Abstract:
A method, and associated storage medium containing software and a system, comprises extracting a time domain impulse response from parameters that characterize a communication channel, generating a probability distribution function (PDF) of an output voltage based on the impulse response; and computing a relationship between bit error rate and voltage margin based on the final probability distribution function. Generating the PDF of the output voltage may comprise one or more of the following acts: quantizing the impulse response into a plurality of quantized levels, assigning taps to the quantized levels and determining a number of taps assigned to each quantized level, determining allowable voltage levels for each quantized level, and determining a probability of occurrence of each allowable voltage level, determining a PDF for each voltage level; and convolving all of the PDFs for the various voltage levels to obtain the PDF of the output voltage.

Description:
BACKGROUND OF THE INVENTION  
       [0001]     1. Technical Field  
         [0002]     The present subject matter relates in general to a methodology for designing high speed receivers. More particularly, the present subject matter relates to verifying the bit-error rate of a receiver design at various stages of the design process.  
         [0003]     2. Background Information  
         [0004]     A high speed serial data link is generally required to meet a customer-specified bit-error-rate (“BER”). Usually, the BER of a receiver is tested and verified after the receiver has been designed and constructed. Having to re-work the design if the BER proves to be inadequate can be timely and costly. No direct method is known to exist to verify the BER of a receiver design at various stages of the design process.  
       BRIEF SUMMARY  
       [0005]     In accordance with a preferred embodiment, a method, and associated storage medium containing software and a system, comprises extracting a time domain impulse response from parameters that characterize a communication channel, generating a probability distribution function (PDF) of an output voltage based on the impulse response; and computing a relationship between bit error rate and voltage margin based on the final probability distribution function. Generating the PDF of the output voltage may comprise one or more of the following acts: quantizing the impulse response into a plurality of quantized levels, assigning taps to the quantized levels and determining a number of taps assigned to each quantized level, determining allowable voltage levels for each quantized level, and determining a probability of occurrence of each allowable voltage level, determining a PDF for each voltage level; and convolving all of the PDFs for the various voltage levels to obtain the PDF of the output voltage. In some emobiments, the PDF is used to estimate the bit error rate of a receiver during the design process.  
       NOTATION AND NOMENCLATURE  
       [0006]     Certain terms are used throughout the following description and claims to refer to particular system components. As one skilled in the art will appreciate, various companies may refer to a component by different names. This document does not intend to distinguish between components that differ in name but not function. In the following discussion and in the claims, the terms “including” and “comprising” are used in an open-ended fashion, and thus should be interpreted to mean “including, but not limited to.” Also, the term “couple” or “couples” is intended to mean either an indirect or direct connection. Thus, if a first device couples to a second device, that connection may be through a direct connection, or through an indirect connection via other devices and connections. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0007]     For a more detailed description of the preferred embodiments of the present invention, reference will now be made to the accompanying drawings, wherein:  
         [0008]      FIG. 1  shows a communication system in which a transmitter sends information to a receiver over a channel;  
         [0009]      FIG. 2  shows an exemplary method of computing the relationship between bit error rate and receiver sensitivity;  
         [0010]      FIG. 3  illustrates an exemplary relationship between bit error rate and receiver sensitivity;  
         [0011]      FIG. 4  shows an exemplary communication channel impulse response;  
         [0012]      FIG. 5  shows illustrates an impulse response being quantized into a plurality of linearly spaced levels;  
         [0013]      FIG. 6  shows an exemplary histogram of the number of taps assigned to each quantized level;  
         [0014]      FIG. 7  shows the discrete voltage levels for a given tap level; and  
         [0015]      FIG. 8  shows an exemplary design process for a receiver during which the bit error rate of the design is evaluated at various stages of the design process. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0016]     The following discussion is directed to various embodiments of the invention. Although one or more of these embodiments may be preferred, the embodiments disclosed should not be interpreted, or otherwise used, as limiting the scope of the disclosure, including the claims, unless otherwise specified. In addition, one skilled in the art will understand that the following description has broad application, and the discussion of any embodiment is meant only to be exemplary of that embodiment, and not intended to intimate that the scope of the disclosure, including the claims, is limited to that embodiment.  
         [0017]      FIG. 1  shows a communication system in which a transmitter  10  sends information to a receiver  15  over a channel  12 . The transmitter  10  and receiver  15  can be any type of device and the channel  12  represents the physical medium over which the information between transmitter and receiver is transmitted. In at least some embodiments, the transmitter  10 , receiver  15 , and channel  12  are implemented in a network switch in which digital data communications are routed between ports on the switch. The channel  12  may comprise a copper backplane. In general, the channel  12  distorts the transmitted data, particularly at higher frequencies. As such, the receiver  15  preferably has sufficient voltage sensitivity so as to accurately detect data bits transmitted to the receiver from the channel within a desired bit error rate (“BER”). The desired BER is application specific generally given the goals and objectives of the operator of the communication system. The receiver preferably is designed to achieve the desired BER given the particular channel  12  interconnecting the transmitter and receiver.  
         [0018]     In accordance with the preferred embodiment of the invention, a methodology is disclosed for verifying that the receiver  15  will achieve the desired BER at various stages of the receiver&#39;s design. An assessment of the receiver&#39;s voltage sensitivity is determined at various stages of the design. In this disclosure, “sensitivity” refers to the minimum voltage increment a receiver is capable of resolving. For example, a sensitivity of 45 mv means that the receiver cannot resolve voltages in less than 45 mv increments. From the sensitivity value, the BER that the receiver will achieve for the determined sensitivity is computed. This computed BER may be higher than, lower than or equal to the desired BER and adjustments can be made to the design as necessary.  
         [0019]      FIG. 2  illustrates a preferred method for determining the relationship between BER and receiver voltage sensitivity such as that shown in the example of  FIG. 3 . In  FIG. 3 , BER is on the vertical access and sensitivity is on the vertical access. In general, as can be seen by the curve in  FIG. 3 , as the receiver&#39;s sensitivity improves (becomes a lower value), the BER also improves. For example, for a sensitivity of 45 millivolts (mv), the BER is 10 −15 . That is, for a receiver that cannot resolve voltages in less than 45 mv increments, the receiver will receive one bit in error for every 10 15  bits received.  
         [0020]     The order of the acts shown in  FIG. 2  do not necessarily need to be performed in the order shown—other orders are within the scope of this disclosure. The method begins generally at  52  in which the time domain impulse response of the channel  12  is extracted from s-parameters that characterize the channel. The s-channel characterization of the channel  12  can be measured using a network analyzer as would be well known to those of ordinary skill in the art. Alternatively, a tool such as MATLAB can be used to generate an impulse response of the channel and a finite impulse response (“FIR”) can be implemented in Verilog to model the channel. As such, an input impulse can be run through the Verilog modeled channel to compute the channel&#39;s impulse response. The time domain impulse response can be extracted in accordance with any suitable technique. An exemplary time domain impulse response is shown in  FIG. 4 .  
         [0021]     At  54 , the time domain impulse response preferably is linearly quantized.  FIG. 5  shows an example in which an impulse response is quantized into a plurality of linearly spaced levels  80 . Then, at  56  the various taps  82  of the impulse response are assigned to the various quantized levels  80 . As a result, a histogram, such as that shown in  FIG. 6 , can be constructed showing the number of taps  82  assigned to each quantized level  
         [0022]     Referring still to  FIG. 2 , once the taps have been assigned to different levels and a histogram is generated, the number of filter taps in each level are tallied (block  58 ). To determine the allowable voltage levels, all allowable bit sequences for a given level should be considered. Letting the various levels  80  be quantified as g(i) and each level g(i) having n(i) taps, where i ranges from 1 to the number of levels designated as Nf, then the allowable voltage levels are completely determined (block  60 ) by the n(i) input symbol values. As such, the lowest level is −g(i)*n(i) where all n(i) symbols take on a value of −1, while the maximum level is +g(i)*n(i) where all n(i) symbols take on a value of +1. Intermediate levels are obtained as one +1 and (n(i)−1)−1 which values leads to a voltage level −g(i)*(n(i)−2).  FIG. 7  shows the discrete voltage levels for tap level g(i).  
         [0023]     In block  62 , the method comprises determining the profitability of occurrence of each voltage level. This act can be accomplished in a variety of ways. For instance, the probability of occurrence of each voltage level can be determined by the probability of occurrence of the particular bit sequence leading to that discrete voltage level. For example, the discrete level −g(i)*(n(i)−2) is the result of one +ve symbol and (n(i)−1)−ve symbols (symbols have +1 or −1 values). The number of possible combinations having m positive symbols out of n(i) symbols is given by  m C n(i) . Hence, the probability of having m positive symbols of n(i) symbols which can take either +ve or −ve values is given by:  
               C     n   ⁡     (   i   )       m       2     n   ⁡     (   i   )                 (   1   )             
 
         [0024]     In block  64 , from the probabilities, the probability density function (“PDF”) for each level is determined. In block  66 , all of the PDFs for the various g(i) levels are convolved to obtain the final PDF of the output voltage. Finally, the relationship between BER and sensitivity can be computed from the following equation:  
               BER   ⁡     (   v   )       =         ∫     -   ∞         T     m   -   1       +   v       ⁢       P   ⁡     (     y   n     )       ⁢           ⁢     ⅆ     y   n           +       ∫       T   m     -   v     ∞     ⁢       P   ⁡     (     y   n     )       ⁢           ⁢     ⅆ     y   n                     (   2   )             
 
 The curve in  FIG. 3  represents a set of solutions to equation (2). 
 
         [0025]     In accordance with an alternative embodiment, equation (3) below is solved in place of blocks  54 - 66 .  
             Vn   =         h   0     ⁢     a   n       +       ∑     k   =   1     K     ⁢     hk   ⁡     (       a     n   -   k       -     a     n   -   k         )         +       ∑     k   =     K   +   1       N     ⁢       h   k     ⁢     a     n   -   k           +       ∑   l     ⁢       ∑   i     ⁢       g   i   l     ⁢     a     n   -   1     l                     (   3   )             
 
 where the “h” values represent the impulse response, the “a” values represent the transmitted symbols, and ahat n−k  represents the receiver&#39;s sampler decision on symbol a. The value g I  represents cross-talk from the I-th aggressor. The first term, h 0 a n , is the primary received symbol. The second term,  
           ∑     k   =   1     K     ⁢     hk   ⁡     (       a     n   -   k       -     a     n   -   k         )         ,       
 
 is the inter-symbol interference (“ISI”) with DFE correction. The third term,  
           ∑     k   =     K   =   1       N     ⁢       h   k     ⁢     a     n   -   k           ,       
 
 is the residual ISI. The fourth term,  
           ∑   l     ⁢       ∑   i     ⁢       g   i   l     ⁢     a     n   -   1     l           ,       
 
 represents the contribution to the voltage from cross talk. For general pulse amplitude modulation (“PAM”) systems, the transmission symbol can be expressed as: 
 
 a   i   l =2 m/ ( M− 1)−1,  m= 0 , . . . , M− 1  (4)
 
 and has equal probability P(a i   l )=1/M for each level. For example, in binary signaling, M=2 and 
 
 a   i   l ={−1,1},  m= 0,1
 
         [0026]     If h 0  represents the main tap of the signal path, h 0 a n  would be the ideal noise free received voltage for transmission symbol a n . For each transmitting level, the corresponding received signal levels are V m =h o ·{2m/(M−1)−1}, and the decision threshold between the m-th and (m+1)-th levels are T m =h o ·{(2m+1)/(M−1)−1}, m−0 . . . M−2. Once the signal channel and cross talk channel are known, the probability P(V n ) for received signal amplitude V n  can be computed, and the probability for effective eye open (i.e., signal amplitude above the decision threshold) |T n −V n | can also be derived.  
         [0027]     Because there are N filter taps and M possible symbol values, there a total of MAN possible discrete outputs. Further, assuming that the input symbols have equal probability, each of these values occurs with a probability of 1/M{circumflex over ( )}N.  
         [0028]     Once the relationship between BER and sensitivity is determined, that relationship is used at various stages of the design process to re-assess the margin of the design.  FIG. 8  shows an exemplary design process for a receiver. At  102 , the communication channel  12  is modeled as described above. That model is used to compute the relationship between BER and sensitivity as described previously. The receiver design may undergo the four phases  104 ,  108 ,  112 , and  116  as shown in  FIG. 8 , although in other embodiments, additional or different phases can be included. In phase  104 , the receiver architecture is defined. Any suitable tool or mechanism for performing this act is acceptable such as by the use of MATLAB. In phase  108 , the receiver architecture is translated into a behavioral description. Any suitable tool or mechanism for performing this act is acceptable such as by the use of VERILOG. In phase  112 , the receiver design is then translated into mixed digital and analog portions. In phase  116 , a transistor level description is specified for the design and the design is considered complete at  120 .  
         [0029]     For any or all of the design phases shown, an assessment preferably is made as to whether the receiver has sufficient sensitivity margin given a specified BER and channel  12 . As such, for each phase, the expected sensitivity of the receiver is determined. The sensitivity determination can be made in accordance with a variety of techniques and is generally specific to the particular design phase at issue. For example, how the sensitivity is determined for phase  104  may differ from the determination for phases  108 ,  112 , and  116 . Additional detail regarding sensitivity determinations for each phase will be provided below. Regardless of how the sensitivity is determined, the sensitivity value is used in the BER-sensitivity relationship. As mentioned above, if at a particular phase of receiver&#39;s design, the receiver is to have a sensitivity of 45 mv, then, referring to  FIG. 3 , such a receiver would be determined to have a BER of 10 −15 .  
         [0030]     If the BER determined for a particular phase of a receiver&#39;s design complies with the target BER, then the design process continues to the next phase. However, if the BER at a particular phase of the design does not comply with the target BER (i.e., the error rate is higher than what is desired for the receiver), then the architecture of the receiver can be refined at, for example, phase  104 . A failure of the BER to achieve the specified goal for phases  112  and  116  may result in a return to phase  104  or any other prior phase. For example, if the assessment of margin at  118  results in a determination that the BER is insufficient, then the receiver&#39;s design can be refined by returning to any of phases  104 ,  108 , and  112  as is desired by the system designer.  
         [0031]     At phase  104 , sensitivity preferably is determined by estimating the sensitivity based on knowledge of receiver architecture. At phases  108 ,  112 , and  116 , sensitivity preferably is determined via Monte Carlo simulations. For transistor level verification, a Nanosim-Integration-VCS (“NIV”) simulator, or comparable system, can be used to run mixed analog (transistor) and digital (Verilog) simulations. In such a simulation a behavioral analog-to-digital converter (“ADC”) and a functional digital-to-analog converter (“DAC”) can be created to move analog signals across the interface as digital signals with the required precision because the Synopsys NIV flow does not allow analog signals to pass across the Verilog to transistor netlist interface.  
         [0032]     While the preferred embodiments of the present invention have been shown and described, modifications thereof can be made by one skilled in the art without departing from the spirit and teachings of the invention. For example, any one or more of the preceding sense amplifier improvements can be combined together as desired. The embodiments described herein are exemplary only, and are not intended to be limiting. Accordingly, the scope of protection is not limited by the description set out above.