1. Motivation. 2. Periodic non-gaussian noise

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Nigel Casey
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1 . Motivation One o the many challenges that we ace in wireline telemetry is how to operate highspeed data transmissions over non-ideal, poorly controlled media. The key to any telemetry system design depends on the system s ability to adapt to a changing environment. While adaptive equalization can account or requency-dependent cable attenuation by inverting channel distortion [Campbell 96, pp. 68], there still exists the need to reduce other sources o noise, or example, the near-end crosstalk (NEXT) that exists in a multiconductor cable. Typically, a multiconductor cable is used as a medium in a wireline telemetry system or two reasons:. Multiple cables increase the number o communication channels and thereore increase the total operating bandwidth o the system.. In addition to data cables, a power cable is needed to supply electricity to the telemetry transmitter at the remote end. The principal source o intererence is now the coupling between the power cable and data cable. This noise is ar rom white and can reduce the SNR by more than 0 db, an amount that can severely hamper the telemetry system s perormance. The structure o the paper is as ollows. First we discuss the observed periodic non- Gaussian noise and explain why it is diicult to reduce this noise using requency domain iltering. Next, we introduce an innovative time domain approach, Active Noise Cancellation, that can reduce in-band crosstalk without distorting the signal o interest. Finally, we outline the speciication o this cancellation algorithm using a homogeneous synchronous datalow (HSDF) graph and describe its implementation on an embedded DSP processor.. Periodic non-gaussian noise The crosstalk intererence can be described as a collection o noise pulses superimposed on top o a slow varying 60 Hz sine wave originated rom the power supply.

2 cycle Figure. Oscilloscope capture o approximately one cycle o crosstalk. Figure is an oscilloscope capture o the actual crosstalk intererence. The double arrow line above the igure approximately marks one period o the 60 Hz crosstalk. To better describe the eective noise, we can decouple the crosstalk into a 60 Hz sine component and a collection o periodic noise pulses as seen in Figure. 60 Hz power supply sine wave K K Periodic noise can be decoupled into 60Hz power supply sine wave and cyclic noise pulses. = + Noise pulses that repeat at a period o /60 seconds. K Figure. Decoupling o crosstalk into a 60 Hz sine component and periodic noise pulses. Each o the noise pulses in Figure is a collection o impulses as shown in Figure 3(a). Hence the crosstalk creates a non-gaussian noise, because the noise is periodic, that maps to a wideband noise in the requency domain, because the noise consists o impulses in the time domain. The wideband noise completely overlaps the transmitted QAM signal which has a bandwidth o, or example, =5 c. 5 khz, as seen in Figure 3(b). b = 70 khz and is modulated by a carrier o

3 (a) One noise cycle has a duration o 6.7 milliseconds (b) QAM Signal Wideband Noise c b c c b + Figure 3. (a) Each 60 Hz noise cycle consists o a group o sampled impulses. (b) QAM signal with overlapping wideband noise. As a result, requency domain ilters cannot remove the wideband noise without actually removing the desired QAM signal as well and requency domain iltering becomes an ineective approach to eliminating the periodic crosstalk noise. 3. Quadrature Amplitude Modulation Quadrature Amplitude Modulation avoids the spectral ineiciency o Double Sideband Amplitude Modulation by mapping a stream o bits onto a constellation and modulating the coordinates o the constellation with two orthogonal carriers 90 o apart in phase. Thus, the transmitted signal is st () = xp()cos( t ωct) xq()sin( t ωct) At the receiver end, st ( ) is multiplied by cos( ωct) and sin( ωct) to recover the original data, the products are xp()( t + cos ωct) xq()sin t ω t c yp() t = xp()cos t ωct xq()sin t ωctcosωct = xp()sin t ωct + xq()( t cos ωct) yq() t = xp()cos t ωctsin ωct + xq()sin t ωct =

4 The sidebands o the second harmonics o the carriers are then removed by low-pass iltering, and the receiver baseband signals y ( p t ) and y the originals [Campbell 96, pp. 6-53]. q ( t ) are then within a actor to st () sin( ω c t) X cos( ω c t) X yp() t yq() t Lowpass Filter Lowpass Filter ADC ADC S L I C E R Output bit stream Figure 4. QAM Receiver Structure. Figure 4 illustrates a QAM receiver. It is clear that intense computation is needed to multiply st ( ) with the carriers and to lowpass ilter the resulting signals y ( p t ) and y (). t q To reduce unnecessary computation, Schlumberger developed and patented a technique that eliminates the need or signal reconstruction. 4. Existing Noise Cancellation Techniques Early research has been done in the noise cancellation area. The most amous work is perhaps the Least Mean Square Algorithm, illustrated in Figure x j x j x j w j w j w 3 j Σ y j 5, introduced by Widrow and Ho [Widrow 75] in the mid w nj 70s. However, the LMS algorithm presented by Widrow was aimed at removing single tone intererence and not w + = w + µε x j j j j ε j + Σ Figure 5. Widrow-Ho LMS Algorithm. d j -

5 periodic wideband noise. 5. Active Noise Cancellation The idea o noise cancellation is to collect an estimation o the periodic wideband noise during receiver training. The collected noise estimate is then subtracted rom the received QAM signal during steady state data transmission. Figure 6 is a block representation o the receiver operation during training. Received Signal High Pass Filter A/D + Σ - sn [ ] Buer Band Pass Filter Zero Crossing? Power Supply Figure 6. Block diagram o receiver operation during training. The structure to the right o the dash line is responsible or noise extraction. The transmitted signal is known during receiver training, or example, the signal can be a 5.5 khz tone. It is clear that with the transmitted signal known a priori, noise estimate can be computed as Noise Estimate s[ n] = Actual received signal Training signal. Furthermore, the training signal can be extracted at the receiver using a narrow band notch ilter centered at the carrier requency 5.5 khz. The notch ilter is implemented using a second-order IIR biquad with the ollowing transer unction. Yz () Sz () k0( z ) = kz kz Equation. Notch ilter transer unction. The ilter structure is illustrated in Figure 7. The coeicients k 0, k, and k can be adjusted to obtain the desired ilter sharpness and ilter build-up time.

6 sn [ ] k 0 yn [ ] k 0 k k 0 Figure 7. IIR biquad bandpass ilter. The buer block in Figure 6 can be implemented using a circular buer and updated using the ollowing ormula. The variable i represents the ith sample in the 60 Hz noise cycle. α α bueri[ n] = s[ n] + ( ) bueri[ n ] β β N α α k = ( ) sn [ k] β k= 0 β Equation. Buer update equation. N is the number o 60 Hz noise cycles during training duration. The ratio αβ is the buer update actor and must be chosen careully to optimize the cancellation algorithm. From Equation, it is clear that i the update actor is zero, then no update is made to the noise buer and it retains its initial values. I the actor is one, then only the most current noise cycle is kept. Thereore, an update actor close to zero implies that the noise estimate will be approximately a running average while a actor close to one means that the most recent noise cycle will be weighted more. Averaging is a more conservative approach but the noise estimate will remain valid or a longer duration. On the other hand, an emphasis on more recent noise cycles is an aggressive approach that will produce a better result in the short term in exchange or the need to requently reacquire the noise pattern which may not be possible during steady state. The zero-crossing block in Figure 6 is used to combat 60 Hz crosstalk drit. Whenever the positive zero-crossing occurs in the power supply, the zero-crossing block will reset

7 the buer pointer to the head o the buer array, i.e. sample number one o the noise estimate. Actual noise cancellation occurs in steady state. Figure 8 is a block diagram o the receiver operation during steady state. The noise estimate is subtracted rom the received QAM signal sample-by-sample to achieve an improved receiver noise perormance. Figure 8. Noise Cancellation in steady state. QAM Receive Signal + Σ - Adaptive Equalizer Slicer Buer Zero- Crossing? Power Supply 6. Homogeneous Synchronous Datalow Synchronous Datalow (SDF) [Pino 95] is a well-suited model o computation or digital communication systems which oten process an endless supply o data. The simplest orm o an SDF is a homogeneous SDF graph where the number o tokens consumed and produced on each arc is a constant one. HSDF its nicely with the speciication o our Active Noise Cancellation. Figure 9 illustrates the algorithm using an HSDF graph. The actor iring sequence will be {ADC Read, Int-to-Float, Notch Filter, Estimate Noise, Zero-Crossing, Buer Write} during training and {ADC Read, Int-to-Float, Cancel Noise, Zero-Crossing} during steady state. (a) Training (b) Steady State ADC Read Notch ilter Estimate Noise Buer Write Zero Crossing ADC Read Int-toloat Int-to- Float Cancel Noise Zero Crossing Figure 9. HSDF graph representation o receiver operation in (a) training and (b) steady state.

8 7. Perormance Active Noise Cancellation has been simulated using Analog Device s SHARC simulator and its perormance analyzed using MATLAB. Crosstalk intererence is created by appending multiple cycles o the measured noise, seen in Figure. Active Noise Cancellation on average improves the Mean Square Error by 7dB as illustrated in Table. Also notice rom the table that an accurate zero-crossing inormation is crucial to proper noise cancellation because incorrect cancelling can worsen the noise. Table. Perormance o Active Noise Cancellation. Method Average MSE Average SNR Required values under Gaussian noise to obtain an BER o db 35 db No Active Noise Cancellation -5 db 5 db Active Noise Cancellation without Zero-Crossing inormation -3 db 3 db Active Noise Cancellation with Zero-Crossing inormation -3 db 3 db 8. Conclusion We have developed an eective Active Noise Cancellation algorithm to improve receiver perormance in the presence o non-gaussian wideband noise. Modeling o ANC using HSDF proves that the algorithm is simple enough to be implemented on most existing DSPs. We plan to show the eectiveness o ANC in a real noise environment and to veriy that an average o -3 db MSE can be obtained while maintaining a BER o Reerences [Campbell 96] Heather A. Campbell, Simulation o Quadrature Amplitude Demodulation in a Digital Telemetry System, Master Thesis, Massachusetts Institute o Technology, Feb [Pino 95] Jose Luis Pino, Shuvra S. Bhattacharyya, and Edward A. Lee, A Hierarchical Multiprocessor Scheduling System or DSP Applications, Proc. o 9 th Asilomar Con. on Signals, Systems, and Computers, October 995. [Widrow 75] B. Widrow, J.R. Glover, et al., Adaptive Noise Cancelling: Principles and Applications, IEEE Proc., vol. 63, no., pp , Dec. 975.

( ) D. An information signal x( t) = 5cos( 1000πt) LSSB modulates a carrier with amplitude A c

( ) D. An information signal x( t) = 5cos( 1000πt) LSSB modulates a carrier with amplitude A c An inormation signal x( t) 5cos( 1000πt) LSSB modulates a carrier with amplitude A c 1. This signal is transmitted through a channel with 30 db loss. It is demodulated using a synchronous demodulator.