Application of MDS matrices in serial and round-based implementations We know that MDS matrices are used in the diffusion layers of block ciphers. 

My question: what types of MDS matrices can be applied to serial or
round-based implementations or both of them?

I appreciate you to address some references.
what types of MDS matrices can be applied to serial or round-based
  implementations or both of them?


Serial matrices utilise a trade-off to reduce hardware requirement while incurring additional time cost. Examples of MDS matrices that can be serialized implemented are : cyclic , Hadmard, linear feedback serial (LFS), sparse diagonal serial invertible (DSI), ref. LED, PHOTON, PRIMATES use efficient serialized MDS matrices, ref.

It is possible to transform serial MDS to round-based , as following stated in ref. 


  One may also consider unrolling DSI/LFS matrices to simulate round-
  based matrices for comparison with cyclic/Hadamard matrices in a
  round-based implementation scenario. That is to implement k copies of
  DSI/LFS matrices in series to achieve the MDS property in one clock
  cycle. The XOR count of all the matrices would simply be k times of
  what the tables have shown


MDS matrix is defined over $F_{2^n}$ and the choice of basis is important on implementation efficiency. for round-based hardware implementation, the choice of basis is important in lightweight construction. ref  

I sugest to read the following papers to obtain deep knowledge:


Lightweight MDS Serial-type Matrices with Minimal Fixed XOR Count
Shorter Linear Straight-Line Programs for MDS Matrices Yet another XOR Count  Paper
Lightweight Multiplication in GF(2n) with Applications to MDS Matrices