Generalized Multistream Spatial Modulation With Signal Constellations Based on Hurwitz Integers and Low-Complexity Detection

A Variational Inference-Based Detection Method for Repetition Coded Generalized Spatial Modulation

“…8, we can also confirm that due to the exhaustive search for the ML detection in (13), in general, the complexity of the ML detection is much higher than that of the CAVI algorithm (except that K is sufficiently small, i.e., K ≤ 2 as mentioned earlier). Thus, the CAVI algorithm can be seen as a low-complexity approach to the ML detection in (13) and [25], [26] with negligible performance degradation (as shown in Figs. 4 and 5).…”

“…l+1 (x l+1 ) −1 as shown in (25), there is no significant additional computational complexity to update the term ln det(R In summary, the computational complexity of the CAVI algorithm is independent of the number of active transmit antennas, K, while it grows linearly with the number of transmit antennas, L, and quadratically with the number of receive antennas, N . Note that the complexity of the ML approach in (13) or the approach in [25], [26]…”

“…. Although the complexity for a given x can be an order of O(K 3 ) as shown [26], the overall complexity is O(K 3 L K ) for K L. Thus, if K ≥ 3, the complexity of the ML approach in [25], [26] or that in (13) is much higher than that of the CAVI algorithm 1 in this paper, while the performance of the CAVI algorithm is worse than that in [25], [26], because it provides an approximate solution to the ML problem in (13) (or that in [25], [26]).…”

“…It is noteworthy that an ML approach is also studied in [25], [26]. In particular, as in [25], we focus on the detection of active transmit antennas assuming that the data symbols of active antennas are Gaussian (which is a Gaussian approximation).…”

“…Secondly, in order to lower the computational complexity of the detection, we consider arXiv:1811.05110v1 [cs.IT] 13 Nov 2018 a two-step approach and propose a low-complexity iterative algorithm for the first step based on variational inference. The resulting approach can also provide an approximate solution to the ML problem in [25], [26] with the complexity that grows linearly with the number of transmit antennas and is independent of the number of active transmit antennas. On the other hand, the complexity of the approaches in [25], [26] grows exponentially with the number of active transmit antennas.…”