1. MotivationOne of the many challenges that we face in wireline telemetry is how to operate high-speed data transmissions over non-ideal, poorly controlled media. The key to anytelemetry system design depends on the system’s ability to adapt to a changingenvironment. While adaptive equalization can account for frequency-dependent cableattenuation by inverting channel distortion [Campbell 96, pp. 68], there still exists theneed to reduce other sources of noise, for example, the near-end crosstalk (NEXT) thatexists in a multiconductor cable. Typically, a multiconductor cable is used as a mediumin a wireline telemetry system for two reasons:1. Multiple cables increase the number of communication channels and thereforeincrease the total operating bandwidth of the system.2. In addition to data cables, a power cable is needed to supply electricity to thetelemetry transmitter at the remote end.The principal source of interference is now the coupling between the power cable anddata cable. This noise is far from white and can reduce the SNR by more than 10 dB, anamount that can severely hamper the telemetry system’s performance.The structure of the paper is as follows. First we discuss the observed periodic non-Gaussian noise and explain why it is difficult to reduce this noise using frequency domainfiltering. Next, we introduce an innovative time domain approach, Active NoiseCancellation, that can reduce in-band crosstalk without distorting the signal of interest.Finally, we outline the specification of this cancellation algorithm using a homogeneoussynchronous dataflow (HSDF) graph and describe its implementation on an embeddedDSP processor.2. Periodic non-Gaussian noiseThe crosstalk interference can be described as a collection of noise pulses superimposedon top of a slow varying 60 Hz sine wave originated from the power supply.1 cycleFigure 1. Oscilloscope capture of approximately one cycle of crosstalk.Figure 1 is an oscilloscope capture of the actual crosstalk interference. The double arrowline above the figure approximately marks one period of the 60 Hz crosstalk. To betterdescribe the effective noise, we can decouple the crosstalk into a 60 Hz sine componentand a collection of periodic noise pulses as seen in Figure 2.Each of the noise pulses in Figure 2 is a collection of impulses as shown in Figure 3(a).Hence the crosstalk creates a non-Gaussian noise, because the noise is periodic, that mapsto a wideband noise in the frequency domain, because the noise consists of impulses inthe time domain. The wideband noise completely overlaps the transmitted QAM signalwhich has a bandwidth of, for example, fkHzb=70 and is modulated by a carrier offkHzc=525. , as seen in Figure 3(b).KKK=+Periodic noise can be decoupledinto 60Hz power supply sinewave and cyclic noise pulses.60 Hz power supplysine waveNoise pulses that repeat at aperiod of 1/60 seconds.Figure 2. Decoupling of crosstalk into a 60 Hz sine component and periodic noise pulses.As a result, frequency domain filters cannot remove the wideband noise without actuallyremoving the desired QAM signal as well and frequency domain filtering becomes anineffective approach to eliminating the periodic crosstalk noise.3. Quadrature Amplitude ModulationQuadrature Amplitude Modulation avoids the spectral inefficiency of Double SidebandAmplitude Modulation by mapping a stream of bits onto a constellation and modulatingthe coordinates of the constellation with two orthogonal carriers 90o apart in phase. Thus,the transmitted signal isst x t t x t tpcqc() ()cos( ) ()sin( )=−ωωAt the receiver end, st( ) is multiplied by cos( )ωct and − sin( )ωct to recover the originaldata, the products areyt xt txt t txt t xt tpp cq ccpcqc() ()cos ()sin cos()( cos ) ()sin=− =+−212 22ωωωωωyt xt t t xt txt t xt tqpccq cpcq c() ()cos sin ()sin()sin ()( cos )=− + =+−ωω ωωω22122One noise cycle has aduration of 16.7milliseconds(a)(b)ffcffcb+2ffcb−2WidebandNoiseQAM SignalFigure 3. (a) Each 60 Hz noise cycle consists of a group of sampled impulses. (b)QAM signal with overlapping wideband noise.The sidebands of the second harmonics of the carriers are then removed by low-passfiltering, and the receiver baseband signals ytp( ) and ytq( ) are then within a factor 2 tothe originals [Campbell 96, pp. 26-53].Figure 4 illustrates a QAM receiver. It is clear that intense computation is needed tomultiply st( ) with the carriers and to lowpass filter the resulting signals ytp( ) and ytq().To reduce unnecessary computation, Schlumberger developed and patented a techniquethat eliminates the need for signal reconstruction.4. Existing Noise Cancellation TechniquesEarly research has been done inthe noise cancellation area.The most famous work isperhaps the Least Mean SquareAlgorithm, illustrated in Figure5, introduced by Widrow andHoff [Widrow 75] in the mid70s. However, the LMSalgorithm presented by Widrowwas aimed at removing singletone interference and notcos( )ωctLowpassFilterADCX− sin( )ωctLowpassFilterADCSLICEROutputbitstreamXst()ytp()ytq()Figure 4. QAM Receiver Structure.Σwj1wj2wj3wnjΣ+-εjz−1z−1z−1xjxj−1xj−2z−1ww xjj jj+=+12µεyjdjFigure 5. Widrow-Hoff LMS Algorithm.periodic wideband noise.5. Active Noise CancellationThe idea of noise cancellation is to collect an estimation of the periodic wideband noiseduring receiver training. The collected noise estimate is then subtracted from thereceived QAM signal during steady state data transmission. Figure 6 is a blockrepresentation of the receiver operation during training.A/DHigh PassFilterBand PassFilterBufferReceivedSignalZeroCrossing?Power Supply+-Σsn[]Figure 6. Block diagram of receiver operation during training.The structure to the right of the dash line is responsible for noise extraction. Thetransmitted signal is known during receiver training, for example, the signal can be a 52.5kHz tone. It is clear that with the transmitted signal known a priori, noise estimate can becomputed asNoise Estimate s n Actualreceived signal Training signal≡= −[] .Furthermore, the training signal can be extracted at the receiver using a narrow bandnotch filter centered at the carrier frequency 52.5 kHz. The notch filter is implementedusing a second-order IIR biquad with the following transfer function.YzSzkzkz kz()()()=−−−−−−01112211Equation 1. Notch filter transfer function.The filter structure is illustrated in Figure 7. The coefficients k0,