FBMC-SMT principles

The rectangular impulse adopted in OFDM systems is not time and frequency well localized, making it sensitive against timing and frequency offset (e.g. introduced by channel, local oscillator mismatch). Unfortunately, time and frequency well localized pulse doesn't exist for the conventional OFDM according to Ballian-Low theorem. However, if PAM symbols instead of QAM symbols are considered, time and frequency well localized pulse can be achieved in a multicarrier system (MCM) called Filter Bank Multi-Carrier (its variant Staggered Multi-Tone, FBMC-SMT). The transmitted signal is expressed as $$x(t) = \sum_{k=-\infty}^{\infty}\sum_{n=0}^{N_{\textrm{sub}}-1}j^{n+k} s_{k,n} g\left(t-k\frac{T}{2}\right)e^{j\frac{2\pi}{T}nt},$$ where $g(t)$ here generally denotes the pulse shape (e.g. rectangular in OFDM) and $s_{k,n}$s are real-valued data symbols. In FBMC-SMT, the pulse $g(t)$ can be designed to achieve better time and frequency properties thanks to advanced prototype filter design methods. Usually, the prototype filter $g(t)$ spans an integer $K$ (overlapping factor) multiple length of symbol period, i.e. $$T_{F} = K\cdot T.$$ It is also noteworthy to mention that pure real and imaginary data values alternate on subcarriers and symbols, which is therefore called offset QAM (OQAM). Since PAM symbols convey only one half of information content compared to QAM symbols, a data rate loss of factor 2 is implicit. Nevertheless, the symbol period in FBMC-SMT is also halved to $\frac{T}{2}$ to compensate the efficiency loss of OQAM modulation. Furthermore, cyclic prefix is not essential anymore in FBMC-SMT due to the well localized pulse shape.