The paper is generally well-written and provides useful illustrations. It is novel and I believe technically correct. It provides an important result for a small field. Comments: It's worth noting that computationally efficient methods to measure TMs have been developed [A]. [A] Sharma, Manoj, et al. "Inverse Scattering via Transmission Matrices: Broadband Illumination and Fast Phase Retrieval Algorithms." IEEE Transactions on Computational Imaging (2019). I had not seen the use of a definition on the rhs of an equation before, as is done in (4). This made the text a little difficult to parse. Typos: Line 80: "Experimantly" Line 277: "ore"

Originality: The problem formulation is interesting. The main part of the algorithm relies on the well-known multidimensional scaling (MDS) and procrustes methods. Quality: The quality of work presented in this paper seems good and the authors tried to explain the problem clearly. Adding some more details on the experiments would be helpful. Clarity: The paper is well written. Significance: Phase retrieval problem itself is considered an interesting and challenging research problem that arises in many applications. The case where the random operator is also unknown makes it a more challenging problem, but I am not aware of many scenarios where such a problem arises. The authors motivated the problem with OPU setup, but the results presented in the paper are on a very small scale and not very convincing about potential advantages of the proposed framework. In short, I like the problem on the algorithmic level, but I am doubtful about the practical significance.

The paper is written in a confusing way that the setup is not explained clearly. There is no clear reason to me why there need to be multiple signals -- since the measurements are taken on all difference of pairs x_q-x_r. The setting of multiple signals also seems to have nothing to do with the described MDS algorithm. [The author responded that one cannot determine the global phase with one signal -- that is true, but the authors have auxiliary vectors r_1,...,r_K and why do they need s \xi vectors?] The organization is not good, either. Assumptions such as “DMD is binary” seems to be popped up all of a sudden from nowhere. The paper also cited some other algorithm without explaining what the problems other algorithms solve. It would be more readable if the authors can reorganize the paper and explain more clearly in the motivation part/problem setup what the constraints are due to hardware limitations. The authors further mention that they use the algorithms developed in this paper to implement the RSVD algorithm in [8]. I think they can be more specific here. What the authors actually implement is to compute A = BG for some given matrix B and a Gaussian random matrix A. [The authors seems to suggest in their response that it is a harder problem to do the matrix-vector multiplication simulation simultaneously for multiple signals, but why is it so? Is it due to hardware constraints?] It seems that the point is to use an optical system to simulate the computation of A = BG via some decoding algorithm. What is the advantage of this? [The authors responded that an optimal system is much faster than both CPU and GPU. Perhaps that should be made more explicit in the paper. Neither the introduction nor the experiment mentions speed comparison.]