Interference-to-noise Ratio Research Articles

Model-Based Subspace Projection Beamforming for Deep Interference Nulling

This paper considers the problem of adaptive array processing for interference canceling to drive very deep nulls in difficult signal environments. In many practical scenarios, the achievable null depth is limited by covariance matrix estimation error leading to poor identification of the interference subspace. We address the particularly troublesome cases of low interference-to-noise ratio (INR), relatively rapid interference motion, and correlated noise across the receiving array. A polynomial-based model is incorporated in the proposed algorithm to track changes in the array covariance matrix over time, mitigate interference subspace estimation errors, and improve canceler performance. The application of phased array feeds for radio astronomical telescopes is used to illustrate the problem and proposed solution. Here even weak residual interference after cancellation may obscure a signal of interest, so very deep beampattern nulls are required. Performance for conventional subspace projection (SP) is compared with polynomial-augmented SP using simulated and real experimental data, showing null-depth improvement of 6 to 30 dB.

Sum Capacity of a Class of Symmetric SIMO Gaussian Interference Channels Within $ {\cal O}(1)$

The N +1 user, 1 ×N single-input multiple-output (SIMO) Gaussian interference channel where each transmitter has a single antenna and each receiver has N antennas is studied. The sum capacity within O(1) is characterized for the symmetric case where all direct links have the same signal-to-noise ratio (SNR) and all undesired links have the same interference-to-noise ratio (INR). The gap to the exact capacity is a constant which is independent of SNR and INR. To get this result, we first generalize the deterministic interference channel introduced by El Gamal and Costa to model interference channels with multiple antennas. We derive the capacity region of this deterministic interference channel. Based on the insights provided by the deterministic channel, we characterize the generalized degrees of freedom (GDOF) of Gaussian case, which directly leads to the O(1) capacity approximation. On the achievability side, an interesting conclusion is that the GDOF regime where treating interference as noise is found to be optimal in the two-user interference channel, does not appear in the N + 1 user, 1 × N SIMO case. On the converse side, new multiuser outer bounds emerge out of this work that do not follow directly from the two-user case. In addition to the GDOF region, the outer bounds identify a strong interference regime where the capacity region is established.

Performance Analysis of ZF and MMSE Equalizers for MIMO Systems: An In-Depth Study of the High SNR Regime

This paper presents an in-depth analysis of the zero forcing (ZF) and minimum mean squared error (MMSE) equalizers applied to wireless multiinput multioutput (MIMO) systems with no fewer receive than transmit antennas. In spite of much prior work on this subject, we reveal several new and surprising analytical results in terms of output signal-to-noise ratio (SNR), uncoded error and outage probabilities, diversity-multiplexing (D-M) gain tradeoff and coding gain. Contrary to the common perception that ZF and MMSE are asymptotically equivalent at high SNR, we show that the output SNR of the MMSE equalizer (conditioned on the channel realization) is ρmmse = ρzf+η\ssrsnr, where ρzf is the output SNR of the ZF equalizer and that the gap η\ssrsnr is statistically independent of ρzf and is a nondecreasing function of input SNR. Furthermore, as \ssr snr\ura ∞, η\ssrsnr converges with probability one to a scaled F random variable. It is also shown that at the output of the MMSE equalizer, the interference-to-noise ratio (INR) is tightly upper bounded by [(η\ssrsnr)/(ρzf)]. Using the decomposition of the output SNR of MMSE, we can approximate its uncoded error, as well as outage probabilities through a numerical integral which accurately reflects the respective SNR gains of the MMSE equalizer relative to its ZF counterpart. The e-outage capacities of the two equalizers, however, coincide in the asymptotically high SNR regime. We also provide the solution to a long-standing open problem: applying optimal detection ordering does not improve the D-M tradeoff of the vertical Bell Labs layered Space-Time (V-BLAST) architecture. It is shown that optimal ordering yields a SNR gain of 10log10N dB in the ZF-V-BLAST architecture (where N is the number of transmit antennas) whereas for the MMSE-V-BLAST architecture, the SNR gain due to ordered detection is even better and significantly so.

Low SNR Capacity for MIMO Rician and Rayleigh-Product Fading Channels with Single Co-channel Interferer and Noise

This paper studies the ergodic capacity of multiple-input multiple-output (MIMO) systems with a single co-channel interferer in the low signal-to-noise-ratio (SNR) regime. Two MIMO models namely Rician and Rayleigh-product channels are investigated. Exact analytical expressions for the minimum energy per information bit, E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> /N0 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</sub> , and wideband slope, S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> , are derived for both channels. Our results show that the minimum energy per information bit is the same for both channels while their wideband slopes differ significantly. Further, the impact of the numbers of transmit and receive antennas, the Rician K factor, the channel mean matrix and the interference-to-noise-ratio (INR) on the capacity, is addressed. Results indicate that interference degrades the capacity by increasing the required minimum energy per information bit and reducing the wideband slope. Simulation results validate our analytical results.

RFI Mitigation in Microwave Radiometry Using Wavelets

The performance of microwave radiometers can be seriously degraded by the presence of radio-frequency interference (RFI). Spurious signals and harmonics from lower frequency bands, spread-spectrum signals overlapping the “protected” band of operation, or out-of-band emissions not properly rejected by the pre-detection filters due to the finite rejection modify the detected power and the estimated antenna temperature from which the geophysical parameters will be retrieved. In recent years, techniques to detect the presence of RFI have been developed. They include time- and/or frequency domain analyses, or statistical analysis of the received signal which, in the absence of RFI, must be a zero-mean Gaussian process. Current mitigation techniques are mostly based on blanking in the time and/or frequency domains where RFI has been detected. However, in some geographical areas, RFI is so persistent in time that is not possible to acquire RFI-free radiometric data. In other applications such as sea surface salinity retrieval, where the sensitivity of the brightness temperature to salinity is weak, small amounts of RFI are also very difficult to detect and mitigate. In this work a wavelet-based technique is proposed to mitigate RFI (cancel RFI as much as possible). The interfering signal is estimated by using the powerful denoising capabilities of the wavelet transform. The estimated RFI signal is then subtracted from the received signal and a “cleaned” noise signal is obtained, from which the power is estimated later. The algorithm performance as a function of the threshold type, and the threshold selection method, the decomposition level, the wavelet type and the interferenceto-noise ratio is presented. Computational requirements are evaluated in terms of quantization levels, number of operations, memory requirements (sequence length). Even though they are high for today’s technology, the algorithms presented can be applied to recorded data. The results show that even RFI much larger than the noise signal can be very effectively mitigated, well below the noise level.

Performance of Cellular Mobile Systems Employing SNR-Based GSC in the Presence of Rayleigh and Nakagami-$q$ Cochannel Interferers

This paper studies the performance of cellular mobile systems employing a signal-to-noise ratio (SNR)-based generalized selection combining (GSC) algorithm in the presence of background white noise and multiple cochannel interfering signals. Closed-form expressions are derived for the received signal-to-interference-plus-noise ratio (SINR) distribution and outage probability, considering the case when the interfering signals experience mixed Rayleigh and Nakagami-q fading conditions, and the desired signal replicas are attenuated by flat Rayleigh fading. These expressions are obtained via the new representation of the total interference-to-noise ratio (INR) distribution for the mixed mode of fading experienced by different interferers. The derived expressions for the aforementioned statistical measures are valid for an arbitrary number of interferers and system diversity order and can be employed to investigate the impact of various system and fading parameters on the performance measures. Several case studies can be deduced from the results presented in this paper, including interference-limited systems, wherein the impact of white noise can be neglected.

Performance analysis of maximum ratio combining with imperfect channel estimation in the presence of cochannel interferences

In this paper, we analyze the performance of maximum ratio combining (MRC) systems with imperfect channel estimation in the presence of cochannel interference (CCI) with an arbitrary power interference-to-noise ratio (INR). The maximum combining weights are the imperfect estimates of the desired user's fading channel coefficients and are assumed to be complex Gaussian distributed. The quantified measure for estimation error is the correlation coefficient between the true fading channel coefficients and their estimates. Exact closedform expressions are derived for the probability density function(pdf) of the signal-to-interference-plus-noise ratio (SINR), as well as performance metrics including outage probability and the average symbol error probability (ASEP) for some modulation formats. Simulation results demonstrate the accuracy of our theoretic analysis.

Investigation of radio astronomical windows between 1 MHz and 2060 MHz in Universiti Malaya, Malaysia

An indoor and an outdoor radio frequency survey was conducted in Universiti Malaya, Malaysia, as a test site, for the purpose of developing radio astronomy research in Malaysia. This is the first radio astronomical survey of any such done in Malaysia. Observation and analysis were done in the radio frequency spectrum between 1 MHz and 2060 MHz. In this paper, the experimental setup and procedure of surveying are outlined and the measured data are interpreted. The eight radio astronomical windows were investigated from a 24 h observation, with the emphasis on two of the most important radio astronomical windows which are protected by the Malaysian Communications and Multimedia Commission (MCMC). Some intermittent observations were also done for referencing purposes. The radio frequency interferences (RFIs) are found to be relatively low. The overall relative Interference-to-Noise ratio (INR) at this test site ranges between 5.72% and 11.74%. The average strength of RFI in the eight focused radio astronomical windows at this site ranges between −100 dBm and −90 dBm (equivalently between 9.23 × 10 4 Jy and 93.29 × 10 4 Jy at resolution bandwidth of 125 kHz).

Outage Performance and Average Symbol Error Rate of M-QAM for Maximum Ratio Combining with Multiple Interferers

In this paper, we investigate the performance of maximum ratio combining (MRC) in the presence of multiple cochannel interferences over a flat Rayleigh fading channel. Closed-form expressions of signal-to-interference-plus-noise ratio (SINR), outage probability, and average symbol error rate (SER) of quadrature amplitude modulation (QAM) with M-ary signaling are obtained for unequal-power interference-to-noise ratio (INR). We also provide an upper-bound for the average SER using moment generating function (MGF) of the SINR. Moreover, we quantify the array gain loss between pure MRC (MRC system in the absence of CCI) and MRC system in the presence of CCI. Finally, we verify our analytical results by numerical simulations.

Space–Time Power Schedule for Distributed MIMO Links Without Instantaneous Channel State Information at the Transmitting Nodes

A space-time optimal power schedule for multiple distributed multiple-input multiple-output (MIMO) links without the knowledge of the instantaneous channel state information (CSI) at the transmitting nodes is proposed. A readily computable expression for the ergodic sum capacity of the MIMO links is derived. Based on this expression, which is a non-convex function of power allocation vectors, a projected gradient algorithm is developed to optimize the power allocation. For a symmetric set of MIMO links with independent identically distributed channels, it is observed that the space-time optimal power schedule reduces to a uniform isotropic power schedule when nominal interference is low, or to an orthogonal isotropic power schedule when nominal interference is high. Furthermore, the transition region between the latter two schedules is seen to be very sharp in terms of nominal interference-to-noise ratio (INR). For MIMO links with correlated channels, the corresponding space-time optimal power schedule is developed based on the knowledge of the channel correlation matrices. It is shown that the channel correlation has a great impact on the ergodic capacity and the optimality of different power scheduling approaches.

Fuzzy inference based robust beamforming

This paper presents a new approach to robust beamforming based on fuzzy logic theory that is suitable for both point and scattered sources. The presented technique is based on the optimum beamformer and makes it robust to an imperfect estimate of the direction of arrival (DOA) even when powerful interferences are within the uncertainty range of the desired source. This robust approach solves the deficiencies of the classical non-robust space reference beamformers (SRB) in which the real DOA and the presumed one are taken as equal, although they are not. At low signal-to-noise ratio (SNR) the fuzzy inference-based beamformer relies on the fuzzy description of the DOA estimation, and at high SNR it places more emphasis on the estimated DOA. Interference rejection is well achieved for Interference to noise ratios (INRs) over the SNR. When the number of antennas is large, the fuzzy inference based beamformer can be implemented by means of a general side lobe canceller (GSLC) architecture and stability improves while the beamformer is still capable of suppressing weak interferences. The proposed schemes are compared with existing techniques, showing that the fuzzy inference beamformer can be an alternative when considering scenarios with DOA uncertainty and interferences. The main goals of the proposed scheme are: DOA robustness, adjustability, and numerical stability, which shortens the distance between theory and implementation.

Auxiliary antenna-assisted interference mitigation for radio astronomy arrays

Interferometric image synthesis in radio astronomy is plagued by signal corruption from man-made sources. The very weak signals of interest can be overwhelmed by such interference. Recent work has proposed using array signal processing techniques of adaptive beamforming, adaptive filtering, and subspace projection to remove interference prior to image synthesis. In some practical scenarios, we have found poor cancellation performance when using such methods. Because signal-of-interest levels in radio astronomy (RA) are usually well below the noise, even interference to noise ratios (INR) less than unity can affect signal estimation. At these low INRs, it is difficult to estimate interference parameters or statistics with sufficient accuracy for high-performance adaptive cancellation or subspace projection. By adding a few (one to three) low-gain (relative to the primary telescope dishes) auxiliary antennas to an array, it is possible to overcome this problem. This paper will show that using such antennas (e.g. commercial-grade 3-m dishes) with an existing array can significantly improve interference rejection. New extensions to subspace projection spatial filtering methods are presented, along with analytical and simulated results for performance comparison.

Performance analysis of the minimum variance beamformer in the presence of steering vector errors

We present an analysis of the signal-to-interference-plus-noise ratio (SINR) at the output of the minimum variance beamformer in the presence of steering vector errors. The analysis yields an explicit expression for the SINR in terms of the variance of the steering vector errors and the other parameters affecting performance, including signal-to-noise ratio (SNR), interference-to-noise ratio (INR), signal-to-interference ratio (SIR), angular separation between desired signal and interference, array size and shape, correlation between desired signal and interference, and finite sample size.

Performance analysis of the minimum variance beamformer

We present an analysis of the signal-to-interference-plus-noise ratio (SINR) at the output of the minimum variance beamformer. The analysis is based on the assumption that the signals and noise are Gaussian and that the number of samples is large compared to the array size, and it yields an explicit expression for the SINR in terms of the different parameters affecting the performance, including signal-to-noise ratio (SNR), interference-to-noise ratio (INR), signal-to-interference ratio (SIR), angular separation between the desired signal and the interference, array size and shape, correlation between the desired signal and the interference, and finite sample size.

Adaptive Array Behavior with Periodic Phase Modulated Interference

We consider a least mean square (LMS) adaptive array [1] receiving a phase modulated interference signal. The phase modulation is assumed to be periodic and to have finite bandwidth. Under these assumptions, we determine the time-varying array weights, the modulation on the array output desired signal, and the time-varying output interference-to-noise ratio (INR) and SINR (signal-to-interference-plus-noise ratio). We present numerical results describing the behavior of a 2-element adaptive array that receives an interference signal with sinusoidal phase modulation. We show how each signal parameter (arrival angle, power, modulation index, and modulation frequency) affects the performance of the array.

Effect of jammer power on the performance of adaptive arrays

The effect of jammer power on the performance of adaptive arrays is studied. It is shown that the output signal-to-interference-plus-noise ratio (SINR) of an adaptive array is a function of jammer power. In the presence of a wide-band jammer, the output SINR of the array decreases with an increase in jammer power and eventually goes to zero. Unlike continuous wave (CW) jammers, a wide-band jammer does not go through power inversion. Instead, as the jammer power is increased, the interference-to-noise ratio (INR) at the array output shows oscillations. For large jammer power, the output INR increases with an increase in jammer power.