Detection, Estimation and Radiation Formation Using Smart Antennas for the Spatial Location

The incoming Electromagnetic signals are taken, amplitude computation is done along with phase vector computation, the advantage of using amplitude-based detection is that the computed direction will be more accurate. To further enhance the detection accuracy, the base station can implement the multi beam based uniformly excited linear antenna array arrangement [2].

The detection of sources underwater is done first computing the covariance matrix. The covariance matrix not only contains signal but also contains information on ambient noise. The subspace matrix is computed after finding out the eigenvalues, filtering them based on magnitude and then obtaining the lowest eigenvalues to get the noise space matrix. Ambient Noise Elimination is responsible for transforming the matrix to have lower noise magnitude with the help of Singular Value Decomposition (SVD) [3].

Direction of Arrival of a wideband acoustic signal is estimated using the maximal eigen-gap estimator which uses a single sensor vector. Computation of narrowband cross spectral density matrices are obtained by combining the optimal weights which produce signal subspaces which gives rise to maximal eigen-gap estimator. The detection scheme obtains the direction of the acoustic signal falling on the base station, it then performs the computation of cross-spectral density to find the optimal phase shifts. These phase shifts are then used for the radiation generation and data transmission. The Power Spectrum is computed using the Eigen-gap estimator which detects the directions of sources [4].

The source detection is done by computing the Discrete Fourier transform (DFT). Total Least Squares (TLS) is computed by making use of offsets values which perform execution of Taylor equation in order to reduce the noise value [5].

Hydro-acoustics and aeronautics applications also require the detection of sources. The closed-form equation of Cramer- Rao bound is used to detect the sources by making use of antenna used for measuring the attitude. The Gaussian noise is computed along with signal matrix in order to compute a real environment detection of directions [6].

The different variation of co-variance matrix is computed known as Augmented Co-Variance matrix. The argument matrix computation is done in order to reduce the noise effect using rank based minimization. The arrangement of antenna elements is done into two separate prime arrays with each array having the determination of directions of sources [7].

The spatial domain based system increases the capacity of communication model. If we make use of single element at the base station then we have no choice except to process the signal from the sources which are having higher signal strength but when we have an array of elements then we have signal along with them we have delayed version of the same signal so that the detection capacity is improved even if the signal is weak. The value of array manifold vector is computed in a linear fashion by making use of Bayesian learning (SBL). Size and computational complexity are the factors used for detection of direction based on likelihood functionality [8].

The detection of directions for the sources is done based on amplitude computation, the eigenvectors are found out for the correlation matrix. The eigenvalues for the correlation matrix are computed and then arranged in a descending order. If there are N antenna elements then N-Nsources value is computed where Nsources are the number of users to be detected. Once those are computed the subspace matrix is determined and then compute the power spectrum for detecting the sources [9].

Hybrid-ADC is used for multi user massive MIMO systems, which computes the spatial covariance matrix which forms the power spectrum using MUSIC method. The group of independent detection arrays are used which form the linear equations containing both the amplitude and directions from the sources. Detection, Estimation and Location is done on the basis of noise subspace [10].

The Bayesian inference method computes the detection for algorithms, IMUSIC method will compute the weight vector based on spatial computation using grid model and computation of steering vector using Taylor method [11].

This array is divided into two sections. The first section makes use of conjugate value and second section will perform the difference between signal amplitude values [12]. Amplitude and phase entities are computed from each of antenna elements. Lower Cost and bandwidth computations are achieved in order to perform the correlation between actual signal hitting the base station and its Hermitian transpose. Multi beams weights are computed and then radiation is formed on each source independently [13].

The measure of pressure and velocity are computed in order to determine the direction of sources. The detection process methods are divided into multiple types. The combination of histogram along with intensity computation is used for likelihood based methods. In the second type subspace is computed over the co-variance matrix in order to determine the directions of sources. The capability of the algorithms to determine the sources which are closely separated into distinct directions is better for second type as compared to first type [14]. The compressive based sensing is responsible for first detecting the direction of sources. Combination of beam space techniques are used for detection of single and multiple directions [15].

The computation of magnitude along with subspace matrix is constructed to derive the Power Spectrum, which uses the Co-Array MUSIC-Group Delay (Co-Array MGD) algorithm. This Co-Array MGD Algorithm is generated by forming a Product of Co-Array MUSIC Magnitude and Co-Array Group Delay Function. The Co-Array Group Delay Function is obtained by taking the negative differentials of the phases, this enables the effective detection of the closely-spaced sources in the spatial domain [16].

Long Term Evolution (LWA) array will execute the beam-forming on the applications which are used for indoor as well mobile based communication. The array is created using a feeding element along with four port based SIW. Different beam directions are determined by making use of phase shifts and then weights are attached to individual element in order to determine the directions of sources [17].

The detection of directions involves sequence of steps, the first step is to compute the steering vector followed by amplitude computation. The computation of array correlation matrix is done combining both signal impinging on the antenna elements and noise signals. The eigenvalues are computed and then decrease in the value of Eigen are performed in the sorted order. After that the eigenvectors are found for those eigenvalues and then noise subspace is found to detect the directions of signal. The beam-forming is done by computing the steering vectors, finding the mean square error along with step size in order to compute the phase shifts which can be applied to individual antenna elements and then form the main beam towards the radiation formation [18].

The channel state information (CSI) is computed by making use of antenna elements which can be applied to individual element in order to compute the phase shifts. The training data is first generated from the mobile signal that will be pure signal. The steering vector is computed for the pure signal direction along with other interference vector directions. The next step is to compute the error signal, compute the step size and finally the phase shift is applied to individual antenna element to form the main beam and side lobes towards the interference directions [19].

The communication is performed by making use of duplex approach at the base station. During the reception the antenna elements are used to receive the electromagnetic waves and process the waves in order to detect the directions. During the transmission phase the phase shifts are computed and then applied to individual antenna elements to form the beam and side lobes. The uplink transmission happens from the mobile source towards the base station. During the downlink process the transmission of data from the base station to the mobile source [20].

The antenna elements are arranged in a linear fashion with each element equally spaced between antenna elements. The phase shift vectors are computed by making use of previous phase shifts, step size, error computation along with phase shifts. The phase shifts are computed based on the value of maximum signal to noise ratio (SNR). The fading is computed based on gamma variables and then chi square computation is done to compute the updated values of weights. The weights are computed in order to form the main beam towards the source and then side lobes towards interference users [21].

The antenna will be configured in a smart and rewire elements configuration. The signal coming from sources are hopped on multi other elements and then send towards the base station. The relay based antenna elements can be used in middle in order to perform the reflection of transmitted beam so that it can be reflected towards the mobile user [22].

The detection of the desired users in the spatial domain is obtained by computing the Power Spectrum, wherever the peaks arises it denotes the location of the desired user. Thus the computation of Power Spectrum is done in multiple steps such as: The First step is to compute the steering vector in a specific direction, the Second step is to steer the beam towards the source. The accuracy is increased by making use of minimum variance distortion-less response, the pattern synthesis focuses on computing the phase shifts, which can be applied to individual antenna elements. The Peaks of the Power Spectrum represent the detection of the desired users in the spatial domain [23].

The estimation of angles for the mobile sources by performing the amplitude computation as well as phase computation. There are multiple ways in which phase shifts computation can happen based on either amplitude peak detection or correlation based method then phase shift will get applied to individual antenna elements [24]. The elements are arranged in a linear fashion with each element spaced at an equal distance The phase shifts are computed in such a way that main beam is formed towards the actual source direction and then side lobe radiation is formed towards the unwanted directions. Comparison of algorithms are done based on computation of mean square error values and NLMS has the low error [25].

The elements are arranged in a uniform linear array (ULA) fashion. There is an error due to difference obtained between original signal and signal received at the base station and the error can be reduced by making use of MVDR based processing [26].

Long Term Evolution (LTE) along with Wimax technology are responsible for making use of beam formation process by applying the phase shifts to individual elements. The generation of main beam in a specific direction is done based on phase shifts which have been applied. Beam Division Multiple Access (BDMA) is used to form the beam towards the source by applying the phase shifts to antenna elements [27].

The beam-forming based co-efficient are computed by making use of Capon spatial spectrum Signal by computing the co- variance matrix which contains the steering vector of all the directions where sources are available. The phase shifts are computed and then applied to each of the antenna elements in order to form the main beam towards the desired user direction and have side lobe towards the interference direction [28].

Digital based phase shifts are computed in an adaptive fashion and then applied to the individual antenna elements. Classic approach makes use of library of weights which does not take into consideration the noise present in electromagnetic wave as well as noise present within the antenna elements. The adaptive approach will take the noise also into consideration and then adjust them to take of cancellation of interference [29].

The beam which are narrow in nature towards the source can be utilized for larger amount of data transfer. The steering of beam across the directions at mmWave frequencies help in finding the location of resource and then follow the resource by applying dynamic phase shift based on changing location of the resource. Bayesian method which can predict the mobility nature of the resource and then target the beam towards detection of resource [30]. The transmission of data in the Sensing Data Network consists of base station (BS) which makes use of array of antenna elements there by increasing the throughput in the entire area. Energy Source along with hybrid based system is used to apply the phase shifts to the individual antenna elements [31].

The emitting signals from the antenna elements produce main radiation, side lobes for disturbance signal and null values. All the elements are spaced at equal intervals with a spacing of distance (d). The main radiation is formed towards the actual direction of mobile with side lobes towards disturbance. The beam is shifted in different directions with phase shifts applied to each antenna elements.

The antenna elements used in the base station are attached to individual array elements with each element applied with a phase vector which is computed based on incoming electromagnetic waves along with noise vector. The phase vector must be computed in an intelligent manner with the help of a software algorithm which can be embedded on a device present at the base station.

4.1 Weighted Linear Method (WLM)

The phase shifts are computed and used in the communication based use cases. The algorithm is robust in nature along with low complexity value. During the computation of weight vector the training signal knowledge is important for computation of phase shifts. The phase shifts are computed using the following.

$P S_{W L}(k+1)=P S_{W L}(k)+$

$\frac{A C i n v * E M S_{v}(\theta)}{E M S v^{H}(\theta) * A C_{i n v} * E M S_{v}(\theta)}$

$+\sum_{k=1}^{N_{\text {disturb }}} \frac{A \operatorname{Cinv} * E M S_{v}\left(\theta_{k}\right)}{E M S v^{H}\left(\theta_{k}\right) * A C_{i n v} * E M S_{v}\left(\theta_{k}\right)}$

Where,

$P S_{W L}(k)=$ previousphaseshifts

$P S_{W L}(k+1)=$ phaseshiftsofnextiteration

$E M S_{v}(\theta)=$ directionalvector

$E M S v^{H}(\theta)=$ inversefordirectionalvector

$A C_{i n v}=c o-$ relationinverse

$N_{\text {disturb }}=$ numberofdisturbances

$E M S_{v}\left(\theta_{k}\right)$=directionalvectorforkthdisturbance $\theta_{k}$

$E M S v^{H}\left(\theta_{k}\right)=$hermitiantransposeforEM $S_{v}\left(\theta_{k}\right)$       (5)

4.2 Widely Linear Conjugate Gradient Method (WLCG)

$w p s(k+1)=\left[w p s^{T}(k) * w p s^{H}(k)\right]^{T}$

Where,

$w p s(k)=\frac{\text { Where }}{2 R\left\{E M S^{H}\left(\theta_{o}\right) * v v(k)\right\}}$

$v v(k)=v v(k-1)+\alpha w(k) * p w k(k)$

$\alpha w(k)=\frac{R\left\{g w_{k}^{H}(k-1)+p w k(k-1)\right\}}{R\left\{p w_{k}^{h}(k) * u w k(k)\right\}}$

$P w(k)=g w_{k}(k)+\beta w(k)+p w k(k-1)$

$\beta w(k)=\frac{R\left\{g w_{k}^{H}(k) * g w_{k}(k)\right\}}{R\left\{g w_{k}^{H}(k-1) * g w_{k}(k-1)\right\}}$

$g w_{k}(k)=g w_{k}(k-1)-\alpha w(k) * u w_{k}(k)$

$u w_{k}(k)=A C(k) * P w(k)+C w(k) * P^{*} w(k)$

$C w(k)=\lambda C w(k-1)+x w(k) * x w^{H}(k)$

$\lambda=$ operatingwavelength

$A C(k)=\lambda A C(k-1)+x w(k) * x w^{H}(k)$

$\beta w(k)=\frac{R\left\{g w_{k}^{H}(k) * g w_{k}(k)\right\}}{R\left\{g w_{k}^{H}(k-1) * g w_{k}(k-1)\right\}}$

$g w_{o}(k)=E M S\left(\theta_{o}\right)-A C(k) * v w_{o}(k)-C w(k)$ * $v w^{*}{ }_{o}(k)$

$\operatorname{EMS}\left(\theta_{o}\right)=$ desireddirectionvector

$E M S^{H}\left(\theta_{o}\right)=$ hermitiandirectionvector       (6)

The complexity of WL method can be future reduced based on usage of co-variance block on the input signal. The method is built on top of MVDR method so that better performance, low complexity and very high stability can be achieved. The phase shifts are computed using the following.

4.3 Low Complexity – WLCG Method (LCWLCG)

The method is created by the amalgamation of WL and WLCG methods, the auto-correlation of the signals is measured by using the training signal with its Hermitian Transpose helps in building the signal which is used for improving the accuracy of phase shifts which have been computed. The adjustment of the phase shifts based on noise computation along with step size rate adjustment helps in reducing the mean square error and helps in performing better convergence. Step size is also adjusted dynamically by making use of optimum value.

$P S_{L C W L C G}=\frac{v_{w}(k)}{2 * R\left\{E M S^{H}\left(\theta_{o}\right) * v_{w}(k)\right\}}$

Where,

$E M S^{H}\left(\theta_{o}\right)$ = hermitian transpose direction vectorfor $\theta_{o}$

$v_{w}(k)=$correlation between two signals with step

$v_{w}(k)=v_{w}(k-1)+\alpha w(k) * p w(k)$

$\alpha w(k)=$ stepsize

$\alpha w(k)=$ $\frac{R\left\{p w^{H}(k) * g w(k-1)\right\}(\lambda-\eta) R\left\{p w^{H}(k) E M S\left(\theta_{o}\right)\right\}}{R\left\{p w^{H}(k) * u w(k)\right\}}$

$\eta$ varied between 0 to $0.5$

$p w(k+1)=g w(k)+\beta w(k) * p w(k)$

$p w(k)=E M S\left(\theta_{o}\right)$

$u w(k)=A C(k) * p w(k)+C w(k) * p^{*}(k)$

$R w(k)=\lambda R w(k-1)+x w(k) * x w^{*}(k)$

$C w(k)=\lambda C w(k-1)+x w(k) * x w^{*}(k)$

$R w(0)=\delta w I$

$\delta=0.5$

$\operatorname{EMS}\left(\theta_{o}\right)=$ desired angle direction vector

$\lambda=$ wavelength

$x w(k)=$ signal

$x w^{*}(k)=$ conjugatetransposeofsignal       (7)

In this paper performance analysis of algorithms for Direction of Arrival (DoA) methods as well as the Beamforming (BF) methods have been performed.

Experimental simulations are conducted and comparison is done for multiple cases with respect to the Bias, Resolution and Time complexity of each algorithm for the Direction of Arrival (DoA) methods, NSM DoA algorithm consistently delivered the following Bias [0.0258, 0.0258, 0.1170, 0.2286] and Time (ms) [0.7386, 0.7386, 0.8134, 0.8253], thus it is better for both the scenarios which uses smaller as well as larger number of antenna array elements.

Similarly for the case of Beamforming (BF) methods the Mean Square Error and Beam-directions have been computed and compared. The following comparison results were found: The MSE when working with fewer number of antenna array elements, the Low Complexity-Widely Linear Conjugate Gradient Method (LCWLCG) Algorithm provided the fast convergence rate of 45 iterations, whereas Weighted Linear Method (WLM) and Widely Linear Conjugate Gradient Method (WLCGM) got converged at 80 iterations.

When the large number of antenna array elements are used at the base station, the Mean Square Error (MSE) gets reduced and fast convergence rate of 25 Iterations is obtained by using the Low Complexity-Widely Linear Conjugate Gradient Method (LCWLCG) Algorithm. When LCWLCG Algorithm is compared with other algorithms such as Weighted Linear Method (WLM) and Widely Linear Conjugate Gradient Method (WLCGM) the signal convergence rate is very slow it almost takes around 80 iterations to get converged thus has higher mean square error value.

Beamforming using Smart Antenna System produces narrow sharp pencil-line main beam towards the desired user and deep spectral nulls are pointed towards other interfering users who are present at different angular directions in the spatial field, thus suppressing these unwanted interfering users improves the overall system throughput and efficiency.