Multi-antenna receiving system



The author would like to thank the following people for their unwavering help and support which made the final year project an enriching and interesting experience throughout the duration of the project.

First and foremost, the author would like his supervisor, A/P Ser Wee, for his time, support and guidance given to the author. He was of tremendous help to the author in finding the research directions and the development of the project.

The research scientist from Temasek Lab @ NTU who is in charge of this Industrial Sponsored Project, Dr. Joni Polili Lie, for giving valuable viewpoints and ideas for the development of the project. He was of tremendous help to the author in understanding the various aspects of the research development.

The technical and admin staff from the Centre for Signal Processing, Mr Yang Yong Sheng, Mrs. Teo Siok Khim and Mrs. Teng Siew Jiuan Catherine, for their invaluable help in providing the necessary technical and administrative matters throughout the project.

Last but not least, the author would like to acknowledge and show his appreciation to all the people who have helped him in one way or another.


1.1 . Background

Array signal processing is the signal processing of the output of an array of sensors to enhance the Signal-to-Interference-plus-Noise Ratio (SINR) compared to that of a single sensor using conventional or adaptive beamforming. [1]

One of the main concerns in array signal processing is to determine the location of an energy emitting source and the number of these sources relative to the location of the array. In order to determine the location, we are interested in estimating the direction-of-arrival (DOA) of a signal in the presence of noise and interfering signals through high resolution direction finding (DF) with a single channel receiver. [2]

1.2 . Original Project Objective

The main objective of this project is to implement a multi-antenna receiving system consisting of multiple radio-frequency (RF) antennas connected to a switching network which the author is required to source for.

1.3 . Original Project Scope

The RF signal at the many-to-one switching network will flow through the single receiver structure consisting of a RF-to IF down-converter and an acquisition system. The antennas and single channel receiver will be provided but the author is expected to source for the necessary RF switching components and other devices to build the switching network. Upon successful integration of the necessary RF components to form the switching network, the student is expected to test and verify the switching network using signal flow analysis.

1.4 . Change of Project Scope

Since this is the first phase of the project, one of the major problems faced by the author and the research scientist from Temasek Lab@NTU is that they are unable to get the funding for the purchase of the hardware of the switching network. Therefore, there is a slight change from the original project scope whereby the author will focus on the research on the switching network and software implementation of the antenna arrays on LabVIEW together with the software analysis of the receiving system on MATLAB.


2.1. Introduction

High resolution direction finding (DF) algorithms can allow the antenna array system to attain accurate direction-of-arrival (DOA) estimation in the presence of co-channel and multipath interference.

One such algorithm is the Multiple Signal Classification (MUSIC) algorithm which is used for frequency estimation and emitter location. [3] Another such algorithm is the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm which is used to determine parameters of a mixture of sinusoidal in background noise. [4] The Weighted Subspace Fitting (WSF) algorithm is more widely used in multiple target detection of signals.

Many of the high resolution DF algorithms, such as MUSIC, ESPRIT, WSF etc, requires the number of receivers in the system to match the number of array antennas in order to support beamforming techniques and DOA estimation. [2]

However, due to the large amount of receivers needed in the system, these antenna arrays processing system is expensive to implement in applications where the requirements are wide instantaneous frequency coverage and tight constraints in volume, weight and size.

2.2. Previous Approaches involving more than 1 receiver

Over the years many methods for high resolution direction finding were proposed which allows for the number of antennas used in the array to be greater than the number of receivers.

In one of these approaches, J. Sheinvald and M.Wax proposed in the article Detection and localisation of multiple signals using subarrays Data [5] that even thought the number of receivers needed is significantly reduced to a minimum of two, the proposed method requires multi-dimensional search algorithms to determine the DOA of multiple signal sources. Furthermore, discovering the DOA of the multiple sources is often quite computationally demanding and there is no confirmed guaranteed global convergence.

In the approach by K. M. Buckley and X. L. Xu in the article Recent Advances in High Resolution Spatial Spectrum Estimation [6], the application of computationally efficient MUSIC algorithm and Capons beamformer is made possible by estimating the DOA from a restricted number of antenna outputs from a sub-array of antennas.

J. G. Worms proposed in the article RF Direction Finding with a Reduced Number of Receivers by Sequential Sampling [7], a similar approach was proposed that combined the cost-function of each sub-array incoherently. However, the numbers of signal sources that can be discovered and resolved by the approaches are limited by the number of elements in the sub-array. Furthermore, the above approach resulted in poor estimation performance.

The approach proposed by E. Fishler and H. Messer in the article Multiple source direction finding with an array of M sensors using two receivers [8] is based on the reconstruction of the array covariance from the sub-array data. An advantage in this approach is that it allows the direct application of the MUSIC estimator.

2.3. Single receiver approach

In Angle of arrival solution using a single receiver [9], it was proposed that DOA estimation processing architectures using only one receiver channel to sample the antenna array element was possible. By synchronizing the sampling and switching of the antennas, the underlying method of these approaches is to sequentially sample the antenna elements as fast as possible such that the effect of sequentially sampling of the antenna can be approximated by phase shifts.

As a result, the received signal vector, as in the case of a full channel antenna array system, can be approximated. In this way, the approach allows the application of computationally efficient algorithms such as the MUSIC estimator. [9]

However, deploying such an approach requires the antennas to be sampled at very high rates and the sampling rate will increase proportionally with receiver bandwidth and the number of antennas. [9] It was recommended in the article Angle of arrival solution using a single receiver that the sampling rate should be in excess of 1GHz.

Although it seems that the above approach fulfils the requirement of using only one receiver, however there is a need for very high speed RF switches and Analog-to-Digital Converters (ADC). [9] Furthermore, there is also the need for the ability to handle the large amount of data due to the high sampling rate which will increase the cost and complexity of the DF system, hence, diminishing the gain due to the reduced number of receivers.

2.4. High resolution DF with a single channel receiver

A method for high resolution DF with an antenna array was proposed in the paper High resolution DF with a single channel receiver by C.M.S See. It was stated that unlike previously developed algorithms, the proposed approach can achieve high resolution DF with only one receiver, thereby offering significant hardware savings. [2] Furthermore, the method does not require the need for high speed RF switches and ADC, thus saving more on the expensive hardware that is no longer needed.

The proposed approach requires the signal received by the antenna array to be pre-processed by a beamformer network where each of the beamformer output ports are sequentially sampled by an RF switch. As the power of each beamformer output ports is a function of the array covariance matrix, a Kronecker form can be derive which leads to a unique least squares estimates of the array covariance matrix using the power measured from all the beamformer output ports. [2]

With the array covariance matrix estimated, conventional high resolution DF algorithms, such as MUSIC, can be applied to determine the DOA estimation of the multiple sources arriving at the receiving antenna array.

2.5. Proposed Approach

In the proposed approach, as shown in the figure below, the signals received by a N element antenna array is pre-processed by an analog beamformer network with M output ports. The M channel signals are sequentially sampled by an M to 1 RF switch. The single channel output from the RF switch is down converted by a single channel receiver and sampled at Nyquist rate by an ADC for digital signal processing. [2]

The received signal power associated with each beamformer output, zi(t), is estimated from the sampled data and is given by

where ai is the vector of beamformer weights and ni(t) is the receiver noise. Without any loss of generality, it can be assume that the dominant noise comes from the receiver. The signal received by the antenna array, r(t), is given by

where A(?) = [ a(?1) ... a(?d) ] with a(?i) being the steering vector associated with angle of arrival ?i and s(t) is the source waveform . The measure power of the beamformer outputs is a function of the array covariance matrix and the beamformer weight vector:

Once the array covariance matrix is reconstructed from , high resolution DF algorithms, such as MUSIC, can be used to estimate the DOA of the signal sources. It is important to point out that the signal power of each beamformer port can be estimated in frequency or in time domain. When wideband receiver is used to achieve wide instantaneous spectrum coverage, the signal power at eh frequency of interest can be estimated in the frequency domain using Fast Fourier Transform. [2]

2.6. Advantages

Apart from achieving significant hardware savings by enabling high resolution DF with only one receiver, the proposed method also offers the following advantages:

  1. As it derives the array covariance matrix from the beamformer output power, the sampling of the beamformer output power, the sampling of the beamformer outputs can be done at very low rate. Hence only low speed RF switches will be needed here. [2]
  2. It does not require the received signals to be oversampled and the ADC sampling rate is only low bounded by the Nyquist rate. [2]
  3. When only one receiver is used, the DF processor based on the proposed method does not require receiver calibration. This will further simplify and reduce the cost of the hardware. [2]

As seen from these above advantages, the proposed approach can offer low cost and parsimonious DF architecture for high resolution DOA estimation.


3.1. Beamforming and Spatial Filtering

Beamforming is a signal processing technique used in sensor arrays for directional signal transmission or reception. Each antenna elements are separated from its nearest element by half of the transmit signal wavelength. The spatial selectivity is achieved by using adaptive or fixed receive/transmit beam pattern. [10]

The idea is to point the array in one direction at a single time and measure the output power. The steering locations result in maximum power yield the DOA estimates. The array response is steered by forming a linear combination of the sensors output. [11]

In the above figure, sensor outputs are each multiplied by a complex weight and then summed. This beamformer depicted in the above figure which samples the propagating wave field in space, is typically used for processing narrowband signals. With narrow-band systems the time delay is equivalent to a phase shift, therefore in this case the array of antennas, each one shifted a slightly different amount, is called a phased array. [12] The output at time k, y(k), is given by a linear combination of the data at the J sensors at time k:

where * represents complex conjugate. To simplify notation, it is conventional to multiply the data by conjugates of the defined weights. Each sensor is assumed to have any necessary receiver electronics and an ADC if beamforming is performed digitally.

The beamformer in the figure below samples the propagating wave field in both space and time and is often used when signals of significant frequency extent (broadband) are of interest. The output in this case can be expressed as:

where K 1 is the number of delays in each of the J sensor channels. If the signal at each sensor is viewed as an input, then a beamformer represents a multi-input single output system. [13]

Beamforming takes advantage of interference to change the directionality of the array. When transmitting, a beamformer controls the phase and relative amplitude of the signal at each transmitter in order to create a pattern of constructive and destructive interference in the wave front. [10] When receiving, information from different sensors is combined in such a way that the expected pattern of radiation is preferentially observed.

An array with attached delay lines provides a spatial/temporal sampling of propagating sources. The above figure illustrates this sampling of a signal propagating in plane waves from a source located at DOA ?. With J sensors and K samples per sensor, at any instant in time the propagating source signal is being sampled at N=JK non-uniformly spaced points. T (?), the time duration of the first sample of the first sensor to the last sample of the last sensor, is termed the temporal aperture of the observation of the source at ?. [10]

As the notation suggest, temporal aperture will be a function of DOA ?. Plane wave propagation implies that at any time k a propagating signal, received anywhere on a planar waveform perpendicular to a line drawn from the source to a point on the plane, has equal intensity. Propagation of the signal between 2 points in space is then characterized as pure delay. In the above figure, ?1 (?) represents the time delay due to plane wave propagation from the 1st reference to the ith sensor. [10]

The correspondence between FIR filtering and beamfroming is closest when the beamformer operates at a single temporal frequency w0 and the array geometry is linear and equi-spaced as illustrated in the figure below.

3.2. Beamformer Classification

A beamformer is a processor used together with an array of sensors to provide a versatile form of spatial filtering. The sensor array collects spatial samples of propagating wave fields, which are processed by the beamformer. The aim is to estimate the signal arriving from a desired direction in the presences of noise and interfering signals. A beamformer performs spatial filtering to separate signals that have overlapping frequency content but originate from different spatial locations. [10]

Beamformers can be classified as either data independent or statistically optimum, depending on how the weights are chosen. The weights in a data independent beamformer do not depend on the array data and are chosen to present a specified response for all signal/interference scenarios. On the other hand, weights in a statistically optimum beamformer are chosen based on the statistics of the array data to optimize the array response. In general, the statistically optimum beamformer places nulls in the directions of interfering sources in an attempt to maximize the signal to noise ratio (SNR) at the beamformer output. [10]

In statistically optimum beamforming, there are mainly four types of beamformers - Multiple Sidelobe Canceller (MSC), reference signal, maximum SNR and Linearly Contstraint Minimum Variance (LCMV). Data independent beamformer design techniques are often used in statistically optimum beamforming, e.g. constraint design in linearly constrained minimum variance beamforming. The statistics of the array data are not usually know and may change over time so adaptive algorithm are typically employed to determine the weights. The adaptive algorithm is designed so the beamformer response converges to a statistically optimum solution. Partially adaptive beamformers reduce the adaptive algorithm computational load at the expense of a loss in statistical optimality. [14]

3.3. Data Independent Beamforming

The weights in a data independent beamformer are designed so the beamformer response approximates a desired response independent of the array data or data statistics. The design objective for the data independent beamformer is approximating a desired response which is similar to that for classical Finite Impulse Response (FIR) filter design. [10]

In classical or conventional beamforming, beams are formed in a classical sense where a desired response of unity at a point of direction and zero elsewhere is approximated. Consider the problem of separating a single complex frequency component from other frequency components using the J tap FIR filter illustrated in the above figure. If frequency w0 is of interest, then the desired frequency response is unity at w0 elsewhere. A common solution to this problem is to choose w as the vector d(w0). This choice can be shown to be optimal in terms of minimizing the squared error between the actual response and desired response. [10]

The actual response is characterized by a main lobe (or beam) and many sidelobes. The Dolph-Chebyshev method can be used to achieve the desired sensitivity pattern by allowing the minimization of main-lobe width for a specific side-lobe level. A main lobe is produced together with nulls and side-lobes. As well as controlling the main-lobe width (the beam), and the side-lobe levels, the position of the nulls can be controlled. This is useful to ignore noise or jammers in one particular direction while listening for signal sources in other directions. [15]

In spatial filtering, one of the main interests is in receiving a signal arriving from a known location point ?o. Assuming the signal is narrowband frequency of w0, a common choice for the beamformer weight vector is the array response vector d(?o,w0). The resulting array and beamformer is termed a phase array since the output of each sensor is phased shifted prior to summation. If a source from another DOA is of interest, delays can be electronically implemented at the sensor outputs to compensate for that DOAs inter-sensor propagation delays thereby temporarily aligning the source. The delays and summing device constitute a beamformer. A more versatile approach is to use filters at the sensor outputs and sum the filter outputs. [10]

3.4. Statistically Optimum Beamforming

In statistically optimum beamforming the weights are chosen based on the statistics of the data received at the array. In other words, the goal of applying statistically optimum beamforming is to optimize the beamformer response so that the output contains minimal contributions due to noise and signals arriving from directions other that the desired signal direction. [10]

In statistically optimum beamforming, there are mainly four types of beamformers - Multiple Sidelobe Canceller (MSC), Reference Signal, Maximum SNR and Linearly Constraint Minimum Variance (LCMV).

3.5. Multiple Sidelobe Canceller (MSC)

The multiple sidelobe canceller (MSC) consists of a main channel and several auxillary channels as illustrated in the figure below.

The auxiliary channel weights are chosen to cancel interference entering through the sidelobes of the main channel response. The main channel can be either a single high gain antenna or a data independent beamformer. It has a highly directional response, which is pointed in the desired signal direction. Interfering signals are assumed to enter through the main channel sidelobes. [16] The auxiliary channels also receive the interfering signals. The goal is to choose the auxiliary channel weights to cancel the main channel interference. This implies that the response to interferers of the main channel and linear combination of auxiliary channels must be identical. The overall system then has a response of zero as illustrated in part (b) of the figure above which depicts the main channel, auxiliary branch, and overall system response when an interferer arrives from direction ?1. [16]

Choosing the weights to minimize output power can cause cancellation of the desired signal since it also contributes to total output power. As the desired signal gets stronger it contributes to a larger fraction of the total output power and the percentage cancellation increases. [16]

The MSC is very effective in applications where the desired signal is very weak relative to the interference, since the optimum weights will not pay any attention to it, or when the desired signals is known to be absent during certain time periods.

3.6. Use of Reference Signal

The use of reference signal is where much is known of the desired signal and a signal to generate that closely represent the desired signal, and then the weights could be chosen to minimize the mean square error between the beamformer output and the reference signal. The weight vector depends on the cross covariance between the unknown desired signal and the reference signal. Acceptable performance is obtained provided this approximates the covariance of the unknown desired signal with itself. [10]

For example, if the desired signal is amplitude modulated, and then acceptable performance is often obtained by setting the reference signal equal to the carrier. It is also assumed that the reference signal is uncorrelated with the interfering signals. The fact that the direction of the desired signal does not need to be known is a distinguishing feature of the reference signal approach. [10]

3.7. Maximization of Signal to Noise Ratio

For the maximization of SNR approach, weights are chosen to directly maximize the SNR. A general solution for the weights requires knowledge of both the desired signal, noise and covariance matrices and attaining these knowledge greatly depends on the application itself. [10]

3.8. Linearly Constrained Minimum Variance Beamforming

In most of the applications, none of the above approaches is satisfactory. The desired signal may be of unknown strength and may always be present, resulting in signal cancellation with the MSC and preventing estimation of signal and noise covariance matrices in the maximum SNR processor.

Lack of knowledge about the desired signal may prevent utilization of the reference signal approach. These limitations can be overcome through the application of linear constraints to the weight vector. Use of linear constraints is a very general approach that permits extensive control over the adapted response of the beamformer.

The basic idea behind linearly constrained minimum variance (LCMV) beamforming is to constrain the response of the beamformer so that signals from the direction of interest are passed with specified gain and phase. The weights are chosen to minimize output variance of power subject to the response constraint. This has the effect of preserving the desired signal while minimizing contributions to the output due to interfering signals and noise arriving from directions other than the direction of interest.

The generalized sidelobe canceller (GSC) represents an alternatve formulation of the LCMV problem, which provides insight, is useful for analysis, and can simplify LCMV beamformer implementation. It also illustrates the relationship between the MSC and LCMV beamforming. Essentially, the GSC is a mechanism for changing a constrained minimization problem into unconstrained form.

The primary implementation advantages of this alternate but equivalent formulation stem from the facts that the weights are unconstrained and a data independent beamformer is implemented as an integral part of the adaptive beamformer. The unconstrained nature of the adaptive weights permits much simpler adaptive algorithms to be employed and the data independent beamformer is useful in situations where adaptive signal cancellation occurs.

3.9. Signal Cancellation in Statistically Optimum Beamforming

Optimum beamforming requires some knowledge of the desired signal characteristics. For the maximization of SNR method and the reference signal method, both requires the statistics of the desired signal. For the MSC method, the signals direction is required. For the LCMV beamformer, the response vector d(?,w) of the desired signal. If the required knowledge is inaccurate, the optimum beamformer will attenuate the desired signal as if it were interference. Cancellation of the desired signal is often significant, especially if the SNR of the desired signal is large.

Another cause of signal cancellation is the correlation between the desired signal and one or more interference signals. This can result either from multipath propagation of a desired signal or from smart (correlated) jamming. When interference and desired signals are uncorrelated, the beamformer attenuates interferers to minimize output power. However, with a correlated interferer the beamformer minimizes output power by processing the interfering signal in such a way as to cancel the desired signal. If the interferer is partially correlated with the desired signal, then the beamformer will cancel the portion of the desired signal that is correlated with the interferer.

3.10. Adaptive Algorithms for Beamforming

The optimum beamformer weight vector equations require knowledge of second order statistics which are not usually known. However, with the assumption of ergodicity, these statistics and therefore the optimum weights can be estimated from the available data. Statistics may also change over time due to moving interferers. To solve these problems, weights are typically determined by adaptive algorithms.

There are two basic adaptive approaches block adaptation and continuous adaptation. For block adaptation, statistics are estimated from a temporal block of array data and used in the optimum weight equation. For continuous adaptation, weights are adjusted as the data is sampled such that the resulting weight vector sequence converges to the optimum solution. If a non-stationary environment is anticipated, block adaptation can be used, provided that the weights are recomputed periodically. Continuous adaptation is usually preferred when statistics are time-varying or when the number of adaptive weights M is moderate to large.

3.11. Interference Cancellation and Partially Adaptive Beamforming

A fully adaptive beamformer uses all available degree of freedom and a partially adaptive beamformer uses a reduced set of degrees of freedom. Reducing degrees of freedom lowers computational requirements and often improves adaptive response time. However, there is a performance penalty associated with reducing the degree of freedoms. A partially adaptive beamformer cannot converge to the same optimum solution as the fully adaptive beamformer. The goal of partially adaptive beamformer design is to reduce degrees of freedom without significant degradation in performance.

The degree of interference cancellation is critically dependent on the ability of the adaptive channel to match the main beam response over the interferer frequency extent. This provides a means by which to evaluate partially adaptive beamformers and the majority is on partially adaptive beamforming in narrowband environments.

Several approaches to reducing degrees of freedom are based on processing a subnet of the outputs of the matrix. By selecting various subsets of the auxiliary outputs, the performance of the partially adaptive beamformer can be evaluated. This approach is termed as the element space approach since a subset of the sensor element outputs is utilized.

Another approach call the beam space approach which forms beams by considering the columns of T, a J by H diagonal matrix with real-valued taper weights as diagonal elements. The columns of the matrix are designed as data independent beamformers, each steered to a different location and a sparse matrix of zeros and ones can be used to select a subset of the beam outputs. The objective is to direct a beam at each interfering source so that it can be subtracted from the output of the wo branch.

One way to accomplish this is by selecting enough beams to cover all possible directions from which interferers might arrive. Another is to utilize source direction finding techniques to select which beams correspond to estimated interferer directions. The biggest advantage of the element space approach is the simplicity of implementation. Improved performance obtained using beam spaced processing is especially evident for interference due to either spatially distributed sources or sources with appreciable temporal bandwidth.


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