the transmit power minimization (min power) with individual SINR constraints at each user’s receiver have been proposed. In this paper, we generalize the constructive interference (CI) precoding design under the assumption that the received MPSK symbol can reside in a relaxed region in order to be correctly detected. Moreover, a weighted maximization of the minimum SNR among all users is studied taking into account the relaxed detection region. Symbol error rate analysis (SER) for the proposed precoding is discussed to characterize the tradeoff between transmit power reduction and SER increase due to the relaxation. Based on this tradeoff, the energy efficiency performance of the proposed technique is analyzed. Finally, extensive numerical results show that the proposed schemes outperform other state-of-the-art techniques.

Molecular circuits for dynamic noise filtering

Abstract: The invention of the Kalman filter is a crowning achievement of filtering theory—one that has revolutionized technology in countless ways. By dealing effectively with noise, the Kalman filter has enabled various applications in positioning, navigation, control, and telecommunications. In the emerging field of synthetic biology, noise and context dependency are among the key challenges facing the successful implementation of reliable, complex, and scalable synthetic circuits. Although substantial further advancement in the field may very well rely on effectively addressing these issues, a principled protocol to deal with noise—as provided by the Kalman filter—remains completely missing. Here we develop an optimal filtering theory that is suitable for noisy biochemical networks. We show how the resulting filters can be implemented at the molecular level and provide various simulations related to estimation, system identification, and noise cancellation problems. We demonstrate our approach in vitro using DNA strand displacement cascades as well as in vivo using flow cytometry measurements of a light-inducible circuit in Escherichia coli.

Noise Robust Radar HRRP Target Recognition Based on Scatterer Matching Algorithm

Abstract: Since the signal-to-noise ratio (SNR) directly relates to the distance between the target and the radar for a given noise power and radar power, the noise robustness of a recognition algorithm is very important to increase the recognition distance between the target and the radar in the real application. In this paper, a novel noise-robust recognition method for high-resolution range profile (HRRP) data is proposed to enhance its recognition performance under the test condition of low SNR. The target dominant scatterers are first extracted based on the scattering center model of complex HRRP data via the orthogonal matching pursuit algorithm. Then, a scatterer matching recognition algorithm based on Hausdorff distance is developed with the magnitudes and locations of extracted dominant scatterers used as the feature patterns. Here, the noise reduction is accomplished based on the sparse distribution property of dominant scattering centers in a target. Experimental results on the synthetic and measured HRRP data demonstrate that the proposed method can improve the recognition performance under the relatively low SNR condition for both orthogonal and superresolution representations of scattering center model.

A Maximum-Likelihood Channel Estimator for Self-Interference Cancelation in Full-Duplex Systems

Abstract: Operation of full-duplex systems requires efficient mitigation of the self-interference signal caused by the simultaneous transmission/reception. In this paper, we propose a maximum-likelihood (ML) approach to jointly estimate the self-interference and intended channels by exploiting its own known transmitted symbols and both the known pilot and unknown data symbols from the other intended transceiver. The ML solution is obtained by maximizing the ML function under the assumption of Gaussian received symbols. A closed-form solution is first derived, and subsequently, an iterative procedure is developed to further improve the estimation performance at moderate-to-high signal-to-noise ratios (SNRs). We establish the initial condition to guarantee the convergence of the iterative algorithm to the ML solution. In the presence of considerable phase noise from the oscillators, a phase noise estimation method is proposed and combined with the ML channel estimator to mitigate the effects of the phase noise. Illustrative results show that the proposed methods offer good cancelation performance close to the Cramer–Rao bound (CRB).

Location Based Beamforming in 5G Ultra-Dense Networks

Abstract: In this paper we consider transmit (Tx) and receive (Rx) beamforming schemes based on the location of the device. In particular, we propose a design methodology for the Tx/Rx beamforming weight-vectors that is based on the departure and arrival angles of the line-of sight (LoS) path between accessnodes (ANds) and user-nodes (UNds). A network-centric extended Kalman filter (EKF) is also proposed for estimating and tracking the directional parameters needed for designing the Tx and Rx beamforming weights. The proposed approach is particularly useful in 5G ultra-dense networks (UDNs) since the high-probability of LoS condition makes it possible to design geometric beams at both Tx and Rx in order to increase the signal-to-interferenceplus- noise ratio (SINR). Moreover, relying on the location of the UNd relative to the ANds makes it possible to replace fullband uplink (UL) reference signals, commonly employed for acquiring the channel-state- information-at-transmitter (CSIT) in time- division-duplex (TDD) systems, by narrowband UL pilots. Also, employing the EKF for tracking the double-directional parameters of the LoS-path allows one to reduce the rate at which UL reference signals are transmitted. Consequently, savings in terms of time frequency resources are achieved compared to beamforming schemes based on full-band CSI. Extensive numerical results are included using a realistic ray-tracing based system-level simulator in ultra-dense 5G network context. Results show that position based beamforming schemes outperform those based on full-band CSI in terms of mean user-throughput even for highly mobile users.

A stacked contractive denoising auto-encoder for ECG signal denoising.

Abstract: As a primary diagnostic tool for cardiac diseases, electrocardiogram (ECG) signals are often contaminated by various kinds of noise, such as baseline wander, electrode contact noise and motion artifacts. In this paper, we propose a contractive denoising technique to improve the performance of current denoising auto-encoders (DAEs) for ECG signal denoising. Based on the Frobenius norm of the Jacobean matrix for the learned features with respect to the input, we develop a stacked contractive denoising auto-encoder (CDAE) to build a deep neural network (DNN) for noise reduction, which can significantly improve the expression of ECG signals through multi-level feature extraction. The proposed method is evaluated on ECG signals from the bench-marker MIT-BIH Arrhythmia Database, and the noises come from the MIT-BIH noise stress test database. The experimental results show that the new CDAE algorithm performs better than the conventional ECG denoising method, specifically with more than 2.40 dB improvement in the signal-to-noise ratio (SNR) and nearly 0.075 to 0.350 improvements in the root mean square error (RMSE).

Energy-Based Modulation for Noncoherent Massive SIMO Systems

Abstract: An uplink system with a single antenna transmitter and a single receiver with a large number of antennas is considered. We propose a single-shot noncoherent scheme which does not use the instantaneous channel state information (CSI), but rather only the knowledge of the channel statistics, a transmitter that modulates information only in the amplitude of the symbols, and a receiver which measures only the average received energy across the antennas. This system model is motivated by the simplicity of the circuit design and the energy efficiency it entails for both the transmitter and the receiver. We propose constellation designs which are asymptotically optimal with respect to symbol error rate (SER) with an increasing number of antennas, for any finite signal-to-noise power ratio (SNR), under different assumptions on the availability of CSI statistics. We describe in detail the case when there is a bounded uncertainty on the moments of the fading distribution. We present the numerical results on the SER performance achieved by these designs and find that they outperform the existing amplitude-modulation-based noncoherent scheme of amplitude shift keying (ASK). They also achieve a smaller peak-to-average power ratio (PAPR) for scenarios with a low SNR or a large line-of-sight (LOS) component.