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Recently, sequential Monte Carlo methods have been used in the telecommunications field, finding application in receiver design. Several properties of these receivers make their designs very attractive. These receivers do not require channel state information or training. Therefore, they are bandwidth efficient and no communication bandwidth needs to be wasted on training. The receivers are optimal in the sense that they achieve a minimum symbol error rate regardless of the noise distribution, nonlinearities in the system, or distribution of the transmitted symbol. Moreover, these receivers are capable of producing soft-information outputs, which enables the designer to utilize iterative receiver architectures for near-optimal performance. In this work we investigate the convergence properties of these algorithms when utilized in various types of receivers. We quantify the convergence rate. We describe how various parameters (e.g., noise power, channel fading rate, etc) and factors (e.g., state-space model mismatch) affect the convergence rate and point out the factors that should be improved first to gain speed and accuracy in the convergence.