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Table 1 Global computational complexity of detectors studied in this work. Note that they are given in the most compact form and are also ranked in an ascending order, that is, from less to more costly as lines progress to the bottom of the table

From: Low-complexity deep unfolded neural network receiver for MIMO systems based on the probability data association detector

Detector Global Computational Complexity
Simplified DU-PDA \({\mathcal {O}}(LN_\text {t}N_\text {r})\)
Approximate Message Passing (AMP) \({\mathcal {O}}(N_\text {I}N_\text {t}N_\text {r} + N_\text {I}N_\text {t}\sqrt{M})\)
Zero-Forcing (ZF) \({\mathcal {O}}(N_\text {t}^3 + N_\text {t}^2 N_\text {r} + N_\text {t} N_\text {r})\)
Deep Unfolded PDA (DU-PDA) \({\mathcal {O}}(LN_\text {t}^2 + LN_\text {t}N_\text {r} + LN_\text {r})\)
Probability Data Association (PDA) \({\mathcal {O}}(N_\text {t}^4 + \sqrt{M}N_\text {t}^3 + N_\text {t}^2N_\text {r} + N_\text {t} N_\text {r})\)
Sphere Detector (SD) \({\mathcal {O}}(M^{\sqrt{N_\text {t}}})\)
Maximum Likelihood Detector (MLD) \({\mathcal {O}}(M^{N_\text {t}}(N_\text {t} N_\text {r} + N_\text {r}))\)