ASER analysis of fluid antenna systems with rectangular and hexagonal QAM schemes

In this work, simple approximate average symbol error rate (ASER) expressions are derived for fluid antenna systems (FAS) with rectangular quadrature amplitude modulation (RQAM) and hexagonal quadrature amplitude modulation (HQAM) schemes over correlated Nakagami-m fading channels between a single-antenna transmitter and a mobile device equipped with FAS. Then, asymptotic expressions are also obtained to explore the diversity order of the considered system. All derived expressions are represented only in terms of rational functions and they can be easily computed without requiring any special function computation or L-fold integration. To obtain ASER expressions and overcome mathematical intractability of ASER integrals, a tight approximation of the Gaussian Q function, $Q\left(·\right)$, is used. The performance of FAS-RQAM and FAS-HQAM schemes are compared with the conventional maximum ratio combining (MRC) technique and it is shown that FAS-QAM systems can outperform MRC systems by providing lower ASER values. In addition, the proposed expressions are not only valid for integer values but also valid for non-integer values of fading parameter and antenna size. Results are demonstrated for different configurations of all parameters and modulation schemes and the approximate results show a good fit to the exact results obtained by using exact $Q\left(·\right)$ in ASER integrals while asymptotic results match well with approximate ones at high signal-to-noise ratio regime. Our approximate results are also found close to the simulation results for both FAS-RQAM and FAS-HQAM schemes.