A Multi-Channel Quadrature Bandpass Sampling Receiver

D.B.Richardson1 N.L.Scott1 M.Leonard-Taylor1 S.Singh1

1Communications and SensorsIndustrial Research Limited

PO Box 31-310, Lower Hutt, NEW ZEALAND.

Email: d.richardson@irl.cri.nz

Abstract: Traditional multi-channel sonar receivers require costly replication of analogue hardware before digitisation and processing of the signals. This paper describes the design process and architecture used to develop a multi-channel bandpass sampling receiver capable of directly and sequentially sampling each channel signal in quadrature such that the overall sampling rate remains uniform. The capability of the traditional multi-channel systems is retained while hardware complexity and cost are dramatically reduced.

Keywords Quadrature, Bandpass, Sampling, Sonar, Receiver, Multiplexer

1. INTRODUCTION

Traditional multi-beam sonar receiver designs are realised by the use of costly analogue hardware repetition (figure 1). The carrier-based signals must be amplitude-processed and downconverted to obtain the quadrature components for sonar signal beamforming and echo display. Multiple channels require identical amplifiers, filters and downconverters and calibration procedures must additionally be implemented to reduce all analogue-derived errors.

An alternative approach is to multiplex the receiver channel signals into one or more analogue data streams at an earlier stage of reception. The subsequent analogue signal processing, and digitisation occurs with a considerably reduced hardware component count (figure 2).

The Communications Team at IRL have developed and filed a provisional patent for a multi-channel, multiplexed, bandpass sampling receiver, an implementation of which is used in a sonar research platform.

The implementation performs digital downconversion by deriving a complex baseband signal. The

technique is known as uniform, 2nd order quadrature sampling and the subject is described in numerous papers [1], [2], [3]. The design described in this paper has extended this concept to include multiplexing of multiple received bandpass signals on to a shared signal path.

The design maintains data timing uniformity over each individual channel and over all the channels, thus simplifying the interpolation algorithms required for recovery of the baseband information.

2. QUADRATURE BANDPASS SAMPLING

A full description of the theory of uniform quadrature bandpass sampling is beyond the scope of this document and interested readers can refer to the excellent papers on the subject [1], [2], [3], [5]. Nevertheless the basic concepts do need to be outlined to support the derived parameters required in the design.

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Multiple AnalogueSignal Processing Stages

Transducers

DigitalProcess

&ControlI

Q

Figure 1. Traditional Multi-beam Sonar Receiver

MultipleFront End

Stages

Transducers

Multiplexer

DigitalProcess

&Control

Figure 2. Multiplexed Bandpass Sampling Receiver

Bandpass sampling is a technique which translates a bandpass signal to baseband while applying a sampling rate that is more determined by the bandwidth of the signal rather than its band position.

A received sonar signal can be considered to occupy a narrow band about a center frequency and may therefore be treated as narrowband modulation or a complex envelope on a burst of carrier frequency:

xt = I t cos 2 f c t−Q tsin 2 f c t (1)

The in-phase, I and quadrature-phase, Q componentsprovide all the essential information about the return echoes.

Quadrature sampling is a special form of 2nd order sampling where two impulse streams are interleaved into one stream and time-offset from each other by an odd number of quarter wave cycles of carrier frequency. In uniform quadrature sampling the first stream is interleaved midway between the second so that the overall effect is a single uniform stream.

The spectrum of a bandpass signal with a modulation bandwidth of B is illustrated in figure 3a. The diagram includes the concept of a negative frequency band since it illustrates the way the image frequencies are derived. The sampling process is equivalent to the convolution of the bandpass spectrum with an impulse train spectrum.

The result is a series of scaled spectral images of the bandpass signal, spaced at integer multiples of the sampling frequency fs . This is illustrated in figure 3b where the sampling rate is set at 2W. The sampling bandwidth, W is deliberately chosen wider than the bandpass signal bandwidth, B in order to provide a guard band between images.

The complex baseband information (figure 3c) is recovered by removal of the images of the negative spectrum, shifting the spectrum by W/2 and halving the sample rate. The baseband information is recovered by low pass filtering [2].

3. RECEIVER DESIGN PROCESS

3.1 Design Requirements

The following table outlines some of the specifications required for the sonar receiver design.

TABLE 1. Receiver Design Requirements

Carrier Frequency (fc.) 160 kHz

Number of channels (N) 30

Channel Bandwidth (B) 10 kHz

Guard Band (to ease antialiasing filtering)

10 kHz

3.2 Integer Band Positioning

A key factor in the bandpass receiver design is to avoid aliasing by ensuring that there are an integer number of W bandwidths between the origin and the upper bandpass signal band edge. This is done by defining a band position factor k as shown in equation (2).

W=2 f c

2 k−1k∈[1,2,3,4. ..] (2)

3.3 Sampling Rate

For quadrature sampling, the sample rate, fs is restricted to odd multiples of /2 radians of theπ carrier frequency, fc :

f s=4 f c

2 k−1 (3)

Equations (2) and (3) reduce to the Nyquist criterion for minimum rate sampling where

f s=2W (4) 3.4 Multiplexing Rate

The process of multiplexing multiple bandpass channels into a single, interleaved analogue data stream and conforming to integer band-positioning requires that the multiplexing rate fm is synchronised to the per-channel sampling rate fs . If N is the number of channels required then:

f m=N f s (5)

Uniform sampling and quadrature operation is maintained if the multiplexing rate is chosen as:

f m=4 f c (6)

3.5 Channel Number and Bandwidth Limitations

fc-B/2

W(n-1)W nW

fc

W/2

(a)

(b)

(c)

2W 3W

-W/2

fc

fc-B/2fs

Figure 3. (a) Bandpass Spectrum (b) Bandpass Image Spectrum (c) Bandpass Shift To Baseband

There exists a maximum number of channels that are available for sampling, determined by the choice of bandwidth, W which itself is derived from the band position integer, k as shown in equation (2).

Manipulation of equations (3), (5) and (6) reduces to a simple equation that relates the number of channels to the band position:

N=2 k−1 (7)

Therefore the band position factor determines the number of channels that are available up to a maximum value of:

k= floor f c

B1

2 (8)

Table 2. lists channel results for three different band position factors with the corresponding, allowable bandwidth, guard band and sampling rate included for comparison.

TABLE 2. Band position/channel characteristics

Parameter(equation)

k N(7)

W (2)

GuardBand

fs

(4)

kHz kHz kHz

Maximum bandwidth

1 1 320 310 640

Selectedbandwidth

8 15 21.33 11.33 42.67

Minimum bandwidth

16 31 10.32 0.32 20.65

When k = 1, the bandpass signal is placed in the standard low pass position where fs = 2fc . In this case only one channel is available.

The maximum value of k is determined from equation (8) and corresponds to a minimum bandwidth of 10.32 kHz.

For the receiver design in this paper, the ideal value of k has been determined as 8 since 15 channels are available, each with a bandwidth of 21.33 kHz. This allows a guard band of 11.33 kHz which is sufficient for bandpass filtering purposes.

3.6 Quadrature Data Recovery

The bandpass signal demodulation process occurs at sample time. The computational tasks include:

• Extraction of the relevant data for each channel.

• Separation of channel data into even (I components) and odd (Q components) streams. This effectively halves the sampling rate.

• Inversion of the sign of every second even and odd data sample.

• Estimation and correction of the DC level in each channel.

• Time-alignment of the I/Q pairs for each channel.

• Low pass filtering.

4. RECEIVER ARCHITECTURE

The design of a 30 channel, multiplexed, quadrature, bandpass sampling receiver as developed, is shown in block diagram form in figure 4.

Differential signals from a sonar transducer array are fed into 15, dual-channel, front end daughter boards. Each channel contains a low noise amplifier and bandpass filter. The former establishes a satisfactory signal-to-noise ratio from the early stages of the receiver and the latter provides rejection against interference and noise. The use of the removable daughter boards provides considerable flexibility if specification changes or modifications are required, particularly as the initial purpose of the sonar unit was for use as a research platform.

A dual, 16 channel multiplexer samples 2 x 15 receiver signals, extracts the analogue signal segments from each channel and sequences them into two parallel analogue data streams. Figures 5a and 5b illustrate the timing of the multiplexed segments. Figure 5c illustrates the sampling clock repetition time for one of the 15 channels.

Adjustment to the amplitude of the received signals over the time period of a return echo is standard procedure in sonar systems. This is achieved by feeding the two analogue data streams into two parallel time variable gain amplifiers.

Eth

erne

tIn

terfa

ceP

RO

M

TVG

Vref

DAC

Mul

tiple

xer

SerialLink

EthernetLink

DATA

12V PSU

ADC16 BIT

LNA BPFLNA BPF

LNA BPFLNA BPF

TransducerArray

LNA BPF

Daughter Boards

TVGADC

16 BITTVGADC

16 BIT

TVG DATAADC16 BITTVGADC

16 BITTVGADC

16 BIT

FPGA

StableSource

DataClock

Ana

logu

eS

igna

ls

Preamp

Figure 4. Thirty Channel Bandpass Sampling Receiver

The two data streams are sampled by two 16-bit analog-to-digital converters and the sampled data passed to the FPGA. This latter stage provides the computational means for quadrature data recovery, multiplexer and sampling clock adjustments, control of the TVG gain profile and control of the serial data output stream.

Aperture jitter potentially degrades the SNR performance of the receiver. A stable sampling clock, with a jitter performance calculated at approximately 40ps was included as separate to a data clock used for data computations within the FPGA.

An ethernet interface provides both data uplink capability to the PC for display processing and data downlink capability for receiver control messages.

A hardware prototype of the receiver (figure 6) has been developed. Additional circuitry has been included to allow a manual override control of the analogue circuitry for test purposes and to provide external clock and triggering for transmitter signal synchronisation purposes.

5. BENCH TEST RESULTS

Full characterisation of the receiver is part of an ongoing sonar platform test and calibration procedure and the results are, as yet, incomplete. To

demonstrate the validity of the multi-channel bandpass sampling process as outlined, a simple bench test was designed using the prototype hardware.

The test arrangement is illustrated in figure 7. A sonar system was set up using air as the medium for transmission of the sonar signal.

A single channel of a multichannel sonar transmitter/projector combination ensonifies a target area using pulsed, 160kHz carrier signals.

To ease the task of target detection due to the narrow vertical beamwidth of the transducers, cylindrically-shaped target profiles were chosen. Three vertically-extended targets, a, b and c as shown in figure 7, are positioned to form a triangle in the horizontal plane. The targets are reflective to sonar signals and have the following diameter and range:

(a) Ø 0.5mm @ 0.9m;(b) Ø 1mm @ 1m; (c) Ø 25mm @ 1.4m.

The echo signals are received by a transducer made up of fifteen individual sections in an single block.

Both the projector and receiver transducer sections are impedance matched for an air interface.

The received echoes, in the form of sampled data, are pre-processed in the receiver FPGA. Thereafter separate processing and beamforming algorithms are implemented using MATLAB to produce the display.

A 2-dimensional and 3-dimensional spatial representation of the resultant echoes are illustrated in figures 8 and 9 respectively. The diagrams indicate that the range, position and amplitude level for each target is as expected.

Figure 6. The 30 Channel Bandpass Sampling Receiver Hardware Prototype

Figure 7: Bench test arrangement

Rx

Targets

BandpassSamplingReceiver

Transmitter

Pr

Transducers

a b

c

MultiplexerClock

fm = 640 kHz

1

2

3 4

5

6

7 8

9 10

12

11 13

1415

1 2 3

Frame 1 Frame 2

4

2m - 1 = 23.44usec

1

2

3 4

5

6

7 8

9 10

12

11 13

1415

1 2 3

Frame 1 Frame 2

4

MultiplexedAnalog Channel

Segments

2k- 14 fc

= 23.44usecSampling PulseChannel 1

fs = 42.67 kHz

(a)

(b)

(c)

Figure 5. (a) Multiplexer Clock (b) Channel Signal Segments (c) Channel 1 Sample Clock

6. CONCLUSIONS

A multi-channel, multiplexed bandpass sampling sonar receiver has been designed as a reduced cost and reduced component-count alternative to the more costly, traditional, multi-channel sonar receiver using analogue downconversion methods.

The development expanded on previous knowledge and expertise in the field of quadrature bandpass sampling to now encompass a multiple-input, multiplexed receiver design using the same bandpass sampling techniques.

The concept of an overall uniform sampling scheme was implemented in order to simplify the interpolation algorithms required for baseband recovery. In this respect design equations show that there is a maximum number channels that are possible dependent on the required channel bandwidths.

A hardware prototype receiver was built and tested. The results have verified the concept of uniform multi-channel bandpass sampling.

7. REFERENCES

[1] R.G. Vaughan, N.L.Scott, D.R.White, “The Theory of Bandpass Sampling”, IEEE Transactions on Signal Processing, Vol 39 No.9, pp 1973 – 1984, September, 1991.

[2] M.A.Poletti, A.J.Coulson, “On Uniform And Quadrature Bandpass Sampling”, internal reference paper. m.poletti@irl.cri.nz

[3] D.W.Rice, K.H.Wu, “Quadrature Sampling With High Dynamic Range”, IEEE Transactions on Aerospace and Electronic Systems, Vol AES-18 No.4, pp 736-739, November 1982.

[4] J.G.Proakis, D.G.Manolakis, Digital Signal Processing, 2nd edition, Macmillan Publishing Group, 1992

[5] A.J.Coulson, R.G.Vaughan, M.A.Poletti, “Frequency-Shifting Using Bandpass Sampling”, IEEE Transactions on Signal Processing, Vol 42 No.6, pp 1556-1559, August 1995.

[6] A.J.Coulson, R.G.Vaughan, N.L.Scott, “Signal Combination Using Bandpass Sampling”, IEEE Transactions on Signal Processing, Vol 43 No.9, pp1809-1818, August 1995.

[7]D.B.Richardson, N.L.Scott, M.L.T Leonard-Taylor, Eugene Stytsenko, Sudhir Singh “A Multiple Channel Bandpass Receiver Architecture”, provisional NZ patent 561702.

Figure 9: 3D Display Profile - Bandpass Sampling Receiver Test Echo Results

Figure 8: 2D Display Profile - Bandpass Sampling Receiver Test Echo Results