We consider unsourced random access with MIMO receiver - a crucial communication scenario for future 5G/6G wireless networks. We perform a projection-based decoder analysis and derive energy efficiency achievability bounds when channel state information is unknown at transmitters and the receiver (no-CSI scenario). The comparison to the maximum-likelihood (ML) achievability bounds by Gao et al. (2023) is performed. We show that there is a region where the new bound outperforms the ML bound. The latter fact should not surprise the reader as both decoding criteria are suboptimal when considering per-user probability of error (PUPE). Moreover, transition to projection decoding allows for significant dimensionality reduction, which greatly reduces the computation time.