This paper presents a theoretical analysis of the performance of a filter bank-based multicarrier spread spectrum (FB-MC-SS) system. In FB-MC-SS, each data symbol is spread across multiple subcarriers, but — contrary to some other systems — there is no spreading in time. The results of this system are then compared with those of the well-known direct sequence spread spectrum (DS-SS) system with a rake receiver for its best performance. We compare the two systems when the channel noise is white. We prove that as the processing gains of the two systems tend to infinity both systems approach the same performance. However, numerical simulations show that in practice, where processing gain is limited, FB-MC-SS outperforms DS-SS.