We investigate the prospects for observing a specific spectral distortion of the cosmic microwave background, which occurs due to the anisotropy of the radiation when it is scattered by hot plasma of galaxy clusters. Detection of this anisotropic Sunyaev-Zel’dovich effect would enable an independent measurement of the CMB anisotropy multipoles with $\ell =1$, 2, 3, allow the Sachs-Wolfe and integrated Sachs-Wolfe (Rees-Sciama) effects to be separated, and partially solve the cosmic variance problem for low multipoles. We applied the Least Response Method for component separation in the data processing and estimated the required sensitivity of the experiment for such observations. We test our approach on a simulated signal that is contaminated by various foregrounds with poorly defined spectral shapes, along with distortions of the relic blackbody spectrum caused by the Sunyaev-Zel’dovich effect and its relativistic corrections.

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• Cosmic microwave background
• Cosmology