Recently, non-orthogonal codes have been advocated for IoT massive access. Activity detection has been demonstrated to entail common support recovery in a jointly sparse multiple measurement vector (MMV) problem and MMV algorithms have been successfully applied offering various degrees of complexity-performance trade-off. Targeting the small measurement per antenna but large number of antennas setup, independent sensing matrices do offer significant performance advantages. Unfortunately, the IoT random access problem can not readily benefit from this concept as code matrix is fixed over all receiving antennas. Our contributions towards addressing this challenge are as follows. First, independent small-scale fading across antennas and users is established as a possible source of sensing matrix decorrelation. Secondly, two novel algorithms are proposed which exploit this partial de-correlation and collect sensing matrix diversity. Enjoying a low-complexity, these methods do offer great practical advantages as they target small measurement size, which is indeed severely constrained due to limited coherence time/bandwidth, but instead compensate for it by using a large array of antennas. Thirdly, probability of failure (PoF) for these methods are rigorously derived and corresponding measurement inequalities are presented. Fourthly, extensive simulations are conducted to confirm the superior performance of these methods versus state of the art.