Minimum Mean Square Error Criterion Research Articles

Performance Study of Multipath Effect in 5G Millimeter-Wave Channel

5G has been essentially a buzzword for several years, but according to the experts, from 2022 onward, there will be an inflection point between network maturity and the availability of 5G. To make 5G a reality, we must minimize all propagation losses. One of the possible factors that reduces the performance of 5G transmission is the multipath effect. In this paper, we investigate the severity of the multipath effect in the 5G millimeter-wave (mmWave) channel and mitigate the multipath effect using adaptive equalization based on the least mean square (LMS) algorithm to improve the performance of 5G wireless signal transmission. A mmWave channel simulator, NYUSIM, provides complete data for all resolvable multipaths in a specific channel configuration. An analysis of bit-error-rate (BER) based on the minimum BER (MBER) and minimum mean square error (MMSE) optimization criterion is performed to measure the improved performance of a 5G data channel simulated under line-of-sight (LOS) and non-LOS (NLOS) paths. A good overall performance of BER based on the MBER and MMSE criteria is attained using the LMS equalization method in a micro-urban area at a maximum data rate of 50 Mbps. For both LOS and NLOS conditions, the increase in data rate to 55.56 Mbps and 62.5 Mbps causes a significant decrease in BER performance. In conclusion, the primary factor affecting the BER performance is the data rate, not the frequency or transmitter-to-receiver distance.

Performance Study of Multipath Effect in 5G Millimeter-Wave Channel

5G has been essentially a buzzword for several years, but according to the experts, from 2022 onward, there will be an inflection point between network maturity and the availability of 5G. To make 5G a reality, we must minimize all propagation losses. One of the possible factors that reduces the performance of 5G transmission is the multipath effect. In this paper, we investigate the severity of the multipath effect in the 5G millimeter-wave (mmWave) channel and mitigate the multipath effect using adaptive equalization based on the least mean square (LMS) algorithm to improve the performance of 5G wireless signal transmission. A mmWave channel simulator, NYUSIM, provides complete data for all resolvable multipaths in a specific channel configuration. An analysis of bit-error-rate (BER) based on the minimum BER (MBER) and minimum mean square error (MMSE) optimization criterion is performed to measure the improved performance of a 5G data channel simulated under line-of-sight (LOS) and non-LOS (NLOS) paths. A good overall performance of BER based on the MBER and MMSE criteria is attained using the LMS equalization method in a micro-urban area at a maximum data rate of 50 Mbps. For both LOS and NLOS conditions, the increase in data rate to 55.56 Mbps and 62.5 Mbps causes a significant decrease in BER performance. In conclusion, the primary factor affecting the BER performance is the data rate, not the frequency or transmitter-to-receiver distance.

A Robust GPS Navigation Filter Based on Maximum Correntropy Criterion with Adaptive Kernel Bandwidth

Multiple forms of interference and noise that impact the receiver’s capacity to receive and interpret satellite signals, and consequently the preciseness of positioning and navigation, may be present during the processing of Global Positioning System (GPS) navigation. The non-Gaussian noise predominates in the signal owing to the fluctuating character of both natural and artificial electromagnetic interference, and the algorithm based on the minimum mean-square error (MMSE) criterion performs well when assuming Gaussian noise, but drops when assuming non-Gaussian noise. The maximum correntropy criteria (MCC) adaptive filtering technique efficiently reduces pulse noise and has adequate performance in heavy-tailed noise, which addresses the issue of filter performance caused by the presence of non-Gaussian or heavy-tailed unusual noise values in the localizing measurement noise. The adaptive kernel bandwidth (AKB) technique employed in this paper applies the calculated adaptive variables to generate the kernel function matrix, in which the adaptive factor can modify the size of the kernel width across a reasonably appropriate spectrum, substituting the fixed kernel width for the conventional MCC to enhance the performance. The conventional maximum correntropy criterion-based extended Kalman filter (MCCEKF) algorithm’s performance is significantly impacted by the value of the kernel width, and there are certain predetermined conditions in the selection based on experience. The MCCEKF with a fixed adaptive kernel bandwidth (MCCEKF-AKB) has several advantages due to its novel concept and computational simplicity, and gives a qualitative solution for the study of random structures for generalized noise. Additionally, it can effectively achieve the robust state estimation of outliers with anomalous values while guaranteeing the accuracy of the filtering.

Multiple similarity measure-based maximum correntropy criterion Kalman filter with adaptive kernel width for GPS/INS integration navigation

The filter based on the maximum correntropy criterion (MCC) has low sensitivity to non-Gaussian noise, which can effectively improve the robustness of the filter. However, the uncertainty of kernel width restricted the application of the maximum correntropy criterion Kalman filter (MCCKF) in the integrated navigation system. In order to overcome the above difficulty, this paper proposes a multiple similarity measure-based maximum correntropy criterion Kalman filter with adaptive kernel width (ABMCCKF). ABMCCKF uses the MORKF framework and distinguishes the noise polluted by outliers through a designed protecting window, which also ensures that the kernel width is compatible with the noise pollution level. Through the window, ABMCCKF utilizes the optimality of both MCC and the minimum mean square error criterion (MMSE). Simulations and vehicular experiments are used to verify the effectiveness of the method. The results show that the ABMCCKF have a good performance when the optimal kernel width is uncertain.

A Soft Sensor for Estimating Tire Cornering Properties for Intelligent Tires

Intelligent tire systems are promising solutions for achieving precise vehicle state estimations, localization, and motion control in the context of autonomous driving. Tire cornering properties, namely, lateral force, aligning moment, and pneumatic trail, are crucial factors that should be accurately estimated for vehicle dynamics control purposes. In this work, a soft sensor for estimating tire cornering properties based on intelligent tire and machine learning is developed. The intelligent tire system is based on a triaxial accelerometer mounted on the inner liner of the tire tread, which provides acceleration measurements from the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$x$</tex-math> </inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$y$</tex-math> </inline-formula> , and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$z$</tex-math> </inline-formula> directions. Partial least squares and variable importance in the projection scores (PLS-VIP) are used in the feature extraction of the acceleration signals over the contact patch. A Gaussian process regression (GPR) model is trained to predict the cornering properties with confidence intervals under different input conditions. Based on the variances in the GPR predictions and minimum mean-square error criterion, a data fusion method for pneumatic trail estimation is proposed. It is demonstrated that the developed GPR models for cornering properties and the data fusion method for pneumatic trail estimation have satisfactory accuracy and reliability. The experimental results show that the soft sensor proposed in this work is a strong candidate for further applications in the development of vehicle state estimation and control algorithms.

State of charge estimation for Li-ion batteries based on iterative Kalman filter with adaptive maximum correntropy criterion

Nonlinear filter methods are commonly employed for model-driven based battery state of charge (SOC) estimation because of their ability to suppress Gaussian noise. Due to the uncertainty of complicated operational conditions, the minimum mean square error (MMSE) criterion based Kalman filter (KF) methods may not guarantee sufficient SOC estimation accuracy in the presence of non-Gaussian noise. To enhance the anti-interference performance of the KFs based SOC estimation method, a novel methodology that combines the adaptive kernel width based maximum correntropy criterion (AMCC) with the Levenberg-Marguardt (L-M) principle based adaptive iterative extended KF (AIEKF) is proposed. Firstly, the MMSE criterion of the EKF is replaced by the MCC criterion and an adaptive kernel width strategy is designed to weaken the effect of anomalous data. Then, the AMCC-corrected covariance matrix and state are updated using an L-M optimized multi-step iterative filter during the measurement update phase. Finally, the combination of AMCC and AIEKF is devised to execute SOC estimation. Several sets of data from different temperatures and operational conditions are used to verify the validity of the proposed AMCC-AIEKF method. Compared with the adaptive EKF (AEKF) and the adaptive iterative EKF (AIEKF) method, the AMCC-AIEKF method has the advantage in terms of SOC estimation accuracy and robustness under different operational conditions with noiseless, Gaussian noise and non-Gaussian noise.

Model-Driven Based Deep Unfolding Equalizer for Underwater Acoustic OFDM Communications

It is challenging to design an equalizer for the complex time-frequency doubly-selective channel. In this paper, we employ the deep unfolding approach to establish an equalizer for the underwater acoustic (UWA) orthogonal frequency division multiplexing (OFDM) system, namely UDNet. Each layer of UDNet is designed according to the classical minimum mean square error (MMSE) equalizer. Moreover, we consider the QPSK equalization as a four-classification task and adopt minimum Kullback-Leibler (KL) to achieve a smaller symbol error rate (SER) with the one-hot coding instead of the MMSE criterion. In addition, we introduce a sliding structure based on the banded approximation of the channel matrix to reduce the network size and aid UDNet to perform well for different-length signals without changing the network structure. Furthermore, we apply the measured at-sea doubly-selective UWA channel and offshore background noise to evaluate the proposed equalizer. Experimental results show that the proposed UDNet performs better with low computational complexity. Concretely, the SER of UDNet is nearly an order of magnitude lower than that of MMSE.

DV-Hop Algorithm Based on Multi-Objective Salp Swarm Algorithm Optimization.

The localization of sensor nodes is an important problem in wireless sensor networks. The DV-Hop algorithm is a typical range-free algorithm, but the localization accuracy is not high. To further improve the localization accuracy, this paper designs a DV-Hop algorithm based on multi-objective salp swarm optimization. Firstly, hop counts in the DV-Hop algorithm are subdivided, and the average hop distance is corrected based on the minimum mean-square error criterion and weighting. Secondly, the traditional single-objective optimization model is transformed into a multi-objective optimization model. Then, in the third stage of DV-Hop, the improved multi-objective salp swarm algorithm is used to estimate the node coordinates. Finally, the proposed algorithm is compared with three improved DV-Hop algorithms in two topologies. Compared with DV-Hop, The localization errors of the proposed algorithm are reduced by 50.79% and 56.79% in the two topology environments with different communication radii. The localization errors of different node numbers are decreased by 38.27% and 56.79%. The maximum reductions in localization errors are 38.44% and 56.79% for different anchor node numbers. Based on different regions, the maximum reductions in localization errors are 56.75% and 56.79%. The simulation results show that the accuracy of the proposed algorithm is better than that of DV-Hop, GWO-DV-Hop, SSA-DV-Hop, and ISSA-DV-Hop algorithms.

Dual Extended Kalman Filter Under Minimum Error Entropy With Fiducial Points

The multivariate autoregressive (MVAR) model is widely used in describing the dynamics of nonlinear systems, in which the estimates of model parameters and underlying states can be achieved by dual extended Kalman filter (DEKF). However, when the measurements are corrupted by complicated non-Gaussian noises, the DEKF based on the minimum mean-square error (MMSE) criterion may provide biased estimates. In the present article, we develop a novel dual Kalman-type filter, referred to as DEKF under minimum error entropy (MEE) with fiducial points (MEEFs-DEKF) to deal with the non-Gaussian noises. First, the equivalent state-space model and parameter-space model are presented based on the MVAR model. Then, an optimality criterion based on MEE with fiducial points (MEEFs) is applied in the batch-mode regression equation to improve the robustness. Finally, a fixed-point iteration algorithm gives the posterior estimates of state and parameter. Simulation results confirm that the proposed MEEF-DEKF can achieve excellent performance in various noises with different distributions, especially in heavy-tailed and multimodal noises.

Transceiver Optimization for Two-Hop AF MIMO Relay Systems With DFE Receiver and Direct Link

In this paper, we consider precoding and receiving matrices optimization for a two-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay system with a decision feedback equalizer (DFE) at the destination node in the presence of the direct source-destination link. By adopting the minimum mean-squared error (MMSE) criterion, we develop two new transceiver design algorithms for such a system. The first one employs an iterative procedure to design the source, relay, feed-forward, and feedback matrices. The second algorithm is a non-iterative suboptimal approach which decomposes the optimization problem into two tractable subproblems and obtains the source and relay precoding matrices by solving the two subproblems sequentially. Simulation results validate the better MSE and bit-error-rate (BER) performance of the proposed algorithms and show that the non-iterative suboptimal method has a negligible performance loss when the ratio of the source node transmission power to the relay node transmission power is small. In addition, the computational complexity analysis suggests that the second algorithm and one iteration of the first algorithm have the same order of complexity. As the first algorithm typically converges within a few iterations, both proposed algorithms exhibit a low complexity order.

Modulating Intelligent Surfaces for Multiuser MIMO Systems: Beamforming and Modulation Design

This paper introduces a novel approach of utilizing the reconfigurable intelligent surface (RIS) for joint data modulation and signal beamforming in a multi-user downlink cellular network by leveraging the idea of backscatter communication. We present a general framework in which the RIS, referred to as modulating intelligent surface (MIS) in this paper, is used to: <inline-formula> <tex-math notation="LaTeX">$i$ </tex-math></inline-formula>) beamform the signals for a set of users whose data modulation is already performed by the base station (BS), and at the same time, <inline-formula> <tex-math notation="LaTeX">$ii$ </tex-math></inline-formula>) embed the data of a different set of users by passively modulating the deliberately sent carrier signals from the BS to the RIS. To maximize each user&#x2019;s spectral efficiency, a joint non-convex optimization problem is formulated under the sum minimum mean-square error (MMSE) criterion. Alternating optimization is used to divide the original joint problem into two tasks of: <inline-formula> <tex-math notation="LaTeX">$i$ </tex-math></inline-formula>) separately optimizing the MIS phase-shifts for passive beamforming along with data embedding for the BS- and MIS-served users, respectively, and <inline-formula> <tex-math notation="LaTeX">$ii$ </tex-math></inline-formula>) jointly optimizing the active precoder and the receive scaling factor for the BS- and MIS-served users, respectively. While the solution to the latter joint problem is found in closed-form using traditional optimization techniques, the optimal phase-shifts at the MIS are obtained by deriving the appropriate optimization-oriented vector approximate message passing (OOVAMP) algorithm. Moreover, the original joint problem is solved under both ideal and practical constraints on the MIS phase shifts, namely, the unimodular constraint and assuming each MIS element to be terminated by a variable reactive load. The proposed MIS-assisted scheme is compared against state-of-the-art RIS-assisted wireless communication schemes and simulation results reveal that it brings substantial improvements in terms of system throughput while supporting a much higher number of users.

Mixture Correntropy-Based Kernel Extreme Learning Machines.

Kernel-based extreme learning machine (KELM), as a natural extension of ELM to kernel learning, has achieved outstanding performance in addressing various regression and classification problems. Compared with the basic ELM, KELM has a better generalization ability owing to no needs of the number of hidden nodes given beforehand and random projection mechanism. Since KELM is derived under the minimum mean square error (MMSE) criterion for the Gaussian assumption of noise, its performance may deteriorate under the non-Gaussian cases, seriously. To improve the robustness of KELM, this article proposes a mixture correntropy-based KELM (MC-KELM), which adopts the recently proposed maximum mixture correntropy criterion as the optimization criterion, instead of using the MMSE criterion. In addition, an online sequential version of MC-KELM (MCOS-KELM) is developed to deal with the case that the data arrive sequentially (one-by-one or chunk-by-chunk). Experimental results on regression and classification data sets are reported to validate the performance superiorities of the new methods.

Heteroscedasticity and Precise Estimation Model Approach for Complex Financial Time-Series Data: An Example of Taiwan Stock Index Futures before and during COVID-19

In this paper, we provide a mathematical and statistical methodology using heteroscedastic estimation to achieve the aim of building a more precise mathematical model for complex financial data. Considering a general regression model with explanatory variables (the expected value model form) and the error term (including heteroscedasticity), the optimal expected value and heteroscedastic model forms are investigated by linear, nonlinear, curvilinear, and composition function forms, using the minimum mean-squared error criterion to show the precision of the methodology. After combining the two optimal models, the fitted values of the financial data are more precise than the linear regression model in the literature and also show the fitted model forms in the example of Taiwan stock price index futures that has three cases: (1) before COVID-19, (2) during COVID-19, and (3) the entire observation time period. The fitted mathematical models can apparently show how COVID-19 affects the return rates of Taiwan stock price index futures. Furthermore, the fitted heteroscedastic models also show how COVID-19 influences the fluctuations of the return rates of Taiwan stock price index futures. This methodology will contribute to the probability of building algorithms for computing and predicting financial data based on mathematical model form outcomes and assist model comparisons after adding new data to a database.

Complex multi-kernel random Fourier adaptive algorithms under the complex kernel risk-sensitive p-power loss

The complex least mean square (CLMS) adaptive algorithm based on the minimum mean square error (MSE) criterion has been widely used for linear applications with Gaussian noises in complex domain. However, the MSE criterion suffers from performance degeneration in the presence of non-Gaussian noise. To address this issue, a novel complex kernel risk-sensitive p-power loss (CKRSP-L) criterion is first constructed to combat non-Gaussian noises. Then, based on the constructed CKRSP-L criterion, a novel complex kernel risk-sensitive p-power (CKRSP) algorithm is proposed to provide robustness to non-Gaussian noises and performance improvement for linear systems, simultaneously. Further, to extend the CKRSP algorithm into nonlinear systems, a novel complex multi-kernel random Fourier mapping (CMRFM) is proposed to transform the original input data into a complex multi-kernel random Fourier features space (CMRFFS), and thus another novel complex multi-kernel random Fourier kernel risk-sensitive p-power (CMRFKRSP) algorithm is presented for nonlinear applications in complex domain. Finally, the steady-state excess mean square errors (SEMSEs) of CKRSP and CMRFKRSP are also calculated for theoretical analysis of performance. Monte Carlo simulations conducted in different noise environments validate the correctness of the obtained SEMSEs and performance advantages of CKRSP and CMRFKRSP.

Linear and Nonlinear Regression-Based Maximum Correntropy Extended Kalman Filtering

The extended Kalman filter (EKF) is a method extensively applied in many areas, particularly, in nonlinear target tracking. The optimization criterion commonly used in EKF is the celebrated minimum mean square error (MMSE) criterion, which exhibits excellent performance under Gaussian noise assumption. However, its performance may degrade dramatically when the noises are heavy tailed. To cope with this problem, this paper proposes two new nonlinear filters, namely the linear regression maximum correntropy EKF (LRMCEKF) and nonlinear regression maximum correntropy EKF (NRMCEKF), by applying the maximum correntropy criterion (MCC) rather than the MMSE criterion to EKF. In both filters, a regression model is formulated, and a fixed-point iterative algorithm is utilized to obtain the posterior estimates. The effectiveness and robustness of the proposed algorithms in target tracking are confirmed by an illustrative example.

Dynamically Subarray-Connected Hybrid Precoding Scheme for Multiuser Millimeter-Wave Massive MIMO Systems

Hybrid precoding is widely used in millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems. However, most prior work on hybrid precoding focused on the fully connected hybrid architectures and the subconnected but fixed architectures in which each radio frequency (RF) chain is connected to a specific subset of the antennas. The limited work shows that dynamic subarray architectures address the tradeoff between achievable spectral efficiency and energy efficiency of mmWave massive MIMO systems. Nevertheless, in the multiuser hybrid precoding systems, the existing dynamic subarray schemes ignore the fairness of users and the problem of user selection. In this paper, we propose a novel multiuser hybrid precoding scheme for dynamic subarray architectures. Firstly, we select a multiuser set among all users according to the analog effective channel information of the base station (BS) and then design the subset of the antennas to each RF by the fairness antenna-partitioning algorithm. Finally, the optimal analog precoding vector is designed according to each subarray, and the digital precoding is designed by the minimum mean-squared error (MMSE) criterion. The simulation results show that the performance advantages of the proposed multiuser hybrid precoding scheme for dynamic subarray architectures.

Tomlinson-Harashima Precoded Rate-Splitting With Stream Combiners for MU-MIMO Systems

This article introduces multiuser multiple-input multiple-output (MU-MIMO) architectures based on non-linear precoding and stream combining techniques using rate-splitting (RS), where the transmitter often has only partial knowledge of the channel state information (CSI). In contrast to existing works, we consider deployments where the receivers may be equipped with multiple antennas. This allows us to employ linear combining techniques based on the Min-Max, the maximum ratio and the minimum mean-square error criteria along with Tomlinson-Harashima precoders (THP) for RS-based MU-MIMO systems to enhance the sum-rate performance. Moreover, we incorporate the Multi-Branch (MB) concept into the RS architecture to further improve the sum-rate performance. Closed-form expressions for the signal-to-interference-plus-noise ratio and the sum-rate at the receiver end are devised through statistical analysis. Simulation results show that the proposed RS-THP schemes achieve better performance than conventional linear and THP precoders.

Fixed-Point Minimum Error Entropy With Sparsity Penalty Constraints

In recent years, the sparse system identification (SSI) has received increasing attention, and various sparsity-aware adaptive algorithms based on the minimum mean square error (MMSE) criterion have been developed, which are optimal under the assumption of Gaussian distributions. However, the Gaussian assumption does not always hold in real-world environments. The maximum correntropy criterion (MCC) is used to replace the MMSE criterion to suppress the heavy-tailed non-Gaussian noises. For some more complex non-Gaussian noises such as those from multimodal distributions, the minimum error entropy (MEE) criterion can outperform MCC although it is computationally somewhat more expensive. To improve the performance of SSI in non-Gaussian noises, in this brief we develop a class of sparsity-aware MEE algorithms with the fixed point iteration (MEE-FP) by incorporating the zero-attracting ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm), reweighted zero-attracting (reweighted <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm) and correntropy induced metric (CIM) penalty terms into the cost function. The corresponding algorithms are termed as ZA-MEE-FP, RZA-MEE-FP, and CIM-MEE-FP, which can achieve better performance than the original MEE-FP algorithm and the MCC based sparsity-aware algorithms. Simulation results confirm the excellent performance of the new algorithms.

Channel Estimation and Robust Detection for IQ Imbalanced Uplink Massive MIMO-OFDM With Adjustable Phase Shift Pilots

In this paper, we investigate channel estimation and robust detection for uplink massive multi-input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) systems with in-phase and quadrature-phase imbalances (IQI). We represent the received signal with a real-valued model, where the combination of the IQI and the wireless channel is treated as the effective channel. Based on the real-valued model, we then perform the minimum mean square error (MMSE) criterion based estimation for the effective channel. We use adjustable phase shift pilots (APSPs) to reduce the pilot overhead and verify that the MSE of the effective channel estimation can be minimized by scheduling the pilot phase shifts properly. We propose a pilot phase shift scheduling algorithm based on the covariance matrices of the effective channels. Since the channel estimation performance might be degraded due to using APSPs, we develop an MMSE criterion based data detection scheme which is robust to the channel estimation error. Using operator-valued free probability theory, we derive an asymptotic deterministic equivalent for the ergodic achievable sum rate of the proposed detection scheme. The performance of the channel estimation with APSPs and the robust data detection is demonstrated via extensive numerical results.

Signal Intensity Estimation in Transdermal Optical Wireless Links with Stochastic Pointing Errors Effect

Transdermal optical wireless (TOW) communication links have recently gained particular research and commercial attention as a viable alternative for establishing high speed and effective implantable data transmissions, which is vital for a variety of neuroprosthetic and other medical applications. However, the development of this optical telemetry modality with medical implanted devices (IMDs) is adversely affected by skin-induced photon absorption, scattering and pointing errors effects. Thus, in this work a minimum mean-square error (MMSE) criterion is proposed for the estimation of the optical signal intensity in a typical TOW link of varying path loss and misalignment-induced fading characteristics. In this context, the stochastic nature of the transmitter–receiver misalignment has been considered and jointly modeled with transdermal path loss. Additionally, the link is assumed to employ the suitable On–Off Keying (OOK) with intensity modulation and direct detection scheme as well as a PIN photodiode at the receiver side for signal detection. Under these assumptions the results demonstrate that the stochastic amount of pointing mismatch strongly affects the received irradiance estimation.