a systolic array 2-d iir broadband rf beamformer

1244 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: EXPRESS BRIEFS, VOL. 55, NO. 12, DECEMBER 2008

A Systolic Array 2-D IIR Broadband RF BeamformerH. L. P. Arjuna Madanayake, Student Member, IEEE, Sean V. Hum, Member, IEEE, and

Leonard Thomas Bruton, Fellow, IEEE

Abstract—A systolic architecture is proposed for the real-timeimplementation of broadband 2-D IIR beam filters having appli-cations in ultra-wideband (UWB) radio frequency (RF) antennaarrays. Real-time throughputs of one-frame-per-clock-cycle areachieved. A finite-difference time-domain computational electro-magnetic model of a typical indoor propagation environment isused to illustrate that the method significantly reduces the biterror rate of the simulated communication system in the presenceof multi-user interference, thereby demonstrating the potentialapplication of the architecture in RF communications.

Index Terms—Array signal processing, finite-difference time-do-main (FDTD) methods, multidimensional digital filters.

I. INTRODUCTION

H IGHLY directional smart antenna arrays have inter-ference rejection applications in radio frequency (RF)

wireless communications for increasing system capacity.Such arrays may typically be realized using microwavedelay-and-sum networks or digital filters and are increasinglyused in high-capacity carrier-modulated wireless communica-tion systems. Emerging ultra-wideband (UWB) technologiesalso require highly directive steerable antenna arrays for re-ducing bit error rates (BERs) due to multipath effects andmulti-user interference [1], [2]. Although conceptual UWBbeamformers based on analog VLSI delay-and-sum networks[3], digital fractional-delay networks, and 2-D/3-D finite/in-finite impulse response (FIR/IIR) digital filters [4], [5] havebeen proposed, UWB implementations at radio frequencies(RFs) seem to be limited to analog delay-and-sum beam-formers because of the prohibitive computational intensity oftypical digital UWB beamformers. Here, we employ broadbandbeamforming 2-D digital IIR beam plane wave filters [6] thatare new to RF UWB applications and have advantages overconventional beamformers. For example, 2-D IIR beam filtersare free of fractional delays, fully steerable, broadband, andhighly selective.

For a given selectivity, IIR filters have a computational inten-sity that is an order of magnitude smaller compared with equiv-alent 2-D FIR beam filters having the same transfer functions.Here, we combine the high-throughput (but high-circuit-com-plexity) direct-form 2-D IIR beam filter architecture in [7] and

Manuscript received January 27, 2008; revised June 03, 2008. Current ver-sion published December 12, 2008. This paper was recommended by AssociateEditor A. Poon.

H. L. P. A. Madanayake and L. T. Bruton are with the Department of Elec-trical and Computer Engineering, University of Calgary, Calgary, AB, CanadaT2N 1N4 (e-mail: [email protected]).

S. V. Hum is with the Edward S. Rogers Sr. Department of Electrical andComputer Engineering, University of Toronto, Toronto, ON, Canada M5S 3G4.

Digital Object Identifier 10.1109/TCSII.2008.2008053

Fig. 1. (a) Incident plane wave in space, (b) incident plane wave in space-time,(c) frequency-domain ROS of spatially critically sampled signal having tem-poral over-sampling factor� overlaid on a log-scale contour plot of the beamfilter response, (d) multiply replicated ROSs of a signal that has been spatiallyunder-sampled by a factor � and subsequently up-sampled by � and zero-stuffed, also overlaid on the same response plot. Clearly, the aliased ROSs dueto spatial under-sampling lie deep in the stopband and has been attenuated bymore than 30 dB.

[8] with the low-circuit-complexity (but low-throughput) dif-ferential-form architecture in [9] and obtain a novel “best ofboth worlds” 2-D UWB frequency-planar beamforming struc-ture that is of low complexity and capable of high throughput.Unlike generic examples for beam filters in [8], we proposeapplications in UWB wireless communications under severemultipath conditions and justify performance via BER simula-tions using finite-difference-time-domain (FDTD) electromag-netic modeling of the radio channel.

II. REVIEW OF FREQUENCY-PLANAR IIR BEAM FILTERS

A. On the 2-D Space-Time Spectrum of a Plane Wave

The region of support (ROS) of the 2-D space-time spec-trum of a “far-field” propagating plane wave

, having a spatial direction of arrival(DOA) measured from the broadside direc-tion [Fig. 1(a) and 1(b)], is a line through the origin of

, where and are spatial and temporalfrequencies, respectively. The ROS line is oriented at an angle

from the axis, where is theDOA in 2-D space-time [3], [10]. The wave

is sampled using a linear array of UWB antennas

1549-7747/$25.00 © 2008 IEEE

MADANAYAKE et al.: SYSTOLIC ARRAY 2-D IIR BROADBAND RF BEAMFORMER 1245

having uniform spacing , where is thehighest temporal frequency component in the 2-D input signal

and ms . The temporal samplingfrequency , where is used to reduceeffects of bilinear warping in the beam filter frequency response[11], leading to Fig. 1(c), which shows a contour plot of thetransfer function within the 2-D Nyquist square.

B. Spatially Under-Sampling and Broadband Plane WaveFiltering Using 2-D IIR Filters

It is possible to spatially under-sample without deteriorationof performance if the aliased ROSs lie in the stopband ofthe beam filter [10], [12]. We employ spatial under-samplingby a factor so that the antenna distances are increasedto , leading to spatiallyaliased ROSs [6], [9] as shown in Fig. 1(d) for . Thenumber of antennas and analog-to-digital converter (ADC)blocks is decreased from to , re-ducing the amount of RF hardware and ADCs required inphysical implementations. We choose , ,and , implying array distances andsampling frequency . We propose thatspatially under-sampled input signals ,

, be spatially up-sampled byby zero-stuffing in order to obtain the final input signal

of the filter. Further, we employsecond-order 2-D IIR digital frequency-planar (FP) filtershaving 2-D beam-shaped passband regions that encompass theROS of the desired plane wave, while attenuating undesiredplane waves and noise [6].

III. SECOND-ORDER FREQUENCY PLANAR BEAM FILTER

We employ the design approaches in [6] and, in order to ob-tain greater gain selectivity, cascade two identical first-order 2-DIIR frequency-planar beam plane wave filters having their beamaxes oriented at an angle , such that the ROS of the passbandplane wave is selectively enhanced. The proposed transfer-func-tion is the second-order beam function

(1)

where the differential-form frequency-planar filter is,from [6] and [13], given by

(2)

The 2-D input and output sequences are given

by and

, respectively, andthe filter coefficients are found algebraically [6], [13]for as

(3)

for selectivity parameter , and. The second-order fre-

quency-planar beam filter having transfer function (1) has a

Fig. 2. Overview of the proposed two-layer second-order hardware. It consistsof a cascade of two low-complexity DPPs, each implementing a first-order 2-DIIR frequency-planar beam filter. The inputs � �� , � � �� ofthe first DPP/filter are fed by broadband antennas, while the remaining inputsare fed by zero registers. The inputs and outputs of the second first-order filterare � �� and � �� , respectively.

highly selective beam-shaped passband that is 2-D-warped.This is due the use of the double bilinear transform [5], [11],the effect of which is shown in Fig. 1(c) and (d) using acontour plot in dB of . Here, the beamencompasses the passband plane wave, as required.

IV. HIGH-SPEED LOW-COMPLEXITY ARCHITECTURE

is implemented here as a novel low-complexityhigh-speed systolic array, which we call a distributed-par-allel-processor (DPP) circuit [9]. Fig. 2 shows the proposedmassively parallel systolic-array architecture, which consistsof two first-order DPP architectures in cascade. Each DPPconsists of a pipelined mesh interconnection of identical par-allel processing core modules (PPCMs) [9]. These PPCMs areimplemented in fixed-point arithmetic, and clocked at the clocksample frequency , where .

Each UWB antenna in the array is matched to a dedicatedbroadband LNA, low-pass filtered, sampled, and finally quan-tized to bits using a dedicated synchronous high-speedADC (typically about 3 bits of precision is sufficient) oper-ating at the clock rate (Fig. 3). The proposed PPCM(see Fig. 4) requires two parallel multipliers and four paralleladders/subtractors, which are clocked at the spatial framesample frequency and is 33% lower in circuitcomplexity than the direct-form version in [8], which requiresthree multipliers and six adder/subtractors per PPCM. The keyaspect of our proposed architecture is the very high real-timecomputational throughput of one complete array-frame perclock cycle (OFPCC).

A. PPCM Architecture

We rewrite (2) in the form

(4)


Fig. 3. Signal processing for each antenna in the array.

Fig. 4. Proposed hardware architecture for the high-speed low-complexityPPCM.

where , and then take the 1-D inverse -transform of(4) under zero initial conditions (ZICs), from which we proposethe following novel mixed-domain representation:

(5)where , and

(6)Equations (5) and (6) are implemented by the systolic array inFig. 2, as described below.

The PPCMs are pipelined to a depth of ,clock cycles, where the clocked delays are distributed

as shown in Fig. 4. Each integer delay may be a clockedfirst-in-first-out (FIFO) register or may represent the internalpipelining delays of the preceding circuits. The total clockdelays between all inputs and outputs, that is, the delays alongsignal paths , , and ,are all of clock cycles. Timing synchronization betweenPPCMs is achieved by delaying the input streams to the PPCMsusing FIFOs of depth (see Fig. 4). The outputs

of the PPCMs are delayed by integer multiples of the clockperiod such that ,for . ZICs required for stability areobtained by connecting the input of each DPP to a zerovalued register and blanking all internal memory states of theDPP to the value zero at filter startup. The total processingdelay due to pipelining is clock cycles, which istypically acceptable.

B. Inter-PPCM Interconnections

The spatial recursions of the mixed-domain difference equa-tions (5) and (6) are obtained by the interconnecting the PPCMsof each DPP as follows:

(7)

The inputs , , are either fed by the ADCblocks at (the under-sampledsignal) or by a zero-valued register (the zero-stuffed inputs), asshown in Fig. 2.

C. Real-Time Throughput

The critical path delay (CPD) of the PPCMs can be reducedfrom down to ,which implies a maximum clock (frame) frequency of

[14]. For PPCMs in each DPP and a2-D IIR broadband frequency-planar beam filter of order 2,the computational complexity is multiplications persecond and adds (subtractions) per second.

D. Finite Wordlength (FWL) Effects

Following [8], this architecture may use 2’s complementarithmetic, quantization of type truncation, and overflow satura-tion, leading to freedom from 2-D space-time limit-cycles andoverflow oscillations. Current simulation results assume noisecorresponding to 3-bit quantization at the inputs. A precisionof at least 8 bits is recommended for coefficient registers,for low sensitivity to filter coefficient quantization errors. Acomprehensive study of the impact of finite precision ADCsand registers on bit error rate (BER) performance is currentlyin progress.

V. VALIDATION USING AN FDTD CHANNEL MODEL

A. Scenario

To determine the performance of the filter in a practical situa-tion, detailed simulations of a UWB antenna array in a realisticradio environment are reported here. UWB multi-user interfer-ence was introduced, and the ability of the filter to improve thesignal-to-interference ratio (SIR) of the received signal was as-sessed. Performance was evaluated by conducting BER simula-tions involving the array and filter.

The effects of the radio channel were modeled by embed-ding the transmitters and receivers in an FDTD model of thepropagation environment. The simulated environment, shownin Fig. 5, had a single desired (passband) signal source and four

MADANAYAKE et al.: SYSTOLIC ARRAY 2-D IIR BROADBAND RF BEAMFORMER 1247

Fig. 5. Layout of the room for FDTD channel simulation, showing desiredsignal transmitter � and four interference sources � .

interfering transmitters , , 2, 3, 4. A base station shownin Fig. 5 received the data stream from the source with mul-tiple scatterers and transmitters present.

Two Monte Carlo simulations of the systolic implementation(Fig. 2) of the second-order frequency-planar beam filter (1)were carried out, for and antennas. We re-port here the corresponding reductions in BERs, relative to bothBERs for nonbeamformers as well as analog delay-and-sumbeamforming.

B. FDTD Radio Channel Model

It has been shown that the FDTD technique can be used togenerate accurate radio channel models because it simulatesthe physics of wave propagation by directly solving Maxwell’sequations [15]. Recent advances in computing and in multires-olution FDTD techniques have enabled the scale of solvableproblems to grow dramatically, allowing full-wave solutions ofpropagation environments such as that shown in Fig. 5 withmodest resources [15].

The approach in this work was to use a 2-D model of thepropagation environment for simplicity. The floor plan of Fig. 5was simulated in the -plane. The axes show the cell index,where each cell was of size 4.5 mm 4.5 mm over a floor sim-ulated area of 10.8 m 10.8 m. The sources were modeled aspoint sources (line sources in the -direction) having currentsthat were modulated by a Gaussian pulse train associated witheach transmitter. Receiving antennas were assumed to ideallysample the -component of the electric field, though the im-pulse response of the receiving antennas can be incorporatedinto the model if necessary. Walls and partitions were modeledusing nondispersive dielectric materials where the walls wereassumed to have a dielectric constant of 3 and a conductivityof 0.05 S/m; the partitions had a dielectric constant of 4.26 anda conductivity of 0.002 S/m. The walls and partitions were ofthicknesses 135 and 63 mm, respectively.

C. Simulation of the Communication System

BER simulations were conducted for varying levels of inter-ference due to the transmitters . The desired signal source

Fig. 6. (a) 2-D magnitude spectrum of the sampled FDTD signal showing lineof site propagation, diffraction, and reflections, for � � �� antennas, and(b), the spatially under-sampled spectra of the 2-D FDTD signal for � � �

antennas.

and the undesired interference sources were normal-ized to have equal powers at the receiver locations and wereidentically bi-phase-modulated by random streams of data bits.A Gaussian-shaped pulse was used. The resulting antenna cur-rent applied to the th antenna is given by

(8)

where is for the desired source . Five independentstreams drove the transmitting antennas, where, for sources

, data , , andand . is

the peak feed current for the th transmitter and is a constantthat sets the transmitted signal bandwidth1 to Hz. Here,we chose GHz, samples per trans-mitted symbol, a temporal over-sampling factor of(which leads to a sample frequency of GHz) anda symbol rate of Msym/s. Beam filtering occursover spatial locations , employing aspatial under-sampling factors of and for thetwo simulations, thereby reducing the number of antennas from

down to and , respectively. Thisalso reduces mutual coupling between antennas in array.

The spectra in the 2-D Nyquist square areshown in Fig. 6 for and for the FDTD simulated casesof 32 and 8 antennas. The spectra show the effects of spatialunder-sampling, where ROSs repeat along at ,

The benefits of low complexityoutweigh negative effects of spatial aliasing, if any. The de-tection algorithm is based on cross-correlation detectors at theoutputs the antenna, located at for the nonbeamformerand at the output of the beam filter. The beamformed filteroutput is the 1-D signal . Ideal clockrecovery is also assumed.

D. Simulations of BER Versus SIR Using the FDTD Input Data

Recall that the objective is to employ the second-order highlyselective broadband 2-D IIR frequency-planar plane-wave dig-ital filter to directionally enhance the signal from the desiredtransmitter, such that interference from users at other transmit-ters and multipath reflections in the environment is significantlyattenuated. The corresponding BER versus SIR was investigatedfor 8- and 4-element antenna arrays (i.e., , 4) using

1The transmitted signal and corresponding bandwidth refers to the first deriva-tive of the Gaussian pulse.


Fig. 7. Simulated BER versus SIR for 4-antenna case (spatial under-samplingfactor � � �) and 8-antennas array �� with a reference plotsshowing the BERs when 4-element analog delay-and-sum beamforming�� [3] is used as well as for the case where beamforming isnot employed. Note: � is the wavelength of the highest temporal frequencycomponent of the UWB signal.

the second-order 2-D IIR beam plane-wave filter with the band-width selection parameter chosen as .

Additive white Gaussian noise (AWGN), at a level of 20 dBrelative to the received signal, was simulated in order to veryapproximately model the effect of 3-bit quantization noise atthe antennas’ ADCs.

Fig. 6 shows the 2-D magnitude spectrum of the desiredsignal having strong multipath effects. Fig. 7 shows the re-sultant BERs before and after beam filtering. The significantreduction in BER, for a given SIR, is evident. The BERs, for8- and 4-element array cases, were significantly improvedrelative to no beamforming. For a BER of approximately

, the system gains were 21 and 26 dB for four andeight antennas, respectively. Comparing this with the BER im-provement of 8 dB when using a conventional analog 4-elementdelay-and-sum beamformer, for a BER of , it may beconcluded that the 2-D IIR beam filter exhibits comparativelyhigher performance. We assert that these reductions in simu-lated BERs imply the strong potential of the proposed methodfor applications in high-speed UWB digital wireless communi-cations. The performance of the 8-antenna array is about 5 dBbetter than that of the 4-antenna array, certainly because of thelower spatial aliasing. Furthermore, the signal energy for the8-antenna array case is less-distributed in 2-D frequency-spacebecause the lower spatial under-sampling leads to better selec-tivity. Both arrays significantly reduced multi-user interferenceeffects compared with the single antenna (i.e., nonbeamformed)case, and it is seen that beam filtering offer improved systemgains compared to well-known delay-and-sum beamformingusing the same number of antennas (4-element case shown).

VI. CONCLUSION

A systolic-array architecture for second-order 2-D IIR fre-quency-planar beam filters, based on a novel hybrid signal flow

graph, is proposed. The architecture requires two multipliersper PPCM, leading to 33% lower circuit complexity relativeto the speed-maximized direct-form architectures that requirethree multipliers per PPCM [8]. The new architecture may alsobe speed-maximized following the 2-D look-ahead scheme pro-posed in [8], unlike previous low-complexity architectures [9].

The number of antennas was reduced from 32 down to fourand eight elements, respectively, by extending spatial under-sampling [10], [12] to 2-D IIR beamforming. The multipath re-jection is confirmed using a physics-based FDTD electromag-netic model of a typical propagation environment, indicatingsuitability for improving the multipath fading of UWB systems.Real-time implementations of such filters have good potential inUWB applications that involve high-speed digital wireless com-munications, imaging and radar. For future work, we plan onresearching important details such as quantization noise perfor-mance, performance using actual UWB antenna elements, andpower consumption.

REFERENCES

[1] S. Ries and T. Kaiser, “Towards beamforming for UWB signals,” inProc. EUSIPCO, Vienna, Austria, 2004, pp. 829–832.

[2] H. Arslan, Z.-N. Chen, and M.-G. Di Benedetto, Ultra-Wideband Wire-less Communication. New York: Wiley Interscience, 2006, 0-471-71521-2.

[3] J. Roderick, H. Krishnaswamy, K. Newton, and H. Hashemi, “Sil-icon-based ultra-wideband beam-forming,” IEEE J. Solid-StateCircuits, vol. 41, no. 8, pp. 1726–1739, Aug. 2006.

[4] M. Ghavami and R. Kohno, “Frequency selective broadband beam-forming using 2-D digital filters,” in Proc. IEEE Veh. Technol. Conf.,2000, vol. 3, pp. 2522–2526.

[5] M. Ghavami and R. Kohno, “Recursive fan filters for a broadband par-tially adaptive antenna,” IEEE Trans. Commun., vol. 48, no. 2, pp.185–188, Feb. 2000.

[6] L. T. Bruton and N. R. Bartley, “Three-dimensional image processingusing the concept of network resonance,” IEEE Trans. Circuits Syst.,vol. CAS-32, no. 7, pp. 664–672, Jul. 1985.

[7] A. Madanayake and L. T. Bruton, “FPGA prototyping of spatio-tem-poral 2-D IIR broadband beam plane-wave filters,” in Proc. IEEE AsiaPacific Conf. Circuits Syst., Singapore, Dec. 2006, pp. 542–545.

[8] A. Madanayake and L. T. Bruton, “A speed-optimized systolic-arrayprocessor architecture for spatio-temporal 2-D IIR broadband beamfilters,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 55, no. 7, pp.1953–1966, Aug. 2008.

[9] H. L. P. A. Madanayake and L. T. Bruton, “Low-complexity dis-tributed-parallel-processor for 2-D IIR broadband beam plane-wavefilters,” Can. J. Elect. Comput. Eng., vol. 32, no. 3, pp. 123–131, 2007.

[10] L. Khademi, “Reducing the computational complexity of FIR 2-D fanand 3-D cone filters,” M.Sc. thesis, Dept. Elect. and Comput. Eng.,University of Calgary, Calgary, AB, Canada, Sep. 2004.

[11] L. T. Bruton, “Three-dimensional cone filter banks,” IEEE Trans. Cir-cuits Syst. I, Fundam. Theory Appl., vol. 50, no. 2, pp. 208–216, Feb.2003.

[12] L. Khademi and L. T. Bruton, “On the limitations of narrow 2-D fanfilters speech processing,” in Proc. IEEE Pacific Rim Conf. Commun.,Comput., and Signal Process. (PACRIM’03), 2003, vol. 1, pp. 301–304.

[13] R. K. Bertschmann, N. R. Bartley, and L. T. Bruton, “A 3-D inte-grator-differentiator double-loop (IDD) filter for raster-scan video pro-cessing,” in Proc. IEEE Int. Symp. Circuits Syst., May 1995, vol. 1, pp.470–473.

[14] K. K. Parhi, VLSI Digital Signal Processing Systems: Design and Im-plementation. New York: Wiley, 1999, 0-471-24186-5.

[15] A. Alighanbari and C. D. Sarris, “Rigorous and efficient time-domainmodeling of electromagnetic wave propagation and fading statistics inindoor wireless channels,” IEEE Trans. Antennas Propag., vol. 50, no.8, pp. 2373–2381, Aug. 2007.

a systolic array 2-d iir broadband rf beamformer

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