Question on the BPF synthesis

I want to realize a bandpass filter in the cross coupling structure as shown in the figure.
I wonder whether the configuration of a practical bandpass filter had effect on the selection for the lowpass filter prototype(inculding the order-n of thelowpass prototype ).
Anyone who has the information about bpf synthesis procedure in details?
Thanks in advance!

The procedure for designing microwave filter including the following steps:

(1) Reponse synthesis: You should get the transmission zeros and reflection zeros by the reponse synthesis according to the specifications of the filters;

(2) Circuit synthesis: for cross-coupled filter, you can get the coupling matrix for the bandpass prototype circuit according to the transmission zeros and reflection zeros which have been obtained in step (1).

(3)Realization: you can get the design parameters by denormalizing the coupling matrix. According to the design parameters you can get the dimensions of the filter structure.