Output Signal-to-interference-plus-noise Ratio Research Articles

PERFORMANCE EVALUATION OF DFT BEAMFORMERS FOR BROADBAND ANTENNA ARRAY PROCESSING

Broadband beamforming has been an important issue on antenna array processing due to many practical demands on communication, radar, or sonar applications. Although several effects deteriorating array performance have been addressed for narrowband beamforming, few of them are considered for the broadband scenario. Besides, the definition of output signal-to-interference plus noise ratio (SINR) and the way to simulate broadband signal sources are usually vague, which further obstructs the development of broadband beamforming. In this paper, the performance of discrete Fourier transform (DFT) beamformers operating in block processing and sliding window modes are investigated when the correlation matrices are known or estimated by finite data samples. The output SINR of DFT beamformers is well-defined, and the generation of broadband signals is clearly introduced. Simulation results with respect to the signal bandwidth, the number of frequency bins, and the number of data samples are presented for illustration and comparison.

FINITE DATA PERFORMANCE ANALYSIS OF MVDR ANTENNA ARRAY BEAMFORMERS WITH DIAGONAL LOADING

Diagonal loading has been regarded as an e-cient manner to tackle the flnite sample efiect or the steering vector imprecision problem on adaptive array beamforming. However, the reason of the robustness improvement by the loading factor is still unknown and rarely discussed. In this paper, we consider the flnite sample efiect and derive the approximated output signal-to-interference-plus-noise ratio (SINR) of minimum variance distortionless response (MVDR) beamformers with diagonal loading. The obtained SINR expression is more explicit and compact than the existing formulas in the literature. Based on the theoretical results, we investigate the efiects of a loading factor on the output SINR of MVDR beamformers. The theoretical analysis shows the efiectiveness of diagonal loading on alleviating flnite sample efiect. Moreover, the price of using diagonal loading is also discussed. Simulation results are presented for conflrming the validity of the research work.

Robust Capon beamforming against large DOA mismatch

In the presence of significant direction-of-arrival (DOA) mismatch, existing robust Capon beamformers based on the uncertainty set of the steering vector require a large size of uncertainty set for providing sufficient robustness against the increased mismatch. Under such circumstance, however, their output signal-to-interference-plus-noise ratios (SINRs) degrade. In this paper, a new robust Capon beamformer is proposed to achieve robustness against large DOA mismatch. The basic idea of the proposed method is to express the estimate of the desired steering vector corresponding to the signal of interest (SOI) as a linear combination of the basis vectors of an orthogonal subspace, then we can easily obtain the estimate of the desired steering vector by rotating this subspace. Different from the uncertainty set based methods, the proposed method does not make any assumptions on the size of the uncertainty set. Thus, compared to the uncertainty set based robust beamformers, the proposed method achieves a higher output SINR performance by preserving its interference-plus-noise suppression abilities in the presence of large DOA mismatch. In addition, computationally efficient online implementation of the proposed method has also been developed. Computer simulations demonstrate the effectiveness and validity of the proposed method.

An Analytical Expression for Performance of Optimum Combining with Multiple Correlated CCIs and Two Antennas

We derive an analytical expression for the average output signal-to-interference-plus-noise ratio (SINR) of optimum combining (OC) for spatially correlated signals from two antennas in the presence of correlated multiple co-channel interferers (CCIs) and Rayleigh fading. First, the moment generating function (MGF) of the output SINR is derived. Then we obtain the probability density function (PDF) by taking the Fourier transform of the characteristic function (c.f.) corresponding to the MGF. Using the derived expression, the average output SINR performance of OC is evaluated as the number of the correlated multiple CCIs increases.

Generalized eigenvector problem for Hermitian Toeplitz matrices and its application to beamforming

The generalized eigenvector problem (GEP) for Hermitian Toeplitz matrices is studied and some properties related to its eigenvectors and the associated eigenfilters are derived. Zero locations of the eigenfilters are also investigated and all of the results are applied to the maximum SINR (signal-to-interference-plus-noise ratio) beamforming problem based on ULAs (uniform linear arrays), since maximizing output SINR can be formulated as a generalized eigenvector problem where the matrix pair consisting of the desired signal correlation matrix and interference plus noise correlation matrix. Theoretical analysis based on a three-element ULA is provided, supported by simulations.

Study on interference suppression based on joint fractional Fourier domain and time domain

An interference suppression algorithm is proposed to meet challenges of the traditional technique in dealing with the linear frequency modulation (LFM) interference, such as high loss of signal-to-noise ratio (SNR), the output signal-to-interference-plus-noise ratio (SINR) sensitive to input interference-to-signal ratio (ISR) that results in an unstable synchronization, and the spectrum leakage serious in strong ISR situation. This approach firstly makes use of the windowed and lapped technique to the fractional Fourier transform (FRFT) to enhance the ISR improvement and lower the SNR loss. Then by weakening the interference and a secondary threshold process, interference energy can be suppressed as much as possible and the output SINR is less sensitive to the ISR. Finally, a joint fractional Fourier domain and time domain technique is proposed to overcome the residual interference energy caused by the strong interference or the discontinuous-phase interference. Theoretical analysis and simulation results show that the proposed algorithm can achieve better performance than the conventional methods in suppressing both the multi period LFM interference and the multi chirp-rate LFM interference, especially in the strong interference environment.

Minimax robust transmission waveform and receiving filter design for extended target detection with imprecise prior knowledge

It is well known that optimal extended target detection for wideband radar in the presence of colored Gaussian noise and signal-dependent interference can be implemented, based on the prior information of target impulse response, by transmit-receiver design via maximizing the output signal-to-interference plus noise ratio (SINR). However, the prior knowledge of the target is usually imprecise. The target impulse response is very sensitive to target-radar orientation, and the initial phase of target echo is a function of target-radar distance, namely, the exact target impulse response cannot be obtained in transmission waveform design. Additionally, the transmission waveform is desired to be of constant modulus for power efficiency. In this paper, we propose a robust method to jointly design the transmission waveform with constant modulus constraint and the receiving filters. The cost function is established by maximizing the worst-case output SINR and an iterative procedure is presented based on modified sequential quadratic programming. Numerical results show that the proposed method can increase the worst-case output SINR significantly.

Robust forward backward based beamformer for a general-rank signal model with real-valued implementation

A robust forward backward (FB) beamformer for an incoherently scattered general-rank signal model with real-valued implementation is proposed based on the uniform linear array (ULA) structure by introducing a preprocessing transformation matrix. With the preprocessing, the computational complexity is reduced significantly due to a real-valued close-form solution for the optimum weight vector; furthermore, the proposed algorithm can achieve a higher output SINR (signal-to-interference-plus-noise ratio) and has lower sensitivity to the diagonal-loading parameters especially for low input SNR (signal-to-noise ratio) scenarios.

Power Control and Beamforming for Femtocells in the Presence of Channel Uncertainty

Femtocells that are installed in existing macrocellular networks form a two-tiered heterogeneous network, yielding an interference problem between the two layers. How we can mitigate the interference is of great concern for the deployment of femtocells. When the femto base station has perfect channel information, it can mitigate the interference through transmit power control and beamforming. However, it may not be feasible to get perfect channel information due to unavoidable impairments such as channel estimation, quantization, and feedback delay. In the presence of such channel uncertainty, we consider the combined use of transmit power control and beamforming for femtocells in heterogeneous wireless communication environments. By analyzing the effect of channel uncertainty parameters on the performance, we determine the transmit power level to provide the desired signal-to-interference-plus-noise ratio (SINR) of the indoor cell edge femtouser and the beam weight to maximize the output SINR of the macrousers and femtousers by mitigating interference in a collaborate manner. Finally, simulation results show that the proposed scheme is quite effective in the presence of channel uncertainty.

Iterative Robust Minimum Variance Beamforming

Based on worst-case performance optimization, the recently developed adaptive beamformers utilize the uncertainty set of the desired array steering vector to achieve robustness against steering vector mismatches. In the presence of large steering vector mismatches, the uncertainty set has to expand to accommodate the increased error. This degrades the output signal-to-interference-plus-noise ratios (SINRs) of these beamformers since their interference-plus-noise suppression abilities are weakened. In this paper, an iterative robust minimum variance beamformer (IRMVB) is proposed which uses a small uncertainty sphere (and a small flat ellipsoid) to search for the desired array steering vector iteratively. This preserves the interference-plus-noise suppression ability of the proposed beamformer and results in a higher output SINR. Theoretical analysis and simulation results are presented to show the effectiveness of the proposed beamformer.

Adaptive Beamforming with Real-Valued Coefficients Based on Uniform Linear Arrays

A class of adaptive beamforming algorithms with real-valued coefficients is proposed based on the uniform linear array structure by introducing a preprocessing transformation matrix. It is derived from the beamformer with a minimum mean square error (MSE) or a maximum output signal-to-interference-plus-noise ratio (SINR), depending on the specific design criteria. The key parameter of the transformation matrix takes different values for different beamforming scenarios and three representative examples are studied: the linearly constrained minimum variance beamformer (and the generalized sidelobe canceller), the reference signal based beamformer, and the class of blind beamformers based on the constant modulus algorithm. Its advantage is twofold: 1) with real-valued coefficients, the computational complexity of the overall system is reduced significantly; 2) a faster convergence speed is achieved and given the same stepsize, the system arrives at a lower MSE (or a higher output SINR).

Time-varying AR modeling and adaptive IIR notch filter for anti-jamming DSSS receiver

Using Time-Varying AR (TVAR) model and adaptive notch filter is a new method for the non-stationary jammer suppression in Direct Sequence Spread Spectrum (DSSS). The performance of TVAR model for Instantaneous Frequency (IF) estimation will be affected by some factors such as basis functions. Focusing on this problem, the optimal basis function of TVAR model for the IF estimation of the LFM signal is obtained in this paper. Besides the depth and width of notching, the phase properties of notch filter affect the Signal-to-Interference plus-Noise Ratio (SINR) of correlation output to the narrowband jammer suppression in DSSS, in response to the problem the closed solution of correlation output SINR improvement has been derived when a single frequency jammer passes through direct IIR notch filter, and its performance has been compared with those of five coefficient FIR filters. Later, a novel method for LFM jammer suppression based on Fourier basis TVAR model and direct IIR notch filter is proposed. The simulation results show the effectiveness of the proposed method.

Performance Analysis for RUB-Based Multiuser MIMO Systems With Antenna Diversity Techniques

Random unitary beamforming (RUB) is an attractive low-complexity transmission scheme for multiple-input-multiple-output (MIMO) broadcast channels. In this paper, we study the sum-rate performance of RUB-based multiuser MIMO systems with receive diversity. Two combining techniques, i.e., selection combining (SC) and optimum combining (OC), are employed to reduce feedback load and improve sum-rate performance. With these combining techniques, each user only needs to feed back one beam index and the corresponding output signal-to-interference-plus-noise ratio (SINR). For the SC scheme, we derive the statistics of the output SINR and the exact analytical expression of the sum rate. For the OC scheme, we develop an upper bound of the sum rate in the high-signal-to-noise-ratio (SNR) region. The bound is shown to be tight for the case of a moderate number of users, but the number of users must be at least five times the number of transmit antennas. Selected numerical examples show that the proposed design greatly enhances the sum-rate performance while maintaining low feedback load.

Novel robust beamformers for coherent interference suppression with direction-of-arrival estimation errors

Two novel robust beamformers for the reception of a desired signal in the presence of both coherent interferences and direction-of-arrival (DOA) estimation errors are proposed. In the first method, the worst-case constraint and the soft-response constraint (WCSC) are combined together to maintain a distortionless response for the desired signal, while suppressing the coherent interferences with robustness against the DOA estimation errors. Further improvement of the output signal-to-interference-plus-noise ratio (SINR) for the WCSC beamformer can be achieved by removing the desired signal in the received data with a subtraction operation, which is the second method, denoted as SWCSC. In this method, a new array data vector is obtained by first dividing the original data vector into two sub-vectors and then subtracting one sub-vector from the other. From this new data vector, the optimum weight coefficients are obtained and then applied to one of the original sub-vectors. Simulations show that the proposed beamformers can achieve a much better performance in terms of output SINR than the existing ones.

Comparison of Output SINR and Receiver C/N_0 for GNSS Adaptive Antennas

Antenna arrays with space-time adaptive processing (STAP) are commonly utilized to allow the reception of signals in harsh interference environments. The primary applications of STAP have been radar and communications systems, where the STAP weights are optimized for output signal-to-interference-plus-noise ratio (SINR); however, there is increasing demand for STAP in time-of-arrival (TOA) estimation applications, such as global navigation satellite system (GNSS) receivers. It is understood that TOA estimation performance is primarily dependent on receiver postcorrelation carrier-to-noise ratio (C/N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ). In this study, the distinction between SINR and C/N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> is established, and a performance analysis of the common STAP algorithms is performed in the presence of interference. It is demonstrated that output SINR is an inadequate indication of GNSS receiver C/N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> performance. As a result, caution should be used when measuring the relative performance of different STAP algorithms in GNSS applications. Consequently, the present work develops a novel STAP algorithm which maximizes C/N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> . Additionally, the performance of common STAP algorithms is analyzed in the context of this performance bound, and it is demonstrated that, in many cases, their performance is near optimal.

Distributed transmit power allocation for multihop cognitive-radio systems

In this paper, we consider a relay-assisted wideband cognitive-radio (CR) system under the assumption that the frequency band chosen by the CR relay network for unlicensed spectrum usage overlaps with one or more bands dedicated to primary (e.g., licensed) narrowband links. Our objective is to optimize the performance of the CR system while limiting the interference in direction of the primary receivers, without requiring any adaptation of the transmitted signal spectra at the cognitive nodes. To this end, we study appropriate transmit power allocation (TPA) strategies among the cognitive relays. We first investigate the optimal centralized (OC) TPA solution and show that it can be formulated as a linear program. Since the OC-TPA solution requires a considerable amount of information exchange between the cognitive nodes, we develop two distributed TPA schemes, namely (i) a fully decentralized (FD) TPA scheme and (ii) a distributed feedback-assisted (DFA) TPA scheme. The FD-TPA scheme aims at maximizing the output signal-to-interference- plus-noise ratio (SINR) at the destination node of the CR network according to a best-effort strategy. It requires neither feedback information from the destination node nor an exchange of channel state information between the cognitive relays. The DFA-TPA scheme, on the other hand, utilizes feedback information from the destination node, in order to achieve a predefined target output SINR value, while minimizing the overall transmit power spent by the relays. Analytical and simulation-based performance results illustrate that notable performance improvements compared to non-cooperative transmission (i.e., without relay assistance) are achieved by the proposed schemes, especially when more than two hops are considered. In particular, the proposed distributed TPA schemes typically perform close to the OC-TPA solution.

Average SINR Analysis of DS-BPSK UWB Systems With IPI, ICI, ISI, and MAI and Its Application

Analytical expressions for the average output signal-to-interference-plus-noise ratio (SINR) of direct-sequence (DS) binary-phase-shift-keying (BPSK) ultra-wideband (UWB) receivers are derived using the IEEE UWB channel models. The derivation takes into account the interpath interference, the interchip interference (IPI), the intersymbol interference (ISI), and the multiple-access interference (MAI). The effects of the spreading gain and the pulse duration on the average output SINR are examined. Using these results, the optimal integration interval for a transmitted reference UWB receiver is studied.

Analytical Framework for Optimal Combining With Arbitrary-Power Interferers and Thermal Noise

The performance of multiple-input-multiple-output systems with optimum combining (OC) is studied in a Rayleigh fading environment with arbitrary-power cochannel interference and thermal noise. Based on the joint eigenvalue distributions of quadratic functions of complex Gaussian matrices, a closed-form expression for the exact distribution of the output signal-to-interference-plus-noise ratio (SINR) is derived. A closed-form expression for the exact moment-generating function (MGF) of the output SINR of single-input-multiple-output (SIMO) systems is also derived. From the exact MGF, the moments of the output SINR and the symbol error rate of various M-ary modulation schemes are obtained. We verify the accuracy of our analytical results with numerical examples. The new analytical framework provides a simple and accurate way to assess the effects of equal- and unequal-power cochannel interferers and thermal noise on the performance of OC.

Indirect Dominant Mode Rejection: A Solution to Low Sample Support Beamforming

Under conditions of low sample support, a low-rank solution of the minimum variance distortionless response (MVDR) equations can yield a higher output signal-to-interference-plus-noise ratio (SINR) than the full-rank MVDR beamformer. In this paper, we investigate several low-rank beam- forming techniques, and we also propose a new beamformer that we refer to as the indirect dominant mode rejection (IDMR). We analyze the degradation in the output SINR caused by residual cross correlations embedded in the sampled covariance matrix due to low sample support. The IDMR beamformer is based on a parametric estimate of the covariance matrix, in which any cross correlation is canceled out. Simulations reveal that the IDMR beamformer yields a dramatic improvement in output SINR relative to the conjugate gradient (CG), principal component inverse (PCI), and dominant mode rejection (DMR) beamformers. In our investigation of the low-rank CG beamformer, we address the issue of whether the unity gain constraint in the look direction should be enforced a priori via the use of a blocking matrix or effected a posteriori through simple scaling of the beamforming vector. Remarkably, it is proven that the two methods yield exactly the same low-rank beamformer at each and every rank.

Analysis of Multiantenna Architectures for Non-LOS Mobile-to-Mobile Communications in Cochannel Interference

The performance of multiantenna receivers in cochannel interference is investigated for narrowband links in a non-line-of-sight mobile-to-mobile channel. Channel impairments include Doppler spread and angular spread originating from scatterers in the vicinity of both the transmitter and the receiver. The analysis employs a two-ring scattering model and compares the performance of a sectored system employing selection combining (SC) to the performance of adaptive arrays implemented with both omnidirectional antennas and sectored antennas. Performance is estimated for environments with cochannel interference and is measured in terms of output signal-to-interference-plus-noise ratio (SINR). An ensemble of random scattering realizations is utilized in the analysis to estimate the average output SINR. The results demonstrate the improved performance offered by adaptive arrays over sectored systems with SC. Configurations involving both SC and adaptive array processing were also evaluated and found to yield improvements over conventional adaptive array architectures.