An architecture dedicated to the real time processing of wide-band circular antennas Henry Carron, Student Member, IEEE, Jean Louis Boizard and Benoit Albouy Laboratoire d’Acoustique de Métrologie et d’Instrumentation (LAMI) – Université Paul Sabtier - 38,rue des 36 ponts – 31400 Toulouse France – Email : [email protected], [email protected] Abstract – We put forward a method for optimizing the directivity diagram of circular, wide-band antennas in real time. After analytically determining the expression for the directivity diagram of an antenna composed of 19 sensors organized in three rings, we show its variation with frequency and the efficiency of having a filter associated with each ring of sensors. The characteristics of the filters (frequency and phase response) were determined by minimizing the least squares error between the actual and desired diagrams over the whole interval of frequencies and angles of incidence of the wave. Approximations to these filters were then made by means of finite impulse response (FIR) digital filters. An architecture is presented for the real-time processing of the antenna signals and the simulation results obtained show the effects of directivity diagram compensation.

II. A NTENNA ORGANIZATION The antenna developed in the laboratory was composed of two rings or concentric networks and a central detector, regularly spaced out in the same plane. It was made up of six (6) evenly distributed hydrophones in one ring and twelve (12) in the other. This 19-detector acoustic antenna was used in a frequency band going from 6 kHz to 48 kHz (i.e. 3 octaves). Its directivity diagram presented the drawback of varying with frequency, which introduced errors when features were observed in a privileged direction. In the architecture proposed, the diagram has been optimized by means of 3 weighting filters placed at the output of each ring (Figs. 1 and 2).

Index Terms – Beamforming, DSP, FPGA

W3( f )

I.INTRODUCTION

T

O determine the nature of lake or sea beds it is necessary to know the pertinent parameters connected with them. Acquiring the impulse response of the bottom under study and the resulting transfer function is one way of gaining access to the required parameters. This method involves: - implementing instrumentation capable of operating over a wide frequency range; - observing zones having a small area relative to the relief of the bed and presenting no variation with the frequencies of the signals used. One of the first constraints (narrowness of the observing beam) can be dealt with by using multi-detector underwater antennas. These are composed of hydrophones that are omnidirectional in the working frequency band. The resulting directivity diagram can be very selective in the direction of the observation area but the secondary lobes are relatively large. Moreover the principal lobe changes shape with the frequency of the signals observed (the beamwidth increases when the frequency decreases). Signal processing methods that vary in sophistication with the number of hydrophones used can compensate for the effects connected with frequency variation [1, 2, 3, 4]. Some consist of performing digital processing per detector or group of sensors. Such processing is often done later and makes it necessary to record considerable amounts of data. Given the development of DSP (Digital Signal Processing) processor and FPGA (Field Programmable Gate Array) circuits, LAMI turned its attention to the development of wide-band ring antennas used in conjunction with a real-time signal processing system.

?

W2( f )

D( f ,? ) W1 ( f ) Fig. 1 : Antenna organization

Sensor i,1 Sensor i,1 Sensor i,2

Outputof thering

Output of the ring

Sensor i,2 Sensor i,j

Fig. 2 : Principle of summing per ring If we consider the directivity diagram of ring i without weighting (Wi(f)=1) then its expression becomes:

D i (? ,? ) ?

ki

?

? ? exp( j.k .? ri, j )

(1)

n ?1

where

? ? ri , j : phase difference between sensors with respect

to the center of the antenna

? ? ? ? ri , j ? OM .u

?

III O PTIMIZATION OF THE DIRECTIVITY DIAGRAM

(2)

where M : position of a detector and u : unit vector in the direction of the wave if we use spherical coordinates ( R ,? , ? )

j. 2? ? ? ?? ) ? ? ri , j ? R i . sin ? . cos ( ki we have ? ? ? r? ? 0 ? 1,1

(3)

The aim of the optimization was to bring the directivity diagram as close as possible to a standard diagram useful for echo sounding. The standard chosen had precisely defined characteristics: a narrow principal lobe centred on ? =0 to collect the whole of the signals coming from the direction orthogonal to the antenna plane (here the angle of aperture at – 3dB was 20°), together with maximum attenuation for the other directions. Figure 4 represents the desired diagram.

where i : ring subscript, j : detector subscript

Ri : radius of ring i and k i : number of sensors in ring i B. Directivity plot The space-time Fourier transform of the phase difference between sensors yields the general expression for the directivity of the antenna. This can be expressed by the relationship: D(? ,? ) ?

3 ki j.2.? j.2.? 1 ? ? ? exp(? .Ri. sin ? . cos( ?? ) ? k i ? 2 j? 1 i

(4)

On a representation of the diagram ( depending on ? and ? ) for a given frequency, we note that the directivity is constant according to ? . This confirms the interest of having an antenna with circular symmetry, as the received signal only depends on the angle of inclination, ? , between the wave and the antenna It is for this reason that the variable ? can be neglected when plotting variations in the diagram, only ? being kept (see figure 3).

Fig 4 : Standard diagram The first step consisted of determining the ideal transfer functions

Wi ( f )

to be applied to each ring, which would

allow the antenna to be focused in the desired direction in accordance with figure 4. These transfer functions were determined by minimizing the mean quadratic error between the diagram desired and the one obtained without weighting. This can be expressed analytically by the following relationships:

?W1 ( f ) ? ? ? D( f ) ? ?D1 ( f ) D 2 ( f ) D3 ( f )?.?W2 ( f )? ? ? ? ? ? ? ? ? ? A ??W3 ( f ) ?? C ? ( A * t . A) ? 1 .A * t

(6)

and

Wi ( f ) ? C (i ).?

(5)

(7)

where A represents the system directivity matrix,

? the standard diagram and i =1,2,3 the ring index. Fig 3 : Directivity diagram

The second step consisted of determining the digital filter coefficients giving an approximation to the functions Wi(f). We chose finite impulse response (FIR) filters for this as they are easy to use and generally present a linear phase. The transfer function for these filters is given by the expression :

N

H i (Z) ?

?

hi ( n). z ? n with N order of the filter

I V. REAL TIME SIGNAL PROCESSING ARCHITECTURE

(8)

n? 0

The coefficients hi(n) were also determined by the least squares method. Figure 5 represents the frequency response of the three FIR filters obtained.

A. Architecture Description The real time processing is represented in figure 7. The output from each ring of sensors is amplified then sampled by a Sigma-Delta analog-digital converter having a series output. Each channel is then processed digitally by a FIR filter in an FPGA circuit. A digital-analog conversion enables the antenna output to be recons tructed. Output of Amplifier + ? ? ADC the first ring Output of Amplifier the second + ? ? ADC ring Output of the third ring

DAC

D(f,? )

Amplifier + ? ? ADC

Fig 7 : real time processing Architecture Fig 5 : FIR frequency response The optimal directivity diagram Dopt (f) was obtained from the expression : ?H 1 ( f ) ? ? ? Dopt ( f ) ? ?D1 ( f ) D2 ( f ) D 3 ( f )?.?H 2 ( f )? (9) ??H 3 ( f ) ?? A glance at figure 6 shows that the result is very close to the chosen standard.(see figure 4 to compare)

B. Advantages of using FPGA Traditionally, digital FIR filters are implemented using programmable DSP (Digital Signal Processing) processors. But the evolution of FPGA devices has provided new options for digital filter design with the benefit of high performance, low cost, short time-to-market, and flexible implementation [8]. FPGA's provide the performance and flexibility required for DSP applications because DSP algorithms are optimally mapped to the device architecture. So FPGA performance can significantly exceed that of a DSP processor [7, 9]. C. Type of implementation The FIR filters were designed with the VHDL description language and implemented in an ALTERA Flex 10K20 FPGA. A big advantage of using VHDL is that the design is scalable or parametrizable. There are various types of architectures for FIR filter implementation. For our application, the sample rate was not very high, so we could use a serial architecture [5]. This had the advantage of requiring less hardware [6]. As can be seen in Figure 8, the series architecture requires a sequencer to synchronize the arithmetic calculation operations. The "CONTROL BLOCK" has to generate two addresses buses : ones for the samples RAM and another for RAM coefficients, the RAM read/write signals and the Reset signal for the MAC (Multiplier-Accumulator).

Fig 6 : Optimized directivity diagram

DATA INPUT Adresses R/W

RAM

CONTROL Reset

MAC

Output

BLOCK Adresses

RAM with Coefficient s

Fig 8 : Serial Architecture V. CONLUSION This study has shown the feasibility of multi-detector ring antennas having a directivity diagram optimized by the use of FIR filters. Miniaturization, increased gate density and cost reduction in FPGA circuits enabled us to use a compact, easily transportable architecture for the real-time digital processing system of the antenna. The power of the VHDL development tools made it easy to represent and simulate the architecture and provided simplicity of evolution and maintenance. The work will continue with the implementation of an antenna calibration procedure using measurements made on an actual site and then with echo acquisition from sedimentary beds so as to classify them. REFERENCES

[1]

Peter H. Rogers and A. L. Van Buren, “New Approach to a constant beamwidth transducer”, J. Acoust. Soc. Am., Volume 64(1), pp 38-43, 1978. [2] A. L. Van Buren, L. Dwight Liker, M. D. Jevnager and A. C. Tims, “Experimental constant beamwidth transducer”, J. Acoust. Soc. Am., Volume 73(6), pp78-93, 1983. [3] J. Lardies, “Acoustics Ring Array with Constant Beamwidth over a Very Wide Frequency Range”, Acoustics Letters, Volume 13, pp 77-81, 1989. [4] J. L. Boizard, E. Gonneau, F. Legrand, “Optimizing The Beamwidth Of Underwater Acoustic Wide Band Antennas”, Underwater Technologies, Tokyo, 1998. [5] Altera Corporation, "Implementing FIR Filters in FLEX Devices", Application Note 73, 1998. [6] Actel Corporation, "Designing FIR Filters with Actel FPGA", Application Note, 1997. [7] Altera Corporation, "Digital Signal Processing In Flex Devices, Product Information Bulletin 23, 1996 [8] Lattice Corporation, "Implementing FIR Filters in the ispLSI 8840, Application Note 8040, 1998. [9] P. Graham, B. Nelson, "Frequency-domain sonar processing in FPGAs and DSPs", Proceedings of IEEE Symposium on FPGAs for Custom Computing machines,1998.