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DIGITAL BEAMFORMING (DBF) - demand for increased capacity is a major driving force for incorporating DBF - marriage between antenna technology and digital technology - 3 major components: antenna array, digital transceiver, digital signal processor - based on capturing the RF signals at each of the antenna elements and converting them into two streams of binary baseband signals (I & Q). Included in the digital baseband signal are the amplitude and phase of signals received at each of the elements of array. Beamforming is carried out by weighting these digital signals, thereby adjusting this amplitude and phases such that when added together they form the desired beam. This process can be carried out by special purpose digital signal processor - Attractive features: 1. A large number of independently steered high-gain beams can be formed without any resulting degradation in signal-to-noise ratio. 2. All of the information arriving at the antenna array is accessible to the signal processors so that system performance can be optimized. 3. Beams can be assigned to individual users, thereby assuring that all links operate with maximum gain 4. Adaptive beamforming can be easily implemented to improve the system capacity by suppressing cochannel interference. Any algorithm that can be expressed in mathematical form can be implemeneted. As a byproduct, adaptive beamforming can be used to enhance the system immunity to multipath fading. 5. DBF systems are capable of carrying out antenna system real-time calibration in the digital domain. Therefore, one can relax the requirements for a closematch of amplitude and phase between transceivers, because variation in these parameters can be corrected in real time. 6. DBF has potential for providing a major advantage when used in satellite communications. If, after the launch of the satellite, it is found that the performance of the beamformer needs to be upgraded, a new suite of software can be telemetered up to the satellite. This means that the life of the satellite can be expanded by retrofits at various intervals, during which the satellite’s capabilities are upgraded. Adaptive beamforming - adaptive beamformer: device that is able to separate signals collocated in the frequency band but separated in the spatial domain, separating a desired signal from interfering signals - algorithm based on maximization of SNR at the array output & least mean squares (LMS) errors - Minimum-variance distortionless response (MVDR) - Sample matrix inversion – fast adaptivity Benefits of using adaptive antennas 1. Coverage - increase the cell coverage range substantially through antenna gain and interference rejection. - Fewer sites required with adaptive antennas employed in base stations - Larger coverage if antenna at greater height above average terrain. Can be eased by using the number of antenna elements 2. Capacity - It is possible to have multiple mobiles on the same RF channel but different spatial channels at a particular cell site - allows a reuse factor of unity, that is a single frequency can be used in all cells. - Can increase the number of available voice channels through directional communication links, depends on the propagation environment, the number of antenna elements and the amount of dynamic channel assignment allowed. - Transmission bit rate can be increased due to the improved SIR at the output of the adaptive beamformer - Allow RF channels to be adjusted through link power control to meet the requirements of user- selectable data transfer rates. 3. Signal quality - in noise-limited environment, minimum receiver thresholds are reduced by 10 logM dB on average. - In interference-limited environments, the additional improvement in tolerable SIR at a single element results from interference rejection afforded against directional interferers. - Can be considered as spatial equalizers 4. Access technology - In uplink, paths from different angles of arrival are separated by using a particular adaptive beamforming technique - Downlink: energy can be focused at the mobile so that long delay multipath components can be reduced substantially - >>combat ISI through spatial discrimination of “interfering” signals on both links 5. Power control - Eased thru the inclusion of adaptive antenna technology 6. Handover - antenna tech provides mobile unit location information that can be used by the system to substantially improve handoffs in both the low and high tiers. Accurate position estimates, prediction of velocities is possible. 7. Base station transmit power - the maximum peak EIRP required per user on a particular channel is decreased compared to without adaptive beamforming 8. Portable terminal transmit power - with adaptive antennas at cells, the transmit power levels from and to the mobile can be kept minimum to provide the requested service. DIFFERENT TYPES OF ADAPTIVE BEAMFORMING 1. Adaptive beamforming for uplink Reasons studies for uplink: traditionally used for radar, remote sensing and sonar reception system spatial channel information available on the uplink Adaptive criteria optimum weights using different criteria are all given by the Wiener solution because it provides the upper limit on the theoretical adaptive beamforming steady-state performance Adaptive Algorithms LMS algorithm: simple to implement , but limited in dynamic range over which it operates. Required power control or alternatively use normalized LMS algorithm SMI technique: fast convergence rate but increase computational complexity & numerical instability RLS algorithm: reduce computational complexity while maintaining similar performance, convergence rate faster than LMS provided that SNR is high, but has forgotten factor that is very dependent on fading rate of the channel Conjugate gradient method Eigenanalysis algorithm Rotational invariance based method Linear least squares error algorithm (LSSE) Hopfield neural network Reference Signals If explicit reference signal available in communication it should be used as much as possible for less complexity, high accuracy, fast convergence a) spatial reference: referred to as angle of arrival(AOA) information of desired signal and its multipath components AOA estimation techniques: wavenumber estimation: based on decomposition of a covariance matrix whose terms consist of estimates of the correlation between the signals at the elements of an array antenna. Example: Multiple signal classification (MUSIC), modified forward-backward linear prediction (FBLP), Principal Eigenvector Gram-Schmidt (PEGS), Estimation of Signal Parameters by Rotational Invariance Techniques (ESPRIT) parametric estimation: variety of maximum likelihood estimation (MLE) : particular likelihood function is formulated for the given radio signals, high computational complexity requirement for array calibration, extra processing load required for estimating AOA b) temporal reference: may be a pilot signal that is correlated with the wanted signal, or known PN code in CDMA Blind Adaptive Beamforming when explicit reference signal is not available a) Constant Modulus Algorithm (CMA) For both compensating fading and canceling cochannel interference Applied to advanced mobile phone services ( AMPS), IS-54 signals, GMSK signals, 16-QAM signals b) Decision-Directed Algorithm Low cost since not computationally intensive, and no array calibration required fast convergence, typically within 50 symbols locks on desired signal with probability of 99.9% at SIR levels as low as 1dB cochannel rejection is typically more than 20 dB implementation based on incoherent differential binary phase-shift keying (DBPSK) demodulation and LMS algorithm converge faster than CMA and SCORE c) Cyclostationary Algorithm Developed and applied to AMPS AMPS exhibit cyclostationary properties due to presence of supervisory audio tone Show considerable improvement in MSE compared to the case of omnidirectional antennas Cylic beamforming can be applied to GMSK signals, only require that cochannel users have slightly different frequencies. Used in GSM and DECT. Shown capacity improvement 2. Adaptive Beamforming for Downlink Objective: to maximize the received signal strength at the desired mobile and to minimize the interference to other mobiles and adjacent base stations, thereby maximizing the downlink SINR If transfer function of the channel at the downlink is known, the downlink SINR can be maximized by multiplying the desired signal with a set of downlink weights. The weights are a scale version of the uplink weights, provided that the frequency of both links is same and the channel is relatively static during reception and transmission. Weight reuse can be applied to TDD systems ( CT2/CT2+, DECT, PHP, DCS1800). In FDD system (IS-54, IS-95, GSM), weight reuse cannot be used because far frequency separation Essence of the problem: to estimate the downlink transfer function Feedback technique was proposed. Using probing signal transmitted by BS. The mobile measure it own response to the probe signal and report them back to BS. The transfer function is estimated using the report. Simple but require complete redesign of protocols and signaling & applicable only for slowly change environments Other way: mobile directly transmit a narrowband testing signal at downlink frequency so that the BS can directly estimate the downlink channel transfer function from that. Not interrupt the normal uplink transmission but still require complete protocol redesign & require additional hardware in MS. Approached using AOA info. Downlink weights are derived by maximizing SIRN based on the same AOA. Use fixed multiple beams for both reception and transmission at the BS. On uplink, BS determine the direction of the path on which the strongest component of the desired signal arrived. On downlink, the BS points the beam in the corresponding direction. Not optimal, but SINR improved since narrowband signal is pointed, and can use high power beam to boost the SINR. Ref: John Litva, Titus Kwok-Yeung Lo, “ Digital Beamforming in Wireless Communications”, pg 157-184, Artech House Publisher, 1996 Ref: John Litva, Titus Kwok-Yeung Lo, “ Digital beamforming In Wireless Communications”, Artech House, London, 1996 Receive beamforming concept - radiation pattern should match the energy profile in order to merge all the radiated power - In wide angular spread case, pointing to a specific direction with narrow beam pattern is not optimal because some part of power spills over Transmit beamforming - It is suitable to transmit pointing towards the most significant reflector in order to minimize the interference between different users located at different angles. - Suitable for narrowband transmission but not for MC-CDMA schemes where many carriers need to be considered. Ref: Santiago Zazo, Ivana Raos, “Transmit Beamforming Design in Wide Angle Spread Scenarios for B3G MC-CDMA Systems”, IEEE Workshop on Signal Processing Advances in Wireless Communications, 2004 BLAST - each antenna transmit an independently modulated signal simultaneously and on the same carrier frequency - minimize redundancy between the various antenna signals in order to favor maximum data rate Space-Time Coding - introduce a lot of redundancy in an effort to maximize the diversity gain and achieve a minimum bit error rate Space selectivity - occurs when the received signal amplitude depends on the spatial location of the antenna, and is a function of the spread of angles of departure of the multipaths from the transmitter, and the spread of angles of arrival of multipaths at the receiver General principle of LA is to: - define a channel quality indicator, or so-called channel state information (CSI), that provides some knowledge on the channel. Metrics used as CSI : SNR & SINR(available from physical layer), PER & BER (Link layer) - adjust a number of signal transmission parameters to the variations of that quality indicator over the signaling dimension explored (time, freq, space or combination thereof) Adaptation based on Mean SNR 1. Measure SNR at receiver (assessment of CSI) 2. Convert the SNR info into BER info for each mode candidate (computation of adaptation thresholds, the minimum required SNR for a given mode to operate at a given target BER) 3. Based on target BER, select for each SNR measurement the mode that yields the largest throughput while remaining within the BER target bounds (selection of the optimal mode) 4. Feedback the selected mode to the transmitter - this assuming ideal conditions (SNR can be measured instantaneously, ideal coherent detection, fading over time only, SNR measured in very short window so it is effectively nonfading) - in practice, feedback delays and other implementation limitations will not allow instantaneous mode adaptation. Conversion of SNR to BER is not simple because the channel may exhibit some fading within the SNR window. > use of second and higher order statistics of SNR instead of Mean. Adaptation based on Multiple Statistics of Received SNR - If multicarrier modulation is used, a two dimensional time- frequency window may be used. - The mapping between SNR and average BER is determined using pdf of the SNR over that window - In physical channel this pdf cannot be obtained via simple analysis because it is a function of many parameters - It can be simplify by estimating limited statistical info such as the k-order moment over the adaptation window, instead trying to estimate the full pdf - Moment based CSI > simplicity and flexibility to LA algorithm, do not depends on any assumption made on the number or transmit and receive antenna “How effective these methods can be in realistic traffic and bandwidth constraints is an open research problem. In particular, it is critical to measure the ability of the scheme to lend itself to a very fast adaptation scenario without significant bandwidth loss” Pros and cons of CSI - SNR based : offer flexibility to adapt the modes on a very fast basis; however, it relies on the computation and adaptation/switching thresholds that maybe inaccurate - Error-based : captures accurate information of the modes, however this accuracy is reach only after a substantial amount of traffic observed. “An important topic of current research is to combine all types of CSI together to yield both accuracy and robustness over a wide range of channels, adaptation rates, and traffic conditions” In multiple antenna system the SNR varies not only over time and frequencies but also depends on: - the way the transmitting signals are mapped and weighed onto the transmit antennas - the processing techniques used at the receiver - antenna polarization and propagation Space-time-frequency adaptation> the adaptation algorithm desired to be able to select the best way of combining antennas at all time (choose between space-time coding approach, BLAST or beamforming approach) LA algorithm design challenges: - determination of adaptation thresholds: picking the least amount of statistical information to be computed while still describing the essence of channel behavior - adaptation rate: fast adaptation consumes higher bandwidth, trade-off btw performance gain and amount of resource allocated to control messages Ref: Adaptive algorithms for weight calculations in adaptive antenna arrays > determine the convergence rate and hardware complexity 1. Time domain processing Applebaum algorithm: applicable only when DOA of the desired signal is known beforehead Least Mean Square (LMS): has been widely used for tap coefficient adaptations of an adaptive processor in antenna array, but it causes signal acquisition and tracking problems due to its slow convergence in multipath fading channel Constant Modulus Algorithm (CMA): useful when the constant envelope of modulated signal is maintained. Direct Matrix Inversion (DMI): fast convergence, but computationally too complex and may cause numerical instability Recursive Least Square (RLS): achieve faster convergence than LMS, less computational than DMI 2. Spatial domain processing : focused on DOA estimation by spectral analysis in the space domain Discrete Fourier Transform (DFT) Maximum Entropy Method (MEM) Multiple Signal Classification (MUSIC) Estimation of Signal Parameters via Rotation Invariance Technique (ESPRIT) Ref: Jin Young Kim, Jae Hong Lee, “Performance of a Multicarrier DS/CDMA System with Adaptive Antenna Array in Nakagami Fading Channel”, IEEE Conference paper, 1998 Steering vector - contains the responses of all elements of the array to a narrow-band source of unit power - associated with each directional source. - For array of identical elements, each component of this vector has unit magnitude - The phase of its ith component is equal to the phase difference between signals induced on the ith element and the reference element due to the source associated with the steering vector - Also known as space vector and array response vector W= array weight vector = weights of the beamformer X= array signal vector= signals induced on all elements R= array correlation matrix = its element denote the correlation between various elements of the array Si= steering vector associated with ith source with direction (Øi, θi) It is useful to express R in terms of its eigenvalue and their associated eigenvectors - eigenvalues can be divided by two sets when the environment consists of uncorrelated direction sources and uncorrelated white noise - noise eigenvalues: eigenvalues in one set are of equal values and it does not depend upon directional sources and is equal to the variance of the white noise - 2nd set: signal eigenvalues: a function of the parameters of directional sources, their number is equal to the number of these sources. Each eigenvalue of this set is associated with a directional source, its value changes with the change in the source power, and bigger than those associated with white noise - R of an array of L elements immersed in M directional sources and the white noise has M signal eigenvalues and L-M noise eigenvalues - R can be represented in the form of spectral decomposition of R, matrix with eigenvalues as diagonal matrix and multiplied by their corresponding unit-norm eigenvectors - BEAMFORMING METHODS 1. Conventional beamformer - simple, sometimes known as delay-and-sum beam former, with all its weights of equal magnitudes - the phases are selected to steer the array in particular direction, known as the look direction - has unity response in the look direction, that is, the mean output power of the processor due to a source in the look direction is the same as the source power - in environment consisting only uncorrelated noise and no directional interferences, this beam former provides maximum SNR - not effective in the presence of directional jammers, intentional or unintentional 2. Null-steering beam former - used to cancel a plane wave arriving from a known direction and thus produces a null in the response pattern in the DOA of the plane wave - DICCANE : estimate the signal arriving from a known direction by steering a conventional beam in the direction of the source and then substracting the output of this from each element. Very effective for canceling strong interference and could be repeated for multiple interference cancellation. Cumbersome when the number of interferences grow - Requires knowledge of the directions of interference sources, the beam former using the weights estimated does not maximize the outpur SNR 3. Optimal beamforming - use ML filter - the processor weights are selected by minimizing the mean output power of the processor while maintaining unity response in the look direction - Minimum Variance Distortionless Response (MVDR) beamformer does not require the knowledge of the directions and power levels of the interferences as well as the level of the background noise power to maximize the output SNR. It requires only the direction of the desired signal 4. Optimization using reference signal - may be employed to acquire a weak signal in the presence of a strong jammer 5. Beam-Space processing - two-stage scheme where the first stage takes the array signals as input and produces a se of multiple outputs, which are then weighted and combined to produce the array output - first stage: fixed weighting of the array signal and amounts to produce multiple beams steered in different directions. The weights are not adaptive - weights applied to different beam outputs to produce the array outputs are optimized to meet a specific optimization criteria and are adjusted during the adaptation cycle - for an L element array, the processor consist of a main beam steered in the signal direction and a set of not more than L-1 secondary beams - weighted output of secondary beams is subtracted from the main beam - weights are adjust to produce an estimate of interference present in the main beam, subtracted to remove it - Secondary beams (auxiliary beams) designed such that they do not contain the desired signal form the look direction to avoid the signal cancellation in the subtraction process - Other names: Howell-Applebaum, partitioned processor, partially adaptive arrays, adaptive- adaptive arrays, multiple-beam antennas - Quiescent pattern (main beam pattern) chosen such that it has desired shape. - Schemes to generate the output of auxiliary beams such that no signal from the look direction is contained in them: subtracting the array signals from presteered adjacent pairs - If number of beams = number of elements of array, it is fully adaptive and has same capabilities as those array using element-space processing - Number of beams < number of elements: partially adaptive. Null-steering capabilities reduced to that equal to the number of auxiliary beams. Estimate weights using adaptive schemes leads to faster convergence. MSE higher than fully adaptive - Useful when number of interferers much less than number of elements. Computational advantage over element-space processing since only need to adjust M-1 weights compared to L weights. - Less computation because it solves an unconstrained optimization problem element-space: the constraints on weights to prevent the signal arriving from the look direction from being distorted and to make array more robust against errors beam-space: these are transferred to the main beam, leaving the adjustable weights free from constraints - beam-space shown superior performance in case of look-direction errors (shown in case of one interferer) - element-space depends on knowledge of the look direction, when actual signal direction is different from the one that is used to constrain weights it cancels this signal as if it was an interference close to the look direction - beam-space: designed to have the main beam steered in the known look direction and the auxiliary beams are formed to have null in this direction. Very small signal cancellation in main beam compared to element-space. - Auxiliary beam-forming techniques: formation of M-1 orthogonal beams , formation of beams in the direction of interferences if known - Auxiliary beam outputs are weighted and summed and the result is subtracted from the main beam output to cancel the unwanted interference present in the main beam. 6. Broad-band Beam Forming - TDL structure normally used - lattice structure consisting of a cascade of J simple lattice filters sometimes used - 7. Partitioned Realization 8. Frequency Domain Beamforming 9. Digital beamforming 10. Eigenstructure Method - eigenvalues R can be divided into two sets when environment consists of uncorrelated directional sources & uncorrelated white noise - largest M eigenvalues correspond to M directional sources, the eigenvector associated : signal eigenvectors - L-M smallest eigenvalues : background noise power, eigenvector associated: noise eigenvectors - eigenvectors of R are orthogonal to each other : as spanning an L-dimensional space, divided into two orthogonal subspaces -signal subspace: subspace spanned by signal eigenvectors - noise subspace: subspace spanned by noise eigenvectors - signal subspace spanned by M steering vectors associated with M directional sources. Exploited by eigenstructure method in number of ways - to cancel interference: array using a weight vector contained in the signal space such that it is orthogonal to the interference-direction steering vector - in case the direction of interference is not known the weight is estimated by minimizing a suitably selected cost function - application: estimating weights of beam-space processors using eigenvectors of the Rn (matrix with signal component removed) as is done for secondary beams: effective to cancel interference in beam space and for achieving the desired performance in short observation time application: for correcting errors in steering vectors, forming beams associated with the largest eigenvalues of R - ADAPTIVE BEAM FORMING 1. SMI algorithm Estimates the array weights by replacing R with its estimate unbiased estimate of R using N samples of array signals expression of optimal weights require inverse of R, using Matrix inversion Lemma as the number of samples grows the matrix update approaches its true value, so the estimated weights approaches it optimal value 2. LMS Constrained LMS : when the weight are subjected to constraints at each iteration 3. RLS 4. CMA 5. Conjugate Gradient Method 6. Neural Network Approach DOA ESTIMATION METHODS 1. Spectral Estimation Methods 2. MVDR Estimator 3. Linear Prediction Method 4. MEM 5. MLM 6. Eigenstructure Methods 7. MUSIC Algorithm 8. Min-Norm Method 9. CLOSEST Method 10. ESPRIT 11. WSF Method 12. Other Methods 13. Preprocessing Techniques 14. Estimating the number of Sources 15. Performance Comparison EFFECT OF ERRORS 1. Correlated Arrivals - Correlation between the desired signal and an unwanted interference exists in situations of multipath arrivals and deliberate jamming 2. Look Direction and Steering Vector Error - occur when the look direction is not the same as the desired signal direction. - The processor treats the desired signal source as an interference and attenuates it. Amount of attenuation depends upon the power of the signal and the amount of error. A stronger signal is canceled more and larger error causes more cancellation of the signal - Possible solutions: make the beam broader using multiple linear constraints and norm constraints, not require broadening of the main beam: use direction finding technique combined with a reduced dimensional ML formulation to estimate the direction of the desired signal accurately - Beam-space are more robust than element-spaced - Pointing error causes error occur in the steering vector, which is used in weight calculation - Factors of steering vector error: imperfection in the knowledge of the position of array elements, errors caused by finite word length arithmetic, 3. Element Failure & Element Position Error 4. Weight Errors Reference: LAL C. Godara, “Application of Antenna Arrays to Mobile Communications, Part II: Beam- Forming and Direction-of-Arrival Considerations” Proceeding of IEEE, August 1997 ----------------------------------------------------------------------------------------------------------------------------- ---- 1965: First fully adaptive array was conceived by Applebaum, designed to maximize the SNR at the array output Widrow introduce Least Mean Squares (LMS) error algorithm: Cancelling unwanted interference Frost and Griffiths further works on LMS algorithm to ensure that desired signals were not filtered out along with the unwanted signals. OPtimisation takes place as before, but antenna gain is maintained constant in the desired direction Ref: --------------------------------------------------------------------------------------------------------------------------------- Summary of “Beamforming: A Versatile Approach to Spatial Filtering” by Barry D.Van Veen & Kevin M. Buckley, IEEE ASSP Magazine April 1988 Purpose of this paper: provide the overview of beamforming from signal processing perspective. Data independent, statistically optimum, adaptive and partially adaptive are discussed provide overview of beamformer design briefly discuss performance & implementation issues Beamformer: a processor used in conjunction with an array of sensors to provide a versatile form of spatial filtering.The sensor arrays collects spatial samples of propagating wave fields, which are processed by the beamformer objective: to estimate the signal arriving from desired direction in the presence of noise and interfering signals. Performs spatial filtering to separate signals that have overlapping frequency content but originate from differential spatial locations. - Desired and interfering signals usually originated from different spatial locations. This separation can be exploited to separate signal from interference using spatial filter at the receiver - Implementing a spatial filter requires processing of data collected over spatial aperture - Typically, beamformer linearly combines the spatially sampled time series from each sensor to obtain a scalar output time series in the manner that an FIR filter linearly combines temporally sampled data 2 advantages of spatial sampling with an array of sensors: Spatial discrimination depends on size of aperture. Aperture increases > discrimination improves Spatial filtering versatility offered by discrete sampling: many application need to change filtering function in real time. It is easily implemented in discretely system by changing the way in which the beamformer linearly combines the sensors data Basic Terminology & Concept A. Beamforming & Spatial Filtering Weight vector, w Data vector, x(k) H = Hermitian (complex conjugate transpose) Beamformer response, r(θ,ω): define as amplitude and phase presented to a complex plane wave as a function of location and frequency. Location is generally 3dimension quantity, but often only consider 1 or 2D direction of arrival (DOA) Array response vector (steering vector or direction vector), d(θ,ω) Θ: direction, ω: temporal frequency - the angles between w and d(θ,ω) determine the response r(θ,ω). - If the angle=90˚, the response is 0. - If angle close to 0˚, the response magnitude will be relatively large - The ability to discriminate between sources at different locations and/or frequencies, say (Θ1,ω1) and (Θ2,ω2), is determined by the angle btw their array response vectors, d(θ1,ω1) and d(θ2,ω2) Problems in spatial sampling: - spatial aliasing: ambiguity in source locations. The source at different locations have same array response vector. Happens if the sensors are spaced too far apart. - If the sensors are too closed, spatial discrimination suffers as a result of smaller than necessary aperture, array vectors are not well dispersed in the N dimensional vector space. - Linear equispaced array when ω1 sinΘ1= ω2 sinΘ2 > in broadband signal when a source at one location and frequency cannot be distinguished from a source at one location and frequency FOCUS of this paper: designing response via weight selection. B. Second Order Statistics C. Beamformer Classification Data independent : the weights do not depend on the array data and are chosen to present a specified response for all signal/interference scenarios Statistically optimum: the weights are chosen based on the statistics of the array data to optimize the array response. In general, it place nulls in the direction of interfering sources in an attempt to maxi Second Order Statistics - evaluation on beamformer usually involves power of variance, so the second order statistics of the data play an important role Beamformer Classification Classified as data independent or statistically optimum, depending on how the weights are chosen Data Independent: the weights do not depends on the array data and are chosen to present a specified response for all signal/ interference scenarios Statistically optimum: weights chosen based on the statistics of the array data to “optimize” the array response. Places nulls in the directions of interfering sources in an attempt to maximize the signal to noise ratio at the beamformer output. The statistics of array data are not usually known and may change over time so adaptive algorithms are typically employed to determine the weights. Adaptive algorithm is designed so that the response converges to statistically optimum solution. 1. Data Independent Beamforming the weights are designed so the beamformer response approximates a desired response independent of the array data or data statistics design objective: approximating a desired response A.Classical beamforming B. General Data Independent Response Design apply to the design of beamformers that approximate an arbitrary desired response 2. Statistically Optimum Beamforming weights are chosen based on the statistics of the data received at the array the goal is to “optimize” the beamformer response so the output contains minimal contributions due to noise and signals arriving from directions other than the desired signal direction Assumptions: data are wide-sense stationary & its second order statistics are known A. Multiple Sidelobe Canceller B. Use of Reference Signal C. Maximization of Signal to Noise Ratio D. Linearly Constrained Minimum Variance Beamforming E. Signal Cancellation in Statistically Optimum Beamforming Adaptive Algorithms for Beamforming Block adaptation: statistics estimated from a temporal block of array data and used in an optimum weight equation Continuous adaptation: weights are adjusted as the data is sampled such that the resulting weight vector sequence converges to the optimum solution Interference Cancellation & Partially Adaptive Beamforming A. Interference Cancellation Vs Degrees of Freedom B. Partially Adaptive Beamformer Design Beamformer Implementations

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