cβ
E
ω
φ
о
со
S
>
Measurement noise %
Figure 6.2: Variations estimation error vs. percent of the power measurement noise.
This decay suggests that it is not possible to find variation of all gates indepen-
dently because there is no information about the null space of the measurement
matrix, JV(A) = {y ∈ RA∣Ay = 0}. Thus, we can only estimate the variation in
a subspace S that does not contain JV(A).
6.2.2 Tomography results in the power framework
To study the performance of the proposed tomography method, we have simulated
the process variation on a number of MCNC benchmarks. A total of 12% variation
is assumed in the simulations. Based on the data in [16] and [76], 20% of the
total variation is inter-die variation, 60% is spatial correlated intra-die variation,
and 20% is random uncorrelated variation. To model the leakage current (static
69
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