AN ULTRA WIDEBAND LINEAR ARRAY BEAMFORMING CONCEPT CONSIDERING ANTENNA AND CHANNEL EFFECTS

Transcription

1 AN ULTRA WIDEBAND LINEAR ARRAY BEAMFORMING CONCEPT CONSIDERING ANTENNA AND CHANNEL EFFECTS Markus Neinhüs 1, Mohamed El-Hadity 2, Sebastian Held 1, Thomas Kaiser 2, and Klaus Solbach 1 1 University Duisburg-Essen, Faculty of Engineering, Department of Hochfrequenztechnik, Germany 2 University Duisburg-Essen, Faculty of Engineering, Department of Communication Systems, Germany ABSTRACT Spatial processing is a promising technique in order to significantly increase the data rate in wireless pulsed transmission systems. It enables beam pointing toward desired signals and null steering to reduce interference with spurious signals or multipath components. In this article, an Finite Impulse Response (FIR) filter controlled linear antenna array for ultra wideband short pulses will be presented. The paper reports the design procedure for ultra wideband radiation pattern. A mathematical framework is given allowing the consideration of antenna and channel characteristics. Finally, we demonstrate the performance of the FIR-filter technique by means of a typical short pulse transmission system, where the line of sight signal is improved in terms of gain and pulse shape, and multipath components are desirably minimized. Key words: UWB Beamforming; Impulse radio; FIR- Filter; Antenna impulse response; UWB channel. 1. INTRODUCTION Recently, interest has grown for ultra wideband (UWB) applications, since the Federal Communication Commission (FCC) released their first report and order regarding UWB transmission systems [1]. They have allotted the spectrum from 3.1 GHz to 1.6 GHz, which enables impulse radio applications, where data is transmitted by trains of ultra short pulses, allowing very high data rates [2]. Array processing and smart antenna concepts offer a promising solution in order to significantly increase the data rate in wireless transmission systems, whose performance is limited by interference, local scattering and multipath propagation [3], [4], [5]. There is a widespread interest in array processing over decades. Examples can be found in radar and in communication systems. Whereas the former application has played the most important role in the past [6], the latter finds its way increasingly to enhance gain and thus enhance the distance, and to reduce interference with spurious signals and multipath components. The need for array processing can directly be assigned to UWB-communication systems, where signals have considerably more multipath components than narrowband signals [7]. Looking at the beamforming concepts being employed in UWB, it can be seen that the well known narrowband phase-shifters [8] have to be replaced by weighting control elements with frequency dependent characteristics, e.g. analogue filters at RF instead of phase shifters. Theoretically, any type of filter fits this requirement, but most appropriate in view of microwave applications are Finite Impulse Response (FIR)-filters, which have already been realized successfully in CMOS technology [9]. Digital beamforming seems to be improper for UWB short pulse applications, since the extremely high bandwidth places great demands on the analogue to digital converters. In realistic environments, the signal received by the antenna array may be affected by the antenna characteristics [1] and channel effects. Hence, for the determination of the filter coefficients we take into account the antenna and channel impulse responses. The former is mainly characterized by the radiation pattern and input impedance of the antenna. For ultrawide bandwidth, those parameters may become strongly frequency dependent functions. If this dependence is moderately flat, we can also use analogue FIR-filters at RF to equalize the frequency dependence of the antenna. Our paper is organized as follows: In the next section the fundamentals of ultra wideband radiation pattern control are presented. In section 3, we consider the antenna characteristics and a simple channel model for our framework. In section 4, we investigate methods to appropriately detect the received signal using a time-domain radiation pattern. In section 5, a typical in-room short pulse transmission system is investigated, which demonstrates the performance of the FIR-beamforming techniques for pulsed signals. Finally, section 6 concludes the contribution. 2. PATTERN CONTROL TECHNIQUES It has been shown that using antennas with high directivity may significantly suppress multipath components in wireless communication systems [11]. However, the

2 Figure 1. Principle of UWB electronic array control. radiation pattern of a single antenna element is normally wide and difficult to adjust. So, the use of two or more antennas, arranged in an array, yields more control to the pattern. In conventional phased array narrowband beamforming, we multiply the signal at each antenna element by a complex weighting factor before summation. The weighting factor phases are chosen to steer the beam to the desired direction [8]. Unfortunately the weighting factors are frequency independent, therefore the narrowband beamformer starts to deteriorate with increasing bandwidth [2]. For instantaneous broadband signals one can replace the complex weighting factors by true-time delay elements (TTD), where the phase varies linearly with frequency [12]. However this techniques still results in a shift of nulls and in a widening of the main beam as a function of frequency. So, for UWB- or pulsed signals it is not possible to place nulls to certain directions as known from narrowband beampattern synthesis [13]. Therefore, our aim is to create frequency independent beam patterns using suitable array weightings. In literature there are presented various techniques allowing frequency independent pattern synthesis [14], [12]. One promising solution regarding the practical realization in microwave frequency range is based on FIR-filtering. Electronic array steering with FIR-filters, where one filter is placed behind each antenna element of the array (Fig. 1), can be considered as an extension of true-time delays with one more degree of freedom. On each antenna element, the FIR-filter causes a phase response that varies with frequency. So, spacial phase shifts due to different frequencies are temporally equalized by FIR-filters. Another objective of the FIR-filters is the equalization of antenna and channel effects. Both antenna and channel characteristics are functions of frequency (see section 3) and they operate like filters in UWB-systems. This filtering may change the shape of the pulse being transmitted, see Fig. 1. If these frequency responses are moderately flat, FIR-filters can compensate them. This method allows ultra wideband radiation pattern synthesis just by Figure 2. General FIR-filter structure with N antenna elements and Mth filter order. adjusting the filter coefficients, whereas the incremental time delays of the filter remain constant, see Fig. 2. In microwave systems those coefficients are realized by broadband amplifiers with bi-phase adjustable gain. The incremental time delays can be implemented by transmission lines of certain length. The concept has been presented in one of our previous publications [15]. Using this method it is possible to apply classical narrowband beamforming techniques to the ultra wideband frequency range FIR-filter control concept In Fig. 1, a linear array with N antenna elements and constant inter-elements spacing d is shown. A short UWB pulse p(t) arrives serially at the antenna elements with a time delay τ, obtained by τ = d c sin θ, (1) where c is the velocity of light. Each antenna element is followed by an FIR-filter, after which the overall signal y(t,θ) is determined by summation. If the FIR-filters are configured to steer the antenna beam pattern to a certain direction, e.g. the line of sight (LOS), the output signal is a constructive superposition of the equalized received signals at the single antenna elements. Fig. 2 shows the structure of the wideband antenna-firfilter system. Each antenna element is connected to M 1 incremental time-delays τ. The delayed input signal is

3 then multiplied by real weighting coefficients a nm, where 1 a nm +1. The overall output-signal y(t,θ) can be obtained in timedomain by N y(t,θ) = y n (t,θ), (2) n=1 where y n (t,θ) is the filter output signal at the nth branch. If the signal behind the nth antenna element is denoted by x n (t,θ), the filter output signal follows y n (t,θ) = x n (t,θ) M m=1 a nm δ t (m 1)τ, (3) where ( ) denotes convolution and δ(.) is the Dirac delta function. Considering that the array has identical antennas, described by their angle dependent impulse response h a (t,θ) (see section 3.1), the received signal at the nth antenna element can be determined as ) x n (t,θ) = p(t) h a (t,θ) δ (t (n 1)τ (4) The resulting time-domain expression for the output signal y(t,θ) can then be expressed by y(t,θ) = p(t) h a (t,θ) (5) N M a nm δ t (m 1)τ n=1 m=1 ) δ (t (n 1)τ Converting Eq. 5 into the frequency-domain, yields Y (f,θ) =P(f) H a (f,θ) (6) N M a nm e j 2π f (n 1)τ +(m 1)τ n=1 m=1 Hence, the frequency response of the overall system H arr (f,θ) is Y (f,θ) H arr (f,θ) = P(f) H a (f,θ) = H ideal(f,θ) (7) H a (f,θ) N M = a nm e j 2π f (n 1)τ +(m 1)τ, n=1 m=1 where the frequency response H ideal (f,θ) describes the ideal radiation pattern, which is constant for all frequencies in the investigated band and which is required, if all system components apart from the array factor are frequency independent. Due to the frequency and angle characteristic of the antenna elements (see section 3.1), the output signal would differ from the ideal case, which shows that we have to divide by every frequency dependent transfer function in the transmission system as shown: H arr (f,θ) = H ideal(f,θ) H i (f,θ) where H i (f,θ) is the ith frequency-angle dependent transfer function of the transmission system. So far, H i (f,θ) is described by the receiving antenna only, such that H i (f,θ) = H a (f,θ). In section 3.3 we also include the transmitting antenna response and the channel response to this product. The real filter coefficients a nm can then be obtained by applying the 2D inverse discrete Fourier transformation (IDFT) on the frequency response H arr (f,θ) after applying appropriate substitutions to the expression [12]. Normally, the inter-element distance d between two antenna elements is λ/2 or less in order to avoid grating lobes [8]. Considering an UWB array, the distance is determined for the highest frequency f h in the band and is given by i (8) d = c 2f h (9) The incremental time delays of the FIR-filters are appropriately chosen, as τ = d c (1) In short, the design procedure includes the following steps: 1. Design of a desired radiation pattern assuming some arbitrary number of elements as a starting point and using known array synthesis techniques for applications like main beam steering, null steering, sidelobe suppression, etc. [8], [14]. 2. Consider the desired radiation pattern to be frequency independent over the investigated frequency band H ideal (f,θ). 3. Divide by the frequency response(s) of receiving antenna, transmitting antenna, channel, etc. from the ideal frequency response H arr (f,θ). 4. After appropriate substitutions, choose preliminary orders N, M and apply the IDFT on H arr (f,θ) real FIR-filter coefficients a nm. 5. Vary orders N and M to repeat step 4 and decide how many antenna elements N and filter order M are required for the investigated frequency band and the tolerated deviations from the desired radiation pattern.

4 array n order m ha(t, θ) (a) θ =-9 θ =-45 θ = θ =45 θ =9 Figure 3. FIR-filter coefficients distribution. It is evident, that the required number of antenna elements N and the FIR-filter order M mainly depend on the relative width of the frequency band to be equalized. But also parameters like beam resolution and main beam direction control the requirements. In [16], we have investigated the required number of antenna elements and filter order on various bandwidths and came to the conclusion that for the full UWB bandwidth 3 : 1, one would require minimum N = 25 antenna elements and M = 15 filter order assuming a certain beam width and sidelobe level. Although these values coincide with the requirements resulting from other techniques and algorithms [13], [12], [14], at least the number of antenna elements is too high for practical applications. So, in section 4 we reinvestigate this matter, now from the time-domain point of view and suggest suitable detection methods to keep the number of antenna elements low. An example of the a nm -coefficients distribution of an UWB array is shown in Fig 3. It can be seen that the main coefficients (magnitude close to +1 or 1) are arranged along a line under a certain angle, which corresponds to θ, the other coefficients are close to zero. A signal, arriving under the angle θ will mainly be superimposed constructively. Hence, for this angle, the UWB-array works similar to true-time delays. For other angles, especially for nulls in the pattern, the superposition is more complex and should be destructive in the ideal case (b) Figure 4. (a) Geometry of the Vivaldi-antenna and its location w.r.t. the spherical coordinate θ. (b) Plot of the impulse response h a (t,θ) for the bandwidth 2-12 GHz in various direction θ. domain, it is straight forward to investigate also the antenna in time-domain. Therefore, the angle dependent transient impulse response h a (t,θ) is the quantity that fully describes the antenna characteristic, including the input reflection coefficient [1]. In this contribution, we use the characteristic of an antipodal Vivaldi-antenna, shown in Fig. 4(a) [17]. Its characteristics, like radiation pattern and input reflection coefficient have been simulated in the frequency band from 2 GHz to 12 GHz using the 3D-EM solver CST Microwave Studio. These parameters were used to calculate the impulse response of the antenna h a (t,θ), see Fig. 4(b). The low variation of the impulse response over angle θ indicates that the isolated Vivaldi-antenna is approximately omni-directional. Corresponding measured data can be found in [18]. 3. ANTENNA AND CHANNEL IMPACT 3.1. UWB antenna element characteristics Since all antenna parameters are strongly frequency dependent, the antenna in a wireless communication system plays a significant role [1]. Therefore, in UWB applications it is not only sufficient to define antenna parameters at the center frequency, but the whole band needs to be considered. When we investigate the communication system in time UWB channel model The channel of a wireless communication system represents the effects of the signal traveling through space, considering reflections, refractions and distortions impinging on walls or objects [2]. In Fig. 5(a), a simple 2D in-room situation with two rooms is constructed. The transmitter TX is placed to the left, the receiver to the right. The two rooms are separated by a wall and a glass door in the upper part. A Ray-tracing algorithm models the direct path between transmitter and receiver (LOS) and the multipath compo-

5 room width (m) 4 2 TX RX room length (m) 4 x (a) receiving antenna array and the FIR-filter structure behind the antenna array, see Fig. 6. The signal, received by the nth antenna elements can be described as x n (t,θ TX,θ RX ) = p(t) h a,tx (t,θ TX ) (12) h c (t,θ TX,θ RX ) h a,rx (t,θ RX ) δ t τ n (θ RX ), where the receiving array spatial time delay τ n (θ RX ) is a function of the angle of arrival, given by hc(t, θrx) (b) Figure 5. Ray-tracing for channel modeling. (a) Investigated environment and (b) resulting channel impulse response in the view of the receiver RX. The numbers on the lines indicate the angle of arrival. nents accruing due to wall reflections and transmissions. The spatial channel can be modeled as the direction dependent impulse response [19] h c (t,θ TX,θ RX ) = L α l δ(t τ l ) (11) l=1 δ(θ TX θ TX,l ) δ(θ RX θ RX,l ), where α l, τ l, θ TX,l and θ RX,l are the attenuation, delay, angle of departure and angle of arrival of the lth path, respectively. Fig. 5(b) shows the channel impulse response h c (t,θ RX ), Eq 14, assuming that the transmitter radiates omni-directional. It can be seen that the LOS signal is the strongest one, appearing first. All other components are echos, arising from single or multiple reflections and transmissions from the walls. The numbers on the lines in the figure indicate the angle of arrival θ RX. Hence, in this example, the LOS-signal arrives at the receiver with an angle θ = with τ n (θ RX ) = { (n 1)τ θ RX (N n)τ θ RX < τ = d c sin (θ RX ) (13) In order to keep the expressions compact, we continue with the following assumptions: The transmitting antenna is considered to be omnidirectional. Then the channel impulse response yields h c (t,θ RX ) = π θ TX= π h c (t,θ TX,θ RX ) dθ TX, (14) and all expressions are no longer a function of the angle of departure θ TX. The angle of arrival θ RX can now be denoted by θ. Then Eq. 12 can be simplified as x n (t,θ) = p(t) h a,tx (t) h c (t,θ) (15) h a,rx (t,θ) δ t τ n (θ) Similar to Eq. 5, the resulting time-domain expression for the output signal y(t,θ) can be expressed as y(t,θ) = N x n (t,θ) n=1 M m=1 a nm δ t (m 1)τ (16) Finally, the overall output signal y(t) is the integration of the signals from all directions of arrival, such that y(t) = π θ= π y(t, θ) dθ. (17) 3.3. Overall mathematical framework The overall short pulse UWB transmission system is a combination of the transmitting antenna, the channel, the As already indicated in section 2.1, the filter coefficients a nm have to be determined such that the frequency dependence of the antennas and the channel is equalized. In an UWB transmission system, where two antennas are placed in free space with distance R from each other, the voltage V RX (f), received by the receiving antenna can be

6 Figure 6. The overall UWB transmission system. obtained as a function of the transmitting antenna voltage V TX (f) by [2], [1] V RX (f) = 1 ZRX (18) 2πRc Z TX H a,tx (f,θ TX ) H a,rx (f,θ RX ) j2πf V TX (f) e j2πfr/c, where Z TX and Z RX are the characteristic port impedances. Thus, from Eq. 18, the product of frequency dependent factors in Eq. 8 turns out to be H i (f,θ) = H a,tx (f,θ TX ) H a,rx (f,θ RX ) j2πf i 4. SIGNAL ESTIMATION One challenge engineers currently work on is the UWB signal detection. A straight-forward method is to detect the maximum of the received signal max y(t, θ). The magnitude is then an indication of the signal strength. Another well known method in communication engineering is to correlate the received signal with a reference signal, e.g. with the single pulse signal being transmitted and then detect the correlation maximum. This gives an information on the strength and shape of the received signal. Even if the received signal is effected by noise, there should be a good correlation magnitude. But, if the received signal is affected by distortions, the correlation magnitude decays. A block diagram of a detection technique is shown in Fig 7(a). The summation signal y(t, θ) from the FIRfilter structure is correlated by a reference signal p ref (t), which, if the FIR-filter structure is configured appropriately, is the pulse signal being applied at the transmitter, p ref (t) = p(t). In this contribution, we take a normalized gaussian doublet, described by 4t 2 p(t) =.5 σ 2 2 e ( σ) t 2, (19) with σ =.5 ns defining the pulse width and hence the frequency spectrum closely confirming to the FCC spectral mask. The time-domain representation of the signal is the green curve, shown in Fig. 7(b). Receiving the signal under the main beam angle, the UWB array constructively superimposes the individual signals behind the antenna elements like in a true-time delay steered array (see Fig. 3) and it equalizes channel and antenna effects. Thus, the summation signal characteristic y(t, θ) (see black curve) is similar to the transmission signal p(t). Receiving the signal under a null in the radiation pattern, an ideal, frequency independent UWB-array would destructively superimpose signals, such that y(t, θ) =. This is not possible under realistic conditions, because the configurable bandwidth and the number of antenna elements and filter order are limited. The aberrations of the achievable pattern are demonstrated in Fig. 8, where the three signals y(t,θ), r 1 (t,θ) and r 2 (t,θ) (refer to Fig. 7(a)) are evaluated for a 15-element array with filter order M = 13. The desired pattern (reference) with deep nulls is compared to the angle dependence of the detected signals using the max-criterion mentioned above. The UWB-array is configured for the frequency range from 4.5 GHz to 8.5 GHz, which is not the whole UWBfrequency range, but covers the main spectral part of the pulse p(t). Due to this simplification, the course of max y(t, θ) mainly agrees with the reference pattern, but it does not coincide well with the desired nulls.

7 .4.2 (a) p(t) y(t, θ) r 1 (t, θ) r 2 (t, θ) normalized pattern (db) max y(t) max r 1 (t) max r 2 (t) reference θ (deg).2 Figure 8. Time-domain radiation patterns: Various detection signals are compared to a desired radiation pattern (b) Figure 7. (a) Block diagram of signal estimation and (b) the time-domain representation of the reference signal (green), the summation signal from the FIR-filter (black), the signal behind the correlator (blue) and the signal behind the bandpass filter (red). Observing the correlation signal r 1 (t,θ), the timedomain pattern max r 1 (t,θ) coincides better with the reference pattern, especially at the nulls. This can be explained by the fact that signals under null-directions apart from being attenuated are distorted by the non-ideal FIRfilter, such that the correlation quantities decays, as desired. Spectral parts of the received signal, which are beyond the configured array bandwidth may constructively superimpose, which is critical mainly for null directions. In order to minimize this effect, we place a bandpassfilter behind the correlator. The output signal is denoted as r 2 (t,θ) and its maximum max r 2 (t,θ) features the best fit with the desired pattern in the figure. It is evident that limiting the UWB-array bandwidth, and bandpass-filtering will disturb the pulse quality and will cause ringing. This effect should be acceptable, if signals under the main beam direction are undistorted and its pulse characteristic is clearly visible. This is normally the case, if the filtering is not too restrictive. Signals under non-mainbeam angles are free to be distorted by the filtering, since they are spurious and do not deliver any information in our concept. 5. PERFORMANCE DEMONSTRATION Finally, we will demonstrate our concept by an overall simulation, where we take into account all transfer func- tions of the transmission system being discussed in this contribution. Therefore, we investigate the overall FIR output signal y(t), Eq. 17 In a first simulation, a single transmitting and a single receiving antenna, both Vivaldi antennas (Fig. 4) are placed in the environment of Fig. 5. The transmitter is excited by a gaussian doublet, Eq. 19. The received signal is plotted in Fig. 9(a), where the LOS signal is followed by various multipath components, as expected. Furthermore, the pulse-shape is disturbed as can be calculated from Eq. 18. In a second simulation, the receiver is a 15 element antenna array, also equipped with Vivaldi antennas followed by an 13th order FIR-filter structure. The UWB-array is configured for the frequency range from 4.5 GHz to 8.5 GHz, so the inter-elements spacing yields d =.5c /f h = mm with the incremental time delay τ = 58.8 ps. The FIR-filter coefficients are computed such that a desired radiation pattern (Fig. 8) with main beam direction θ = 13 is approximated. The desired pattern was produced by a 7-element narrowband array simulation with 15 db sidelobe attenuation and λ/2 element spacing. The corresponding summation signal behind the FIR-filters is plotted in Fig. 9(b). One can see that the pulse shape of the transmitted signal is reproduced, many multipath components are minimized and the overall gain is enhanced. It is not surprising that certain multipath components are still visible, since they arrive from similar directions compared to the LOS signal, e.g. 12, 9, 8, see Fig. 5(b), where the main beam is pointed to. 6. CONCLUSION The objective of this article was to present the design procedure of an FIR-filter controlled linear antenna array for ultra wideband short pulses. A mathematical framework has been derived considering antenna and channel char-

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