This paper presents a new iterative multiuser detection algorithm for asynchronous spectrally-efficient M-ary continuous-phase modulation in additive white Gaussian noise. This detection algorithm is closely related to another algorithm that was recently proposed by the same authors, but it follows from applying the sum-product algorithm to a different factor graph of the same multiuser detection problem. This, in turn, results in a different way to approximate the marginal bit a-posteriori probabilities that are used to perform minimum bit error rate multiuser detection. The girth of the factor graph considered in this contribution is twice as large, which is known to be potentially beneficial for the accuracy of the a-posteriori probabilities. The size of the largest factor graph variable alphabets also multiplies with M, rendering the straightforward application of the sum-product algorithm more complex. Through approximating a suitable set of sum-product messages by a Gaussian distribution, this complexity is significantly reduced. For a set of system parameters yielding high spectral efficiency, the resulting algorithm significantly outperforms the previously proposed solution
