Singal Radiation Problem

As we all know, a signal with very fast rise time travel along a path and radiate to other traces or surfaces. The characteristic impedance of a wire in space is generally known to be on the order of 370 Ohms, which means the impedance along another unintended path could be in this range.

I have a little confusion that why it does mean the impedance along another unintended path could be in this range. as we know that such a big impedance never happen in the PCB plane .

If I understand what you maind... I try to answer.
Where a propagation exist, free space, guided, cabled, ionic etc. etc. , since there is a power transoport, applying the Ohm law, you may think in term of Impedance. For an infinitely long path, inside an isotropic media, the impedence "seen" by the wave in the propagation direction is called Caractiristic Impedence (Zo).
Of course, Zo is a caracteristic of the media, but also of the "mode" of transmission.
On the PCB, usulally we tend to consider the principal mode of transmission, TEM (or quasi TEM for ustrip).
For ustrip, a very little amount of power is radiated, of course along the radiation direction a Zo exist! (but it's very high).
Also a ustrip may be seen as a "waveguide" filled by dielectric. Very often such "waveguide" working under it's cutoff, but a very little power walk in a "guided" mode (evanescent mode), also in this case, because a (little) amount of power is flowing, you may think in terrm of Zo.

Zo may be real or complex. For evanescent mode it's complex.

Another case of propagation on unwanted direction, is the case of the "shielding effectiveness" of the coaxial cables.
It's know that at low freq. (e.g. KHz or less) the coaxial cables shield is not effective, this is due to the fact that the penetration thickness is bigger than the shield thickness. The cable radiate, so propagate in an unwanted direction. Someones call this last Zo "transimpedence". :) Fortunately the radiation at so low freq is limitated by the fact tha often cables are mauch shorter than Lambda/4