ADAPTIVE ANTENNAS. NARROW BAND AND WIDE BAND BEAMFORMING

Transcription

1 ADAPTIVE ANTENNAS NARROW BAND AND WIDE BAND BEAMFORMING 1

2 1- Narrowband beamforming array An array operating with signals having a fractional bandwidth (FB) of less than 1% f FB ( f h h fl x100% f ) / 2 l where f h and f l are the highest and lowest components of the signal respectively The bandwidth of the impinging signal should be narrow enough to make sure that the signals received by the opposite ends of the array are still correlated with each other As the bandwidth of the signal is increased the phase weighting computed to steer the beam at a particular angle is no longer correct, therefore a more complex weighting arrangement is required (Wideband beamforming) 2/27/2017 LECTURES 2

3 Let us demonstrate that the bandwidth of the impinging signal should be narrow enough to make sure that the signals received by the opposite ends of the array are still correlated with each other Let the maximum delay between the first and last element in an array is τ max, this delay should be less than the time period in time domain then: 1/τ max.>>bandwidth of the signal Example: GSM, f=900mhz, BW=200KHz, 10 elements broad side array oriented along y-axis with half wave spacing τ max = (M-1)dsinθ/C =(M-1)(λ/2)/C =(M-1)/2f 1/τ max = 2x900x10 6 /9=200x10 6 >>200KHz The narrowband is valid in GSM system 2/27/2017 LECTURES 3

4 Butler matrix for narrowband switching (fixed) beamforming Butler matrix is a microwave network, employed in beamforming (switched beam networks) and scanning networks for linear and circular antenna arrays at narrowband When it is connected to an array antenna, it will act such that, the array will have a uniform amplitude and constant phase shift between the element of the array. This will result in radiation at one of M different discrete directions covering a 180 o angular sector of space 4

5 The actual direction of the beams depends on which one of the input the signal is introduced i.e., when one of the input ports is excited by an RF signal, all the output ports feeding the array elements are equally excited but with a progressive phase between them. This results in the radiation of the beam at a certain angle If multiple beams are required, two or more input ports need to be excited simultaneously. In that case the beams should be orthogonal ( the angles of minima of one beam pattern are corresponding to the angles of the main beams of the other beams) The phase difference between the array radiating elements due to the path difference and also the beam location are given by 5

6 2 d 2p 1 cos x180 M o p=1,2,... ± tends for the right and left beams The Butler matrix is consisting of hybrid junctions couplers and phase shifters which can be implemented by MW technology such as WG or microstrip technology It requires an (M/2)log 2 (M) 90 hybrids interconnected by rows of (M/2)(log₂ M-1) fixed phase shifters to form the beam pattern Example: Number of array elements is 4 oriented on y axis, d/λ=0.5 -Number of couplers= (M/2)log 2 (M)=4 -Number of phase shifters= (M/2)(log 2 M-1) =2 - p=1,2 ± tends for the right and left beams -Phase shift between elements due to phase shifts are p =1 φ=180/4=45 o θ o =sin -1 (45/180)= o 1R, p= -1 φ=-180/4=-45 o θ o =sin -1 (-45/180)= o 1L, p=2 φ=3x180/4=135 o θ o =sin -1 (135/180)= 48.6 o 2R, p=-2 φ=-3x180/4=-135 o θ o =sin -1 (-135/180)= o 2L,

7 Example: Number of array elements is 8oriented on y axis, d/λ=0.5 7

8 2 d 2p 1 cos x180 M o p=1,2,3,4. ± tends for the right and left beams Because of the dependence of the phase shift on the frequency the beam angle will vary with the frequency, i.e., the Butler matrix forms phase steered beams which squint with frequency Also the beam cluster is narrow for high frequency and vise versa

9 Butler matrix advantages -It is easy to implement and requires few components to build compared to other networks -The loss involved is very small, which comes from the insertion loss in hybrids, phase shifters, crossover and transmission lines Butler matrix disadvantages -Beamwidth and beam angles tend to vary with frequency causing the beam squint with frequency - Also, as the matrices get bigger, more and more crossovers make interconnections complex 9

10 2- Wideband beamforming array An array operating with signals having a fractional bandwidth (FB) up to 25% Ultrawide band array is an array operating with signals having a fractional bandwidth (FB) from 25% up to 200% For wideband signals, since each signal consists of infinite number of different frequency components, the value of the weights should be different for different frequencies and we can write the weight vector in the following form: W f ) [ w ( f ) w ( f )... w ( f )] M ( 1 2 T As the signal bandwidth increases the performance of the narrowband beamformer starts to deteriorate, a tapped delay line (TDL) is used on each branch (element) of the array 10

11 The TDL allows each element to have a phase response that varies with frequency, compensating for the fact that lower frequency signal components has less phase shift for a given propagation distance, whereas higher frequency signal components has greater phase shift as they travel the same length This structure can be considered to be an equalizer which makes the response of the array the same across different frequencies by using temporal signal processing (temporal filter; time delay) The inter-element distance, d, is determined by the highest frequency of the input wave and for a uniform one-dimensional linear array, is given by d = c / 2f h 11

12 -The TDL network permits adjustment of gain and phase as desired at a number of frequencies over the band of interest -The far-field signal is received by M antenna elements. Each element is connected to J delay lines with the time delay of T seconds -If the input signals are denoted by x 1 (t), x 2 (t),..., x M (t), -the output signal is the sum of all M 1 J 1 y( t) w x [ t ( j 1) T m 0 j 0 mj m ]

13 Blass matrix for wideband switching (fixed) beamforming The Blass matrix network uses directional couplers and transmission lines to provide adjustable TDL phase shift for the arrays in order to compensate the phase frequency dependence and generates multiple beams Construction M array elements (columns), each connected to M transmission lines M beam ports (rows), each connected to M transmission lines The rows and columns are intersected on nodes, each has a coupler Phase shifters between two consecutive couplers of the same column may be needed Beam forming Beam port 1; top feed line provide zero progressive time delays between elements that couples out a broadside beam and is relatively unaffected by the other feed Any other feed line provide progressive time delays between elements that couples out a beam at different angles off broadside and is affected by the other feed lines M 13

14 Therefore, when you feed signal into the different inputs, you will get different beams at steering angles ( M beams ) There are M beam ports 1,2,,M provides M excitation vectors S 1,S 2,..,S M For each beam there are M signal amplitudes associated to the array elements grouped as excitation vector of length M For M simultaneous beams there is a superposition M excitation vectors of length M a 11 a 21 a M1 The design is to calculate coupling and phase shifting values of the couplers and the phase shifters to obtain the linear superposition of the M desired excitation vectors on the M outputs 14

15 Blass matrix advantages -The Blass matrix is simple in the sense that it has simpler interconnection layout of the circuit since it does not involve any crossovers as in Butler matrix -There is no beam squinting with frequency Blass matrix disadvantages -It has a low performance because its loss is attributed to the resistive terminations -It requires more components compared to the Butler matrix, which makes it costlier and heavier References B. Allen and M. Ghavami, Adaptive array systems, John Wiley& Sons,