Z(in) for small signal analysis with BJT for unbypassed emitter and r0 in place

I have been studying the small signal analysis of BJT with r_e model with the emitter terminal not bypassed. I am able to derive those Z_i, Z_o,A_v, A_i long as r_o is assumed to be infinite. But I am unable to find Z_i with a finite r_o. Following is the circuit diagram:

Below is the equivalent r_e model:

I tried with google, but have not been able to find any. Everywhere the solution is done omitting r_o.Kindly help me with the analysis or provide some helpful link. Thanks in advance.

EDIT:

let, beta=B

From my analysis, V_b=I_b[Br_e+(B+1)R_E]

So, Z_b=V_b/I_b= [Br_e+(B+1)R_E]

Z_i=R_B||Zb

But the expression for Z_b given in the book by Boylestad and Nashelsky is

Z_b=Br_e+[{(B+1)+R_C/r_o}/{1+(R_C+R_E)/r_o}]R_E

which I am not able to understand. Please explain it.