This article proposes a statistical shmoo for a Decision Feedback Equalizer (DFE). A statistical shmoo shows a Bit-Error Rate (BER) distribution of a system depending on conditions such as a threshold voltage and sampling time. The previous statistical eye diagram can be converted to a statistical shmoo except for the case of a DFE. In the shmoo, rows and columns represent different threshold voltages and sampling times, respectively. Thus, the DFE operation also depends on each row and column. Furthermore, a DFE may have error propagations because of substantial noise. Therefore, this article proposes a statistical shmoo for an ideal and a nonideal DFE. The ideal DFE always makes a correct bit decision, whereas the nonideal DFE may make a wrong bit decision depending on the received waveform. For verification, the obtained statistical shmoo is compared to the transient simulation with their BER values. The lowest BER value achieved by the proposed method is 1E-51 with a calculation time of 862 seconds. While the transient simulation achieved the BER of 8.26E-8 with a simulation time of 2,000,000 seconds. In conclusion, the proposed method provides an accurate statistical shmoo in efficient manner.


Electrical and Computer Engineering


National Science Foundation, Grant IIP-1916535

Keywords and Phrases

Bit-error rate (BER); decision feedback equalizer (DFE); eye diagram; shmoo; signal integrity (SI); statistical shmoo

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version

Final Version

File Type





© 2023 The Authors, All rights reserved.

Publication Date

01 Jan 2023