Spherical microphone arrays have been recently used for room acoustics analysis, to detect the direction-of-arrival of early room reflections, and compute directional room impulse responses and other spatial room acoustics parameters. Previous works presented methods for room acoustics analysis using spherical arrays that are based on beamforming, e.g., delay-and-sum, regular beamforming, and Dolph-Chebyshev beamforming. Although beamforming methods provide useful directional selectivity, optimal array processing methods can provide enhanced performance. However, these algorithms require an array cross-spectrum matrix with a full rank, while array data based on room impulse responses may not satisfy this condition due to the single frame data. This paper presents a smoothing technique for the cross-spectrum matrix in the frequency domain, designed for spherical microphone arrays, that can solve the problem of low rank when using room impulse response data, therefore facilitating the use of optimal array processing methods. Frequency smoothing is shown to be performed effectively using spherical arrays, due to the decoupling of frequency and angular components in the spherical harmonics domain. Experimental study with data measured in a real auditorium illustrates the performance of optimal array processing methods such as MUSIC and MVDR compared to beamforming.