Showing papers on "Complex normal distribution published in 2010"
TL;DR: In this article, the authors show that at least 12 degrees-of-freedom is achievable for all values of complex Gaussian channel coefficients except for a subset of measure zero for the class of linear beamforming and interference alignment schemes considered in this paper.
Abstract: It has been conjectured by Ho-Madsen and Nosratinia that complex Gaussian interference channels with constant channel coefficients have only one degree-of-freedom regardless of the number of users While several examples are known of constant channels that achieve more than 1 degree-of-freedom, these special cases only span a subset of measure zero In other words, for almost all channel coefficient values, it is not known if more than 1 degree-of-freedom is achievable In this paper, we settle the Host-Madsen-Nosratinia conjecture in the negative We show that at least 12 degrees-of-freedom are achievable for all values of complex channel coefficients except for a subset of measure zero For the class of linear beamforming and interference alignment schemes considered in this paper, it is also shown that 12 is the maximum number of degrees-of-freedom achievable on the complex Gaussian 3 user interference channel with constant channel coefficients, for almost all values of channel coefficients To establish the achievability of 12 degrees-of-freedom we use the novel idea of asymmetric complex signaling - ie, the inputs are chosen to be complex but not circularly symmetric It is shown that unlike Gaussian point-to-point, multiple-access and broadcast channels where circularly symmetric complex Gaussian inputs are optimal, for interference channels optimal inputs are in general asymmetric With asymmetric complex signaling, we also show that the 2 user complex Gaussian X channel with constant channel coefficients achieves the outer bound of 4/3 degrees-of-freedom, ie, the assumption of time-variations/frequency-selectivity used in prior work to establish the same result, is not needed
260 citations
TL;DR: In this article, the authors prove that the empirical spectral distribution of a complex random nxn matrix converges to the uniform distribution over the unit disk in the complex plane under the finite fourth moment assumption on matrix elements.
120 citations
01 Dec 2010
TL;DR: This paper shows that the symbol error rate (SER) of a flat fading communications system can be expressed in closed form by expressing the demodulator outputs as random variable (RVs) that have a complex ratio distribution, which is the ratio of two correlated complex Gaussian RVs.
Abstract: Communications systems rarely have perfect channel state information (PCSI) when demodulating received symbols. This paper shows that the symbol error rate (SER) of a flat fading communications system can be expressed in closed form by expressing the demodulator outputs as random variable (RVs) that have a complex ratio distribution, which is the ratio of two correlated complex Gaussian RVs. To complete the analysis, the complex ratio probability density function (PDF) and cumulative distribution function (CDF) are both derived. Finally, using several scenarios based on M-QAM signaling, the SER performance of imperfect channel state information (ICSI) systems is analyzed.
61 citations
TL;DR: In this paper, a family of random matrix ensembles interpolating between the Ginibre ensemble of n × n matrices with iid centered complex Gaussian entries and the Gaussian unitary ensemble (GUE) is considered.
Abstract: A family of random matrix ensembles interpolating between the Ginibre ensemble of n × n matrices with iid centered complex Gaussian entries and the Gaussian unitary ensemble (GUE) is considered. The asymptotic spectral distribution in these models is uniform in an ellipse in the complex plane, which collapses to an interval of the real line as the degree of non-Hermiticity diminishes. Scaling limit theorems are proven for the eigenvalue point process at the rightmost edge of the spectrum, and it is shown that a non-trivial transition occurs between Poisson and Airy point process statistics when the ratio of the axes of the supporting ellipse is of order n −1/3. In this regime, the family of limiting probability distributions of the maximum of the real parts of the eigenvalues interpolates between the Gumbel and Tracy–Widom distributions.
42 citations
13 Jun 2010
TL;DR: It is shown that random matrix theory can be successfully applied to find the SINR distribution of each stream for each user with channel uncertainty, which allows easy calculation of useful performance metrics like symbol error-rate and achievable sum rate.
Abstract: This paper provides a simple closed-form SINR expression for interference alignment over MIMO channels with channel uncertainty. Assuming linear processing (specifically, zero-forcing) at the transmitters and receivers and a complex Gaussian interference channel, we show that random matrix theory can be successfully applied to find the SINR distribution of each stream for each user with channel uncertainty. Perfect channel knowledge constitutes a special case. This SINR distribution allows easy calculation of useful performance metrics like symbol error-rate and achievable sum rate.
29 citations
TL;DR: The experimental results show that using the CGSM of complex wavelet coefficients visually improves the quality of denoised images from the real case.
Abstract: In this paper, we propose the complex Gaussian scale mixture (CGSM) to model the complex wavelet coefficients as an extension of the Gaussian scale mixture (GSM), which is for real-valued random variables to the complex case. Along with some related propositions and miscellaneous results, we present the probability density functions of the magnitude and phase of the complex random variable. Specifically, we present the closed forms of the probability density function (pdf) of the magnitude for the case of complex generalized Gaussian distribution and the phase pdf for the general case. Subsequently, the pdf of the relative phase is derived. The CGSM is then applied to image denoising using the Bayes least-square estimator in several complex transform domains. The experimental results show that using the CGSM of complex wavelet coefficients visually improves the quality of denoised images from the real case.
29 citations
TL;DR: In this article, the authors studied the probability that f has no zeros in the disk and showed that as r → ∞, there exists r 0 so that every random function of the form (★) must vanish from the disk {z| < r 0 }.
Abstract: Consider the random entire function where the ϕ n are independent and identically distributed (i.i.d.) standard complex Gaussian variables. The zero set of this function is distinguished by invariance of its distribution with respect to the isometries of the plane. We study the probability P H (r) that f has no zeros in the disk {|z| < r} (hole probability). Improving a result of Sodin and Tsirelson, we show that as r → ∞. The proof does not use distribution invariance of the zeros, and can be extended to other Gaussian Taylor series. If ϕ n are compactly supported random variables instead of Gaussians, we get a very different result: there exists r 0 so that every random function of the form (★) must vanish in the disk {|z| < r 0 }.
29 citations
TL;DR: The correlated coefficient of non-normal variables is expressed as a function of the correlation coefficient of normal variables using piece-wise linear approximation of each univariate transform of normal to anything, and the second order moments of a multiply truncated bivariate normal distribution.
Abstract: The correlation coefficient of non-normal variables is expressed as a function of the correlation coefficient of normal variables using piece-wise linear approximation of each univariate transform of normal to anything, and the second order moments of a multiply truncated bivariate normal distribution. For the inverse problem, an algorithm iterates this analytic function in order to assign a normal correlation coefficient to two non-normal variables. The algorithm is applied for the generation of randomized bivariate samples with given correlation coefficient and marginal distributions and used in a randomization test for bivariate nonlinearity. The test correctly does not reject the null hypothesis of linear correlation if the nonlinearity is plausible and due to the sample transform alone.
19 citations
TL;DR: New cumulative distribution function (cdf) mapping methods to generate complex Nakagami sequences from complex Gaussian sequences, based on the independent transformation of their real and imaginary parts are developed.
Abstract: The availability of an accurate and systematic channel simulation technique is critical for the verification of the performance of digital radio transceivers designed for use on wireless channels. Despite the abundant results on channel simulation techniques available in the literature, an accurate technique for simulating Nakagami- m fading signals that have nonuniform phase distributions and any prespecified temporal autocorrelation function is not yet available. Such a technique is reported for the first time in this paper. We develop new cumulative distribution function (cdf) mapping methods to generate complex Nakagami sequences from complex Gaussian sequences, based on the independent transformation of their real and imaginary parts. Additionally, we analyze the relationships between the autocorrelation functions of Rayleigh and Nakagami fading signals to determine the autocorrelation function of Rayleigh input that is required to produce a specified autocorrelation function for the Nakagami output. Then, we implement the mapping algorithm to transform Rayleigh sequences with the so-determined autocorrelation functions into Nakagami sequences with the desired prespecified autocorrelation functions. Simulation results verify that our approaches can lead to the accurate simulation of Nakagami fading signals with prespecified autocorrelation functions and nonuniform phase distributions.
18 citations
Posted Content•
TL;DR: In order to derive the gradients needed to develop the complex kernel LMS (CKLMS), the notion of Writinger's calculus is extended to include complex RKHSs, and it is verified that the CKLMS offers significant performance improvements over the traditional complex LMS or Widely Linear complex L MS algorithms, when dealing with nonlinearities.
Abstract: Although the real reproducing kernels are used in an increasing number of machine learning problems, complex kernels have not, yet, been used, in spite of their potential interest in applications such as communications. In this work, we focus our attention on the complex gaussian kernel and its possible application in the complex Kernel LMS algorithm. In order to derive the gradients needed to develop the complex kernel LMS (CKLMS), we employ the powerful tool of Wirtinger's Calculus, which has recently attracted much attention in the signal processing community. Writinger's calculus simplifies computations and offers an elegant tool for treating complex signals. To this end, the notion of Writinger's calculus is extended to include complex RKHSs. Experiments verify that the CKLMS offers significant performance improvements over the traditional complex LMS or Widely Linear complex LMS (WL-LMS) algorithms, when dealing with nonlinearities.
16 citations
15 Sep 2010
TL;DR: In this paper, a complex kernel LMS (CKLMS) is proposed for nonlinear signal processing problems, where the gradients needed to develop the complex kernel are derived from the Wirtinger's calculus.
Abstract: Although the real reproducing kernels are used in an increasing number of machine learning problems, complex kernels have not, yet, been used, in spite of their potential interest in applications such as communications In this work, we focus our attention on the complex gaussian kernel and its possible application in the complex Kernel LMS algorithm In order to derive the gradients needed to develop the complex kernel LMS (CKLMS), we employ the powerful tool of Wirtinger's Calculus, which has recently attracted much attention in the signal processing community Writinger's calculus simplifies computations and offers an elegant tool for treating complex signals To this end, the notion of Writinger's calculus is extended to include complex RKHSs Experiments verify that the CKLMS offers significant performance improvements over the traditional complex LMS or Widely Linear complex LMS (WL-LMS) algorithms, when dealing with nonlinearities
TL;DR: In this paper, a comparative analysis of transmit diversity and beamforming for linear and circular antenna arrays in a wireless commu- nications system is presented, where the perturbations are modeled as additive random errors, following complex Gaussian multivariate dis- tribution, to the antenna array steering vectors.
Abstract: A comparative analysis of transmit diversity and beam- forming for linear and circular antenna arrays in a wireless commu- nications system is presented. The objective is to examine the efiect of random perturbations, angular power distributions on transmit di- versity and beamforming system. The perturbations are modeled as additive random errors, following complex Gaussian multivariate dis- tribution, to the antenna array steering vectors. Using outage prob- ability, probability of error, and dynamic range of transmitter power as performance measures, we have shown signiflcant efiects of array perturbations on the two systems under spatially correlated Rayleigh fading channel. We also examine the efiect of angular power distribu- tions (uniform, truncated Gaussian, and truncated Laplacian), which corresponds to difierent propagation scenario, on the performance of the two systems. Results show that the central angle-of-arrival can
16 May 2010
TL;DR: The probability distribution of enhanced noise, made up by the sum of ratios of complex Gaussian random variables, is used to obtain a closed-form expression for the BER in the scenario under study.
Abstract: The sum of ratios of two complex Gaussian random variables appears frequently in the mathematical analysis of telecommunication systems when zero-forcing equalization is applied. This paper is focused on the study of one of those systems: a simple Orthogonal Frequency Division Multiplexing (OFDM) relay network. The reason behind the election of this particular scenario is the recent interest on employing relay networks in wireless and mobile broadband systems to increase the coverage and throughput in a cost-effective way. Thus, the probability distribution of enhanced noise, made up by the sum of ratios of complex Gaussian random variables, is used to obtain a closed-form expression for the BER in the scenario under study.
TL;DR: The entropy rate formula for a complex Gaussian random process is derived by using a widely linear model and the effectiveness of the approach for order selection for simulated and actual functional magnetic resonance imaging data that are inherently complex valued is shown.
Abstract: We derive the entropy rate formula for a complex Gaussian random process by using a widely linear model. The resulting expression is general and applicable to both circular and noncircular Gaussian processes, since any second-order stationary process can be modeled as the output of a widely linear system driven by a circular white noise. Furthermore, we demonstrate application of the derived formula to an order selection problem. We extend a scheme for independent and identically distributed (i.i.d.) sampling to the complex domain to improve the estimation performance of information-theoretic criteria when samples are correlated. We show the effectiveness of the approach for order selection for simulated and actual functional magnetic resonance imaging (fMRI) data that are inherently complex valued.
TL;DR: Conditions are derived to obtain accurate source localization estimates in a fluctuating ocean waveguide containing random internal waves, and the consequences of the loss of coherence on their accuracy are quantified.
Abstract: A method is provided for determining necessary conditions on sample size or signal to noise ratio (SNR) to obtain accurate parameter estimates from remote sensing measurements in fluctuating environments. These conditions are derived by expanding the bias and covariance of maximum likelihood estimates (MLEs) in inverse orders of sample size or SNR, where the first-order covariance term is the Cramer-Rao lower bound (CRLB). Necessary sample sizes or SNRs are determined by requiring that (i) the first-order bias and the second-order covariance are much smaller than the true parameter value and the CRLB, respectively, and (ii) the CRLB falls within desired error thresholds. An analytical expression is provided for the second-order covariance of MLEs obtained from general complex Gaussian data vectors, which can be used in many practical problems since (i) data distributions can often be assumed to be Gaussian by virtue of the central limit theorem, and (ii) it allows for both the mean and variance of the measurement to be functions of the estimation parameters. Here, conditions are derived to obtain accurate source localization estimates in a fluctuating ocean waveguide containing random internal waves, and the consequences of the loss of coherence on their accuracy are quantified.
14 Mar 2010
TL;DR: The results show that the proposed method can well estimate the RP pdf's parameters of the clean vector in the case of simulated data and fit well with the histogram of phase samples extracted from the real images.
Abstract: This paper proposes a method to estimate the parameters of the relative phase probability density function (RP pdf) of the complex coefficients when the image is corrupted by additive white Gaussian noise. With the complex Gaussian scale mixture (CGSM) assumption of the clean coefficients, we first introduce the relative phase mixture pdf (RPM pdf) by deriving the pdf of the relative phase of the noisy coefficients. Along with the derived pdf, the estimation method based on the maximum likelihood approach is proposed by exploiting the relationships between the RP pdf's parameters and the complex covariance matrix of the corresponding complex coefficient vector. The experiments using the simulated data and the data extracted from the real images are performed to show the effectiveness of the estimation method. The results show that the proposed method can well estimate the RP pdf's parameters of the clean vector in the case of simulated data and fit well with the histogram of phase samples extracted from the real images.
16 May 2010
TL;DR: This paper explores a new technique to calculate and plot the distribution of instantaneous transmit envelope power of OFDMA and SC-FDMA signals from the equation of Probability Density Function solved numerically and shows again that cyclic prefixed DS-CDMA system is one case with optimum IPAPR.
Abstract: This paper explores a new technique to calculate and plot the distribution of instantaneous transmit envelope power of OFDMA and SC-FDMA signals from the equation of Probability Density Function (PDF) solved numerically. The Complementary Cumulative Distribution Function (CCDF) of Instantaneous Power to Average Power Ratio (IPAPR) is computed from the structure of the transmit system matrix. This helps intuitively understand the distribution of output signal power if the structure of the transmit system matrix and the constellation used are known. The distribution obtained for OFDMA signal matches complex normal distribution. The results indicate why the CCDF of IPAPR in case of SC-FDMA is better than OFDMA for a given constellation. Finally, with this method it is shown again that cyclic prefixed DS-CDMA system is one case with optimum IPAPR. The insight that this technique provides may be useful in designing area optimised digital and power efficient analogue modules.
23 Aug 2010
TL;DR: A novel approach by using the complex coefficients derived from complex exponential atomic decomposition of a signal, modeled by a complex Gaussian probability distribution and a statistical model is employed to derive the decision rule from the likelihood ratio test is presented.
Abstract: The voice activity detection (VAD) algorithms by using Discrete Fourier Transform (DFT) coefficients are widely found in literature. However, some shortcomings for modeling a signal in the DFT can easily degrade the performance of a VAD in noise environment. To overcome the problem, this paper presents a novel approach by using the complex coefficients derived from complex exponential atomic decomposition of a signal. Those coefficients are modeled by a complex Gaussian probability distribution and a statistical model is employed to derive the decision rule from the likelihood ratio test. According to the experimental results, the proposed VAD method shows better performance than the VAD based on DFT coefficients in various noise environments.
01 Dec 2010
TL;DR: In this article, the statistical distribution of the enhanced noise after zero forcing frequency domain equalization in an OFDM system transmitting over a Nakagami-m fading channel was studied, and the density function of the ratio between the modulus of a complex Gaussian random variable (i.e., a Rayleigh distributed random variable) and that of a n-dimensional Gaussian variable (e.g., a NAKAGAMI-m distributed variable) was derived.
Abstract: In this paper we study the statistical distribution of the enhanced noise after zero forcing frequency domain equalization in an OFDM system transmitting over a Nakagami-m fading channel With this purpose, we obtain the expression of the density function of the ratio between the modulus of a complex Gaussian random variable (ie, a Rayleigh distributed random variable) and that of a n-dimensional Gaussian random variable (ie, a Nakagami-m distributed random variable) From this expression, we derive the density and the distribution of the resulting noise term after zero forcing equalization Lastly, we present an analytical expression for BER in the scenario under study which is validated through simulations
Dissertation•
28 Apr 2010
TL;DR: In this paper, the ergodic capacity of MIMO Nakagami-m fading channels is investigated under the majorization theory framework, where the distribution of the diagonal elements of the quadratic channel is relatively easy to handle.
Abstract: Multiple-input multiple-output (MIMO) antenna systems have been shown to be able to substantially
increase date rate and improve reliability without extra spectrum and power resources. The increasing
popularity and enormous prospect of MIMO technology calls for a better understanding of the performance
of MIMO systems operating over practical environments. Motivated by this, this thesis provides
an analytical characterization of the capacity and performance of advanced MIMO antenna systems.
First, the ergodic capacity of MIMO Nakagami-m fading channels is investigated. A unified way of
deriving ergodic capacity bounds is developed under the majorization theory framework. The key idea is
to study the ergodic capacity through the distribution of the diagonal elements of the quadratic channel
HHy which is relatively easy to handle, avoiding the need of the eigenvalue distribution of the channel
matrix which is extremely difficult to obtain. The proposed method is first applied on the conventional
point-to-point MIMO systems under Nakagami-m fading, and later extended to the more general distributed
MIMO systems.
Second, the ergodic capacity of MIMO multi-keyhole and MIMO amplify-and-forward (AF) dual-hop
systems is studied. A set of new statistical properties involving product of random complex Gaussian
matrix, i.e., probability density function (p.d.f.) of an unordered eigenvalue, p.d.f. of the maximum
eigenvalue, expected determinant and log-determinant, is derived. Based on these, analytical closedform
expressions for the ergodic capacity of the systems are obtained and the connection between the
product channels and conventional point-to-point MIMO channels is also revealed.
Finally, the effect of co-channel interference is investigated. First, the performance of optimum combining
(OC) systems operating in Rayleigh-product channels is analyzed based on novel closed-form
expression of the cumulative distribution function (c.d.f.) of the maximum eigenvalue of the resultant
channel matrix. Then, for MIMO Rician channels and MIMO Rayleigh-product channels, the ergodic capacity
at low signal-to-noise ratio (SNR) regime is studied, and the impact of various system parameters,
such as transmit and receive antenna number, Rician factor, channel mean matrix and interference-tonoise-
ratio, is examined.
Journal Article•
TL;DR: In this article, the authors developed a method which uses basic knowledge of calculus and matrix algebra to prove that linear combinations of components of n-dimensional normal random variable certainly obey normal distribution.
Abstract: This paper develops a method which uses basic knowledge of calculus and matrix algebra to prove that linear combinations of components of n-dimensional normal random variable certainly obey normal distribution.
Posted Content•
TL;DR: The strong asymptotics of the orthogonal polynomials are obtained by applying the nonlinear Deift-Zhou steepest descent method to the corresponding Riemann-Hilbert problem.
Abstract: In this paper we study the asymptotic behavior of a family of polynomials which are orthogonal with respect to an exponential weight on certain contours of the complex plane. The zeros of these polynomials are the nodes for complex Gaussian quadrature of an oscillatory integral on the real axis with a high order stationary point, and their limit distribution is also analyzed. We show that the zeros accumulate along a contour in the complex plane that has the S-property in an external field. In addition, the strong asymptotics of the orthogonal polynomials is obtained by applying the nonlinear Deift--Zhou steepest descent method to the corresponding Riemann--Hilbert problem.
01 Jan 2010
TL;DR: The CGSM is applied to image denoising using the Bayes least-square estimator in several complex transform do- mains and visually improves the quality of denoised images from the real case.
Abstract: In this paper, we propose the complex Gaussian scale mixture (CGSM) to model the complex wavelet coefficients as an extension of the Gaussian scale mixture (GSM), which is for real- valued random variables to the complex case. Along with some re- lated propositions and miscellaneous results, we present the prob- ability density functions of the magnitude and phase of the com- plex random variable. Specifically, we present the closed forms of the probability density function (pdf) of the magnitude for the case of complex generalized Gaussian distribution and the phase pdf for the general case. Subsequently, the pdf of the relative phase is derived. The CGSM is then applied to image denoising using the Bayes least-square estimator in several complex transform do- mains.TheexperimentalresultsshowthatusingtheCGSMofcom- plex wavelet coefficients visually improves the quality of denoised images from the real case.
Posted Content•
TL;DR: A method to compute the mutual information achieved by an independent identically distributed (IID) complex Gaussian signal on a block Rayleigh-faded channel without side information at the receiver, which represents the highest spectral efficiency that can be attained using Gaussian codebooks.
Abstract: We present a method to compute, quickly and efficiently, the mutual information achieved by an IID (independent identically distributed) complex Gaussian input on a block Rayleigh-faded channel without side information at the receiver. The method accommodates both scalar and MIMO (multiple-input multiple-output) settings. Operationally, the mutual information thus computed represents the highest spectral efficiency that can be attained using standard Gaussian codebooks. Examples are provided that illustrate the loss in spectral efficiency caused by fast fading and how that loss is amplified by the use of multiple transmit antennas. These examples are further enriched by comparisons with the channel capacity under perfect channel-state information at the receiver, and with the spectral efficiency attained by pilot-based transmission.
TL;DR: In this paper, the universality of local eigenvalue statistics for Hermitian covariance matrices Hn =m−1Σn1/2Am,nAmn,n∗ Σn 1/2 was proved for the case where the normalized counting measure converges weakly to a nonrandom measure N(0) with a bounded support.
Abstract: We consider the Hermitian sample covariance matrices Hn=m−1Σn1/2Am,nAm,n∗Σn1/2 in which Σn is a positive definite Hermitian matrix (possibly random) and Am,n is a n×m complex Gaussian random matrix (independent of Σn), and m→∞, n→∞, such that mn−1→c>1. Assuming that the normalized counting measure of Σn converges weakly (in probability) to a nonrandom measure N(0) with a bounded support, we prove the universality of the local eigenvalue statistics in the bulk of the limiting spectrum of Hn.
TL;DR: In this article, the authors considered the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude and proposed a new consistent subspace estimators for the case where the source signals are modelled as unknown deterministic signals.
Abstract: We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the eigenvectors of the sample correlation matrix are heavily biased with respect to the true ones. It has recently been suggested that this situation (where the sample size is small compared to the observation dimension) can be very accurately modeled by considering the asymptotic regime where the observation dimension $M$ and the number of snapshots $N$ converge to $+\infty$ at the same rate. Using large random matrix theory results, it can be shown that traditional subspace estimates are not consistent in this asymptotic regime. Furthermore, new consistent subspace estimate can be proposed, which outperform the standard subspace methods for realistic values of $M$ and $N$. The work carried out so far in this area has always been based on the assumption that the observations are random, independent and identically distributed in the time domain. The goal of this paper is to propose new consistent subspace estimators for the case where the source signals are modelled as unknown deterministic signals. In practice, this allows to use the proposed approach regardless of the statistical properties of the source signals. In order to construct the proposed estimators, new technical results concerning the almost sure location of the eigenvalues of sample covariance matrices of Information plus Noise complex Gaussian models are established. These results are believed to be of independent interest.
Posted Content•
TL;DR: In this article, the authors consider random analytic functions defined on the unit disk of the complex plane as power series such that the coefficients are i.i.d., complex valued random variables, with mean zero and unit variance, and show that the zero set is asymptotically given by the same distribution near the boundary of the disk.
Abstract: We consider random analytic functions defined on the unit disk of the complex plane as power series such that the coefficients are i.i.d., complex valued random variables, with mean zero and unit variance. For the case of complex Gaussian coefficients, Peres and Vir\'ag showed that the zero set forms a determinantal point process with the Bergman kernel. We show that for general choices of random coefficients, the zero set is asymptotically given by the same distribution near the boundary of the disk, which expresses a universality property. The proof is elementary and general.