Improved Receiver Architecture for Digital Beamforming ... - IEEE Xplore

International Conference on Computer, Communication and Electrical Technology – ICCCET2011, 18th & 19th March, 2011

Improved Receiver Architecture for Digital Beamforming Systems Mohammad Salman Baig, B. Ramaswamy Karthikeyan, Dipayan Mazumdar, Govind R. Kadambi, M S Ramaiah School of Advanced Studies, Bangalore, India Abstract-Digital beamforming (DBF) technology is progressed with the development of adaptive algorithms and architectures Modern beam forming systems have been aided by advancements in VLSI design, adaptive algorithms, RF up/down conversion systems and high sampling rate ADCs. Digital beamforming enables full utilization of the maximum number of degrees of freedom in the array. In conventional Nelement array receiving system, each channel element has its own up/down conversion modules, ADC and DDC (Digital down-converter). Hence for N-element beamformer, N RF down-converters, N ADC’s and N DDC’s are required. In this paper, novel receiver architecture for digital beamforming is proposed. One central feature is the usage of ADCs with smaller range to achieve a greater dynamic range of the input signal. This proposed architecture reduces the hardware making it simple, cost effective and easy to implement. The specific ADC implemented in this system has an improved dynamic range due to analog preprocessing and digital post processing. Multiple Beamformation using the same antenna array is achieved by using the LMS algorithm. The performance criteria of a digital beamforming system are the number of antenna elements, the IF sampling rate, the RF frequency and the number of iterations required to converge. In the proposed system we attempt to improve two of these four criteria. The proposed DBF receiver system is realized using Simulink® and its simulation results are being presented. Least Mean Square (LMS) algorithm is being chosen to update complex weights to form the beam in the desired direction Keywords: Adaptive Digital Beamforming, LMS Algorithm, Beamforming Architecture, Beamforming Receiver Systems, Digital Down Conversion, Analog to Digital Converter, MUX, DEMUX I.

INTRODUCTION

Digital Beam forming (DBF) combines antenna technology with high performance up/down conversion, analog to digital conversion and digital signal processing [4] to provide receivers with very high spatial selectivity. In DBF technology digital signal processing is used to estimate the direction in which incoming RF energy is incident on an antenna array. DBF receivers multiply each user’s signal by complex weight vectors that adjust the excitation amplitudes and phases of the signal from each antenna element. DBF concepts first evolved in sonar and radar systems and with the advent of multimillion gate FPGAs it has become feasible to perform DBF for sixteen or more antenna elements at up to 10 GHz carrier frequency. Digital beam formers can be deterministic or adaptive when they track an arriving signal as it moves across in azimuth or elevation. In

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this paper we focus on the architecture of adaptive beam formers which are able to track the angle of arrival of RF signals in real time. DBF technology is rapidly making forays into areas like SDR using advanced phased array antennas to dramatically lower CCI (Co-channel interference). DBF offers additional flexibility and precision in the digital domain which has led to significant improvements in beamforming of multiple independent beams, adaptive pattern nulling, space-time adaptive processing (STAP), direction finding (DF), when compared to the conventional phased array antennas. The adaptive nature of DBF algorithms discussed herein allows the nulls of an antenna radiation pattern to be steered in the directions of interference signals. DBF systems today utilize predominantly digital receivers; the received RF signals are detected and digitized at the element level. The RF signal from an antenna element is down-converted, digitized and further digitally down converted. The adaptive algorithm must process the baseband signal. Each element has its own ADC and DDC channel [9, 10]. Digital beam formers tend of have IF frequencies in excess of 10MHz. This requires ADCs with sampling rates upwards of 30 MSPS with 16 bit resolution. Commercial High speed ADCs consumes high power. The hardware expense and power consumption increase linearly with the number of antenna elements when one ADC is used per antenna element [1]. Efforts have been made to reduce the hardware requirements in DBF receiving system [1, 2, 3]. The processing complexity of receiving system increases as the number of array elements in the array grows. This paper presents a novel architecture for digital beam forming receiver system using adaptive algorithms. This proposal not only reduces the hardware, increases the range of the ADCs and enhances the flexibility allowing it to be used for various applications. II. PRINCIPAL OF DBF SYSTEM The performance of a DBF array depends on how the receiver is designed. Adaptive DBF receiver system comprises of a plurality of single channel digital receivers. Fig.1 illustrates a simple block diagram of a conventional DBF receiver system.

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Figure 1. Block Diagram of Conventional DBF Receiver System

A single digital receiver processes the RF signal from a single antenna element. The signals from each receiver channel are combined to form a desired beam pattern that captures the direction of a unique received signal. This receiver structure has N ADC’s and N DDC’s for N antenna elements.

Figure 2. Block Diagram of Proposed DBF Receiver System

MATHEMATICAL MODELING OF DBF Consider a plane wave incident on the antenna array’s receiver which is given as: (1) y(t)=x(t) cos (wF t- ϕ)

The receiver architecture plays a significant role in determining the overall cost and performance of a DBF receiving system. Thus it is necessary to reduce the cost of a digital beam forming receiver system while considering the performance requirements. Fig. 2 illustrates the block diagram of a proposed DBF receiver system. The core system comprises of four blocks, the RF down conversion block, the ADC block, the digital down conversion block and the adaptive algorithm block. The signal received from each antenna element i.e. both real and imaginary signals are combined separately using a MUX into vector signals, the vector length being the same as the number of antenna elements. These real and imaginary vector signals are then digitized separately using two ADCs for both real and imaginary vector signals. The digitized real and imaginary vector signals are down converted using a DDC with a Numerically Controlled Oscillator (NCO) .After digital down conversion both the real and imaginary vector signals are digitally low pass filtered to remove the higher frequency components. The filtered real and imaginary vectored signals are then separately de-interleaved using a DEMUX into the two LMS algorithm blocks one corresponding to the real part and the other corresponding to the imaginary part. This improved structure has a reduced hardware computation when compared to the conventional beamformer which operates on scalar signals.

ϕ

where is the phase difference between two adjoining elements and . wF is the carrier frequency of the arriving signal Now, the ADC with a sampling rate Ts can be used to digitize this signal. The digitized sampled-data signal is represented as in [9]. (2) y[n] = y(t ) t =nTs = x[nTs] cos[wIF nTs − ϕ ]

y[ n ] = x[ n ] cos( wIF n − ϕ )

(3)

Once the antenna signals are digitized they are passed on to the DDC, which is the second stage of the DBF receiver. The DDC multiplies this digitized signal by a digital local oscillator with a digitized cosine for the phase channel and a digitized sine for the quadrature channel i[n] and q[n]. w IF is the frequency input at the DDC after RF down-conversion and ADC conversion are performed. This can be represented in the mathematical form [9]: (4) i[n] = x[n] cos(wIF n − ϕ ) cos(wDLO n)

q[n] = x[n] cos(wIF n − ϕ ) sin(wDLO n)

(5) Equations (4) and (5) represent the operation at each DDC The digitized signals i[n] and q[n] for each DBF receiver channel where the digital local oscillator has a

w

DLO frequency following form:

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= wIF [9] can be represented in the


ADAPTIVE BEAMFORMING

i[n] =

x[n] [cos(2wIF n −ϕ) + cos(ϕ)] 2

(6)

q[n] =

x[n] [sin(2wIF n − ϕ ) + sin(ϕ )] 2

(7)

Adaptive Beamforming is the process of recursively updating the complex weights for each of the antenna elements used in the array to achieve maximum reception in desired direction. The Adaptive beamforming algorithm rejects all signals of same frequency in other directions of arrival other than the desired Direction of arrival (DOA) this singular fact helps to reduce co-channel interference. The Adaptive DBF receiver performs a highly selective spatial filtering of arriving signals.

After low pass filtering the output signals for each channel, the equations obtained are as follows [9]. The low pass filtering removes the higher frequency component corresponding to 2 wIF

i[n] = x[n] cos(ϕ ) q[n] = x[n] sin(ϕ )

(8) (9)

Diverse adaptive beamforming algorithms with varying complexities has been widely used in different areas such as civilian mobile communications, radar, sonar, medical imaging, radio astronomy etc. Most adaptive beamforming algorithms are concerned with the maximization of the signal to noise ratio [4], [5].

Now consider a signal b[n] which is composed of both

b[n] = i[n] − jq[n] (10)

= x[n](cos(ϕ ) − j sin(ϕ )) = x[n]e − jϕ

(11)

(12)

A generic adaptive beam former is shown in Fig. 3 below. The weight vector w is calculated using the statistics of signal x(t) arriving from the antenna array. An adaptive algorithm will recursively minimize the error e between a desired signal d(t) and the array output y(t).

To recover x[n], the complex signals r[n] has to be multiplied by the complex weight that adjust the magnitude and phase of the signal [9]. If the complex weight is

w * [ n ] = e jϕ , then the product

is:

y[n] = w∗ [n]b[n] = e jϕ x[n]e − jϕ

(13) (14)

= x[n]

(15) Figure 3. A

This type of down conversion where the arriving signal is multiplied by a counter phase is called a complex down conversion as it is distinguished from real-imaginary parts of the signal being processed separately. Expressing the complex weight form [9]:

w*[n]

Generic Adaptive Beamformer

The choice of adaptive algorithm for deriving the adaptive weights is very important and so is the initialization of the weight vector. The choice of the adaptive algorithm determines the speed of convergence and hardware complexity in terms of number of multiplications and additions/accumulates (MAC). The convergence rate is controlled by the adaptation coefficient of the chosen adaptation algorithm and by the eigenvalues of the correlation matrix of input data. For this system, the initialization of the weight vector has a limited effect on the rate of convergence of the algorithm.

in rectangular

w * [ n] = Re{w ∗ [n]} + jIm{w ∗ [n]} (16) Then, the resulting signal follows [9]:

y[n]

can be obtained as

y[n] = w∗ [n]b[n] ∗

(17) ∗

= (Re{w [n]}+ jIm{w [n]})(i[n] − jq[n]) (18)

= r[n] + js[n]

In this paper, Least Mean Square (LMS) adaptive algorithm is chosen because of its simplicity. The LMS algorithm is based on the steepest descent method [4], [5], [6], [7].

(19) Where as in [9]

r[n] = i[n]Re{w∗[n]}+ (−q[n])(−Im{w∗[n]}) ∗

∗

s[n] = i[n]Im{w [n]}+ (−q[n])(− Re{w [n]})

(20)

(21)

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HARDWARE REALIZATION IN SIMULINK

real part and another for the imaginary part. The ninth and final stage performs weight adaptation by the LMS algorithm in two independent LMS blocks – one for the real part of the down-converted signal and one for the imaginary part of the down-converted signal.

The modeled DBF receiver system consists of uniformly spaced linear 8 antenna elements (ULA-uniform linear array). The distance between adjacent antennas is a half wavelength ‘λ⁄2’. The carrier frequency of the system is 3 GHz. The received radio signals are digitized using both a 32-bit idealized ADC and an 18 bit equivalent ADC as shown in Fig. 12 and then down converted to 30MHz. The in-phase and quadrature phase signals generated from the down converted are now separately passed on to the LMS algorithm that update the complex weights to form the beam in the required direction.

Multiple Beamforming This implementation can be extended to the formation of multiple beams in different directions using a common weight vector. For multiple beamforming the inputs from different sources are summed at each antenna element. Then, the weights generated form adaptive algorithm form multiple beams in the desired direction. An example of this is shown in Fig. 9 with two beams and Fig. 10 with three beams. Greater the number of elements better the efficacy of multiple beam formation as the beam widths are inversely proportional to the number of antenna elements in a ULA.

Fig.4 shows the diagram of the DBF Receiver Implementation using MATLAB’s Simulink.

In order to form multiple beams, it is required to increase the number of antenna elements which entails N times the hardware complexity. In general greater the number of antenna elements, better the precision of formation of multiple beams. Hence, there is a trade off between the number of antenna elements and the accuracy of the beams formed. On the data transmission side multiple beams lower the Co-Channel interference (CCI) especially if the beam widths are narrow and allow simultaneous downloads to two separate base stations in mobile communications. RESULTS AND DISCUSSIONS This section provides the Simulation results of the proposed DBF Receiver system. The simulation has been demonstrated for a 8-linear uniform array of antenna elements. The distance between adjacent antennas elements is half wavelength. The carrier frequency of the system is set at 3 GHz. The received radio signals are digitized using an ADC and then down converted to 30 MHz.

Figure 4. DBF Receiver Implementation in Simulink

The architecture of Fig. 4 comprises of five stages, the first stage being the RF down-conversion stage, the second stage being the splitting stage which splits the arriving complex value into a real and an imaginary value. The third stage combines the real parts from 8 elements into an 8x1 vector and the imaginary part from all 8 elements into an 8x1 vector. The fourth stage comprises of two oversampling ADCs which digitize the arriving 8x1 real and imaginary vectors independently. The fifth stage (DDC stage) down-converts the vector ADC output using a NCO as shown in Fig. 11. The DDC output is filtered by the sixth stage which is a digital LPF. The seventh stage performs demultiplexing of the two LPF outputs (real and imaginary). The eighth stage performs serialization of the vectors into individual samples. There are two serializers – one for the

The LMS algorithm based adaptive beamforming weights converges within 200 samples for the step-size µ =0.005 as shown in Fig. 5 for zero noise variance.

Figure 5. Mean square error plot for LMS algorithm

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Typical cases for two beams forming at 60° and 120° is shown in Fig.9 and three beams forming at 60°, 90° and 120° is shown in Fig.10.

Similarly, the LMS algorithm converges within 200 samples for the same step-size with a slight mis-adjustment for a noise variance of 0.001 as shown in Fig. 6.

Figure 9. Polar plot of beam pattern pointing at θ=60°and θ=120° Figure 6. Mean square error plot for LMS algorithm with a noise variance of 0.001

The algorithm is realized to form the main lobe of the 8element antenna array for different beam pointing angles. Typical cases for beamforming at 30° and 60° is shown in Fig.7 and Fig.8 respectively.

Figure 10. Polar plot of beam pattern pointing at θ=60°, θ=90° and θ=120°

cos(wot + ϕ)

Figure 7. Polar plot of beam pattern pointing at θ=30°

sin(wot + ϕ)

Figure 11. Block diagram of Down Conversion block

Fig. 12 shows the block diagram of the ADC used in the beamformer [12]. The ADC architecture comprises of 8 blocks. The first block adds the incoming signal with its maximum value as given by (22). Equation (23) gives the upper and lower bounds of the output of the first block. The second block performs a time integration of the added signal as given by (24). The third block performs a non-linear

Figure 8. Polar plot of beam pattern pointing at θ=60°

The algorithm is also realized to form multiple beams for an 8-element antenna array with the single set of weights.

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function on the integrated signal. The non-linear function is given by (25). Equation (26) gives the relationship between the over-sampling factor and the extension in dynamic range. The fourth block performs an over-sampled analog to digital conversion, the over-sampling factor is a function of the increase in ADC range. The fifth block performs a difference between the current output sample and the previous output sample as given by (30). The sixth block performs the operation when the output is the subtraction of the input value and the sign of the input value as given by (31). The seventh block performs digital down sampling by a factor of four.

Figure 114.Ratio of Dynamic Range to Oversampling rate

Figure 12. Conceptual block diagram of the Claasen-Mecklenbrauker ADC [12] Figure 15. ADC curve plot

The output of the ADC is directly fed to the digital down converter for sample rate conversion. The output of the digital down converter is fed to the adaptive algorithm. The proposed ADC was implemented in Simulink and the Simulink block diagram is shown in Fig. 13 [12]. The relation between the Dynamic range and the oversampling rate is shown in Fig. 14. In this design, the oversampling factor was set to 8 to achieve an increase in dynamic range by 4 bits. This relationship is determined by (26). The sample output for a sinusoidal input is shown in Fig. 15.

yo (t) = xi (t) + Xmax

(22)

0 ≤ yo (t ) ≤ 2 X max

(23)

t'

u (t ) =

1 yo (t )dt T ∫0

va (t) = f (ua (t ))   1 2 R = − log 2   2 N  

(24)

(25)

π   sin   N  1 − π     N  

(26)

Where ‘N’ is the oversampling rate and ‘R’ is the increase in bandwidth of number of bits.

y= x Figure 13. Simulink model for Claasen-Mecklenbrauker ADC [12]

-xmax ≤ x ≤ xmax

y= -2xmax + x

213

xmax < x ≤ 2xmax

(27) (28)


y= +x +2xmax

-2xmax < x < -xmax

Digital Beamforming,” IEEE Transactions on Microwave Theory and Techniques, Vol. 50, No. 12, pp. 3052 – 3058, December 2002. [3] Seong-Sik Jeon, Yuanxun Wang, Yongxi Qian and Tatsuo Itoh, “A Novel Smart Antenna System Implementation for Broad-Band Wireless Communications,” IEEE Transactions on Antennas and Propagation , Vol. 50, No. 5, pp 600-606, May 2002. [4] J. Litva and T. Lo., “Digital Beamforming in Wireless Communications,” First Edition, Artech House, Boston, 2009. [5] B. Widrow and S.Stearns, “Adaptive Signal Processing,” First Edition, Prentice Hall, NJ, 1985. [6] A. P. Kabilan and K. Meena, “Performance comparison of a modified LMS algorithm in digital beam forming for high speed networks,” IEEE International Conference on Computational Intelligence and Multimedia Applications, Vol. 4, pp. 428-433, 2007. [7] R. S. Kawitkar, D. G. Wakde, “Smart Antenna Array analysis Using LMS Algorithm,” IEEE International Symposium on Microwave, Antenna, Propagation and EMC Technologes for Wireless Communications Proceedings, Vol. 1, pp. 370-374, 2005. [8] Steyskal H., “Digital Beamforming – An Emerging Approach,” Military Communications Conference, 1988. MILCOM 88, Conference record. '21st Century Military Communications - What's Possible?’ IEEE, Vol. 2, pp. 399 -403, October 1988. [9] Juan A. Torres-Rosario,“Implementation of a phased array antenna using digital beamforming,” MS Thesis, University of Puerto Rico, 2005. [10] Taco Kluwer, “Development of a test-bed for smart antennas, using digital Beamforming,” M. Sc. Thesis, University of Twente, 2001. [11] Haynes T., “A Primer on Digital Beamforming,” Spectrum Signal Processing, Burnaby, BC, 1988. [12] Theo Claasen, Wolfgang Mecklenbrauker, J. B. H. Peek, Nicolaas Van Hurck, “Signal Processing method for Improving the Dynamic Range of A/D and D/A converters,” IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. 28, No.

(29)

w(n) = v(n) − v(n − 1)

(30)

s(n) = w(n) − sgn(n − 1)

(31)

where

sgn( x ) = 1 x > 0 sgn( x ) = − 1 x < 0

(32)

CONCLUSION The proposed digital beam forming architecture demonstrates rapid convergence to final beam weights within 200 iterations as shown in Fig. 5 and Fig. 6. The performance of the proposed DBF has been demonstrated over a wide range of beam angles. The DBF architecture is able to form single, dual and triple beams. The described ADC is unique in that a single ADC is used to sample two channels and the ADC architecture delivers a greater resolution through appropriate analog pre processing and digital post processing. The choice of the LMS algorithm was driven by the need for simplicity in implementation. For faster convergence algorithms like RLS, RRLS (robust recursive Least squares), fast Kalman should be considered. The rate of convergence (ROC) is dependent on the ratio of the largest to the smallest eigenvalues of the error covariance matrix. The weight vector computation can be further speeded by having a choice of pre computed weights one for each quadrant. The accuracy of the DBF can be enhanced further by adding additional elements. In commercial DBFs, the number of elements is usually a power of two. The proposed beam former can be used in both military and civilian RADAR and SONAR applications and for diagnostic ultrasound. Future work will address beamforming in frequency domain. We have chosen LMS as an adaptive algorithm because it is very simple and easy to apply since it requires no calculations or complex measures. This work can also be extended for other adaptive algorithms depending on the need and application. REFERENCES [1]

[2]

Zheng Shenghua, Xu Dazhuan, Jin Xueming, “A New Receiver Architecture for Smart Antenna with Digital Beamforming,” IEEE International Symposium on Microwave, Antenna, Propagation and EMC Technologies for Wireless Communications Proceedings, Vol. 1, pp. 38-40, 2005. Jonathan D. Fredrick, Yuanxun Wang, and Tatsuo Itoh, “A Smart Antenna Receiver Array Using a Single Frequency RF Channel and

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