基于FPGA的信号发生器 翻译.doc

Reconfigurable Readback-Signal Generator Based ona Field-Programmable Gate ArrayJinghuan Chen, Jaekyun Moon, and Kia Bazargan, Member, IEEEAbstractWe have designed a readback-signal generator to provide noise-corrupted signals to a read channel simulator. It is implemented in a Xilinx Virtex-E field-programmable gate array (FPGA) device. The generator simulates in hardware the noise processes and distortions observed in hard drives. It uses embedded nonuniform random number generators to simulate the random characteristics of various disturbances in the read/writeprocess. The signal generator can simulate readback pulses, intersymbol interference, transition noise, electronics noise, head and media nonlinearity, intertrack interference, and write timing error according to the characteristics specified by the user. A sample implementation operates at a 70-MHz clock speed. The design can easily be scaled for different error rates. The generator can be reconfigured in real time to give the user flexibility and increase the capacity of the FPGA device. The readback-signal generator can be integrated into an FPGA read channel simulatoror serve as a test bench for data-recovery circuits. Index TermsField programmable gate array (FPGA), Gaussian pseudorandom number generator, magnetic recording, read channel, read channel modeling, reconfigurable computing, transition noise.I. INTRODUCTIONINTENSIVE simulation is often carried out to investigate advancedsignal processing techniques for data storage applications.The simulation is normally performed in software thatmay take a very long time. For instance, the simulation of a10 bit-error rate (BER), assuming 10 bit errors are observed,can take days running on a personal computer equipped witha 1-GHz Pentium IV processor. On the other hand, the targetsector retry rates i.e., unrecoverable error rates after error-correction-code (ECC) in commercial hard drives normally gobelow 10 for desktop products and 10 for server-classproducts. One approach to speed up the simulation process is toimplement the whole simulator or part of it in hardware. Becausethe noise characteristics in hard drives are unique, theadditive white Gaussian noise (AWGN) assumption, which iswidely accepted in studying the performance of many communicationsystems, is not reliable. Instead, a dedicated readbacksignalgenerator must be implemented in front of data-recoverymodules in the simulator. This signal generator shall incorporateall major noise processes and distortions and be capable ofManuscript received December 8, 2003; revised February 10, 2004.J. Chen was with the Department of Electrical and Computer Engineering,University of Minnesota, Minneapolis, MN 55455 USA. He is now withMaxtor Corporation, Shrewsbury, MA 01545 USA (e-mail: jinghuan_).J. Moon and K. Bazargan are with the Department of Electrical and ComputerEngineering, University of Minnesota, Minneapolis, MN 55455 USA (e-mail:; ).Digital Object Identifier 10.1109/TMAG.2004.826913generating very low probability events according to the user-definedstatistics. It shall also have the reconfiguration capabilitythat allows the user to choose from various noise and distortioncombinations. Field-programmable gate array (FPGA) becomesthe choice of implementation platform because of its advantageof low-cost and reconfigurability. The FPGA-based signal generatorproposed in this paper can also serve as a test bench fordata-recovery circuits (usually called the “read channel”) sinceit is completely tunable in contrast to typical test spindle setupsand is able to provide a complete set of test conditions.A series of noise processes and distortions in hard drivesdegrades the performance of read channels. Statistical modelsof these noise processes, definition of signal-to-noise ratio(SNR), and analysis of quantization effect are provided in SectionII. In Section III, the design and performance of embeddedrandom number generators are explained. These generatorsproduce random numbers according to the statistics specifiedby the user. In Section IV, we present the architecture of thedesign and briefly discuss time-duplexing and JBits-aidedreconfiguration. In Section V, we demonstrate the noise andnonlinearity statistics in the generated signal. Conclusions aregiven in Section VI.II. MODELS AND ALGORITHMSIn hard drives, each binary datum is stored in a very smallarea, called a bit cell, on the magnetic surface of a disk. Awrite head magnetizes each bit cell to one of two directionsthat represent 0 or 1. A read head picks up the magnetizationflux emitted from the boundaries of bit cells and generates readbackpulses. These pulses will be passed through a preamplifier,analog/digital filters, and data-recovery modules and convertedback to binary data.The noisy environment in hard drives is unique and harsh.These noise processes and distortions can be categorized intointersymbol interference, transition noise, electronics noise,head/media nonlinearity, timing error, and intertrack interference.Noise processes in hard-drive recording systems havebeen modeled in several ways. Moon 1 uses Taylor seriesto approximate transition jitter and width variation. Caroselliand Wolf 2 simplify the structure of recorded tracks by usinga micro-track model. In our implementation, we mimic thephysical reality by actually shifting the pulse position andchanging the pulse shape in runtime. The behavior of thevarious noise processes and distortions follows the statisticslaid down by the user. It should be noted that the statistics aredefined by the user and do not have to be Gaussian, as has beenassumed in many previous modeling works.0018-9464/04$20.00 2004 IEEECHEN et al.: RECONFIGURABLE READBACK-SIGNAL GENERATOR 1745A. Statistical Modeling of Noises and Distortions1) Intersymbol Interference (ISI): Since the read heads areband-limited sensors, readback signals will experience ISI whenthe recording symbol rate exceeds the head bandwidth. A sequence of readback pulses overlap and are distortedwhen ISI extends over a number of symbols. The noiselessreadback signal is given by(1)(2)where is the isolated pulse and is the difference of twoconsecutive data bit (2). The sequence takesvalue in and a nonzero indicates the existence ofa transition. ISI happens when the length of pulse islonger than the symbol period .2) Transition and Electronics Noise: The zigzag boundarybetween two opposing magnetizations causes the position of areadback pulse to shift in time (transition jitter) and its shapeto deform (width variation) 3. The noise introduced by thissort of phenomenon is called transition noise (TN) and is datadependent in the sense that noise arises only in the presence oftransitions that make up a data pattern. Both of these noise processescan be modeled using random variables. We rewrite (1)to reflect the transition noise. Now the isolated pulse is notdeterministic but a random process where the sample space is aseries of pulses that have different pulse width and amplitude.We note that a wider pulse has reduced amplitude so as to makethe area under the pulse remains constant. This is necessary ifthe pulse widening is due to the broadening of the magnetic transition.Position jitter is a random variable falling in the rangeof , where we assume is the limit of jitter on eachside.Electronics noise normally is modeled as an additivewhite Gaussian noise (AWGN) band-limited by W. Its powerspectral density is . Now the noise-corrupted read signalis written as(3)3) Head and Media Nonlinearities: Magnetoresistance(MR) read heads are not linear sensors. When incorrectlybiased, they can cause an unsymmetrical head sensitivityfunction 4. This effect is called the head nonlinearity (HNL).It amplifies the readback signal in a nonlinear fashion acrossthe range of amplitude and results in disparity between positiveand negative pulses. It can be characterized by a nonlinearfunction , which can be measured from a read head.Two more types of media nonlinearity also occur during thewrite process: nonlinear transition shift (NLTS) and partialerasure (PE). They generally create additional transitionposition shift and amplitude loss. Simplistic assumptions havebeen made on the data dependence in 5 and 6. We consideronly the first-order PE effect and combine them as follows:(4)Fig. 1. Generation of write timing error.where is the PE parameter and is the amount of nonlineartransition shift. The NLTS component reduces to zero effectivelyunless two consecutive transitions occur, i.e., .4) Write Timing Error: A slowly varying write timing error(WERR) is added to model accumulated phase jitter in the writeclocksynthesizer circuit. It can be simplified and modeled as aslow-paced “random walk.” As shown in Fig. 1, one write erroris uniformly generated from in every clock cycles.The effect is integrated so it will influence the write positionof all later pulses. The average of the drift is zero in a verylong run and the pace is controlled by .5) Intertrack Interference: A read head does not always positionitself with 100% accuracy on the top of a track. It consequentlysenses the signal from the neighboring track and is subjectto the crosstalk, which is also called intertrack interference(ITI). ITI is brought into the picture by adding up two weightedoutput signals from two independent generators.B. SNR and Statistics of Noise ProcessesThe performance of data-recovery schemes is usually comparedacross a range of SNR. A relationship between SNR andstatistics of generated random noise shall be established so thatthe effectiveness of signal processing effort can be evaluated.We adopt the SNR definition in 7 because it includes datadependenttransition noise while eliminating the dependency onsymbol density. We briefly rephrase the derivation as follows:SNR(5)where is the energy of an isolated pulse given as(6)is twice the average energy of the transition noise in eachtransition, is the power spectral density of the electronicsnoise, and is the percentage of transition noise in totalnoise% (7)Assuming the position jitter and width variation are uncorrelated,we can decompose as(8)where and are the power of position jitter and widthvariation, respectively. When the probability density function(PDF) or cumulative distribution function (CDF) of position1746 IEEE TRANSACTIONS ON MAGNETICS, VOL. 40, NO. 3, MAY 2004jitter and width variation are predefined, can be easily calculatedand, hence, the SNR is known.The statistics of simulated noise processes can be determinedin two ways. The user can provide the CDFs of the noise processesand the corresponding SNR can be calculated. Or, whenthe observed noise can be satisfactorily approximated as theGaussian distribution, in which the first- and second-order statisticscan provide all the necessary information about the noiseprocess, the user of the signal generator will only need to specifythe SNR. Now the SNR becomes an input that effectively definesthe variance of the noise. Additionally, the user shall definethe undistorted isolated pulse , the percentage of the transitionnoise power, and composition of the position jitter andthe pulse variation.We will focus on the second approach in thefollowing paragraphs since it is widely used in the modeling ofreadback signals.As given in 7, when we assume first-order transition noise,we have(9)where and are the variances of transition position jitterand width variation, respectively. and are integrals definedas follows:(10)(11)The quantity of two components in is controlled by aparameter that specifies the jitter noise power expressed as afunction of the total medium noise power(12)From (5)(12), we can obtain the variance of the noise processesas(13)(14)(15)All random variables we have modeled till now are continuous-time. In the FPGA signal generator, which is a digitaldevice, each random variable will be represented by a finitenumber of bits. Loss associated with this quantizationprocess will be discussed in the next section. If we representeach symbol period with discrete numbers and whenand can be approximated to(16)(17)(18)where and are the first (undistorted) and second pulsesin the distorted pulse lookup table, respectively, is the unitshift of the pulse, and is the unit change of pulse widthbetween two pulses in the table.We can design the pulse lookuptable so that , where . Then,(18) becomes(19)By substituting and in (13) and (14), we may write(20)(21)Since the electronics noise is bandlimited by , (15)becomes(22)Now we have established the relationship between SNR andthe statistics of noise processes. Zero-mean Gaussian randomvariables can then be generated in units of with above standarddeviations following the method to be given in the nextsection.III. PSEUDORANDOM NOISE GENERATORTransition noise, electronics noise, and write timing errorsare randomly generated as nonuniform numbers. The embeddedpseudorandom number generators must be uncorrelated andbear good randomness. In our design, uniform pseudorandomnumbers are first produced and then transformed to nonuniformrandom numbers. One effective and popular uniform pseudorandomnoise generator (PRNG) is the linear feedback shiftregister (LFSR) 8. Its output is a maximum-length sequence( -sequence) with a period of , where is the numberof storage units (registers). However, if many sequences ofrandom noise are in demand, the area consumed by LFSRwill be large, a situation that cannot be afforded in an FPGAimplementation. For example, with five 6-bit wide PRNGsthat can generate random numbers with a period longer than, the number of registers will be 300. Facing areaconstraints in this design, we adopted an alternative method,linear hybrid cellular automaton (LHCA) (for example, see 9and 10). The principle of a cellular automaton is that the nextvalue of each register is calculated by a Boolean function fromthe current values of immediate neighbors and itself. A cellularautomaton is said to have a null boundary condition when theleft- and right-most registers in the array connect to zeros. Anull boundary is preferred to a feedback boundary becauseit avoids long feedback paths, and therefore reduces routingCHEN et al.: RECONFIGURABLE READBACK-SIGNAL GENERATOR 1747Fig. 2. Generation of nonuniform pseudorandom numbers.Fig. 3. Splitting PDF into 2 columns.delay. It has been shown that when the Boolean functions arecarefully selected and after the LHCA evolves for a numberof initialization clock cycles, such a register array will outputan -sequence that has the same period as that of an LFSR9. The Boolean functions are called computation rules andcategorized by Wolfram 13. One of the setups that cangenerate -sequences is a careful mix (hybrid) of two Booleanfunctions, Rule 90 and Rule 150, in the calculation of registercontents 9. Rule 90 and Rule 150 are defined as follows:Rule (23)andRule (24)where is the content of register at time . How to determinethe positions of Rule 90 and Rule 150 in a register arraycan be found in 11 and 12.One can easily see that the output from one register in thearray is correlated to that of its immediate neighbor. In order toeliminate the correlation, only one bit of every bits can beused to form a random number where is called the site spacingparameter 9. To compare with LFSR, if , the number ofregisters in a LHCA PRNG that can generate the same group ofrandom numbers as mentioned above will be 60, a factor of 5reduction in the number of registers.Transformation from a uniform to a nonuniform pseudorandomnumber is illustrated in Fig. 2. An -bit uniformrandom number is compared with numbers in a precalculatedCDF conversion table and then encoded to an -bit nonuniformrandom number. This exercise is equivalent to randomlypicking points in the area under the corresponding PDF,grouping all points in a column, and substituting them with theone number (Fig. 3). Attention shall be paid to the choiceof and since they determine the accuracy and precision ofthe PRNG. The width of a uniform random number limitsthe smallest probability we can simulate, which is .Encoding from an -bit to an -bit random number effectivelyquantizes a continuous random variable to an -bit discreterandom variable , when . The width controls themean square loss associated with the quantization process.Max 14 showed that the optimal quantizer is nonuniformwhen the PDF of the random variable is not uniform. However,the digital nature of the FPGA device determines the quantizationlevels to be uniform where is thenumber of levels, which is . We need to compute the boundariesfor the suboptimal quantizer interm of minimizing the quantization loss. The quantization lossis given in (25) and is the PDF of(25)In order to minimize the quantization loss, let(26)It can be easily found that(27)Therefore, the suboptimal quantizer is a uniform quantizer. Ifwe assume zero-mean Gaussian noise, we can get the close-formexpression for(28)where(29)and is the well-known tail-integral of the unit varianceGaussian PDF.Since quantization noise can be seen as an additional perturbationto the random variable, we can define a signal to quantizationnoise ratio (SQNR) to evaluate the loss due to quantizationas follows:(30)(31)is the varia