Guardband Optimization for Cellular Systems Applying Raised Cosine Windowed OFDM

Abstract

In this paper, we study the optimization of the guardbands between adjacent channels in OFDM-based cellular systems. It is well known that OFDM signals have strong sidelobes in spectrum, which lead to large necessary guardbands between adjacent channels to avoid severe adjacent channel interference. To reduce such guardbands and, thus, to increase the spectrum usage efficiency, we propose to apply raised cosine (RC) windowing of the time domain OFDM signals, which is a simple, efficient and effective method. In this context, an interesting tradeoff can be observed, i.e., a higher roll-off factor (ROF) of the RC-window is associated with higher signal overhead in time (in other words, longer OFDM symbol duration), but lower guardband overhead in frequency (due to better sidelobe suppression). We study this tradeoff and found out that the ROF and the guardband size can be jointly optimized, in the sense that the per-channel data rate can be maximized under adjacent channel interference constraints. Our mathematical analysis further shows that such joint optimization can be reduced to a single dimension optimization, i.e. the optimization of the ROF. Afterwards, this optimization procedure is illustrated and verified via numerical simulation, showing that large data rate increase can be achieved when using RC-windowing with an optimized ROF. Finally, practical analysis of the instantaneous per-OFDM symbol interference further verified the effectiveness of the proposed approach.

Appendix: Sidelobe Bound for an OFDM Signal with \(N_B\) OFDM Symbols

We extend Eq. (4) to describe an OFDM signal with $N_B$ OFDM symbols as follows:

$$\begin{aligned} \acute{s}^\mathrm {Ext}(t)=\sum _{b=0}^{N_B-1}s_b(t)w(t-bT_\mathrm {w}), \end{aligned}$$

(25)

where $b$ is the index of the OFDM symbol. The frequency response of this signal can be written as:

$$\begin{aligned} \acute{S}^\mathrm {Ext}(f)=\sum _{k=-\frac{N}{2}}^{\frac{N}{2}-1}\left( \sum _{b=0}^{N_B-1} S_b[k]e^{-j2\pi f bT_\mathrm {w}}\right) W(f-k\varDelta f). \end{aligned}$$

(26)

With $\left| S_b[k]\right| \le \left| S_\mathrm {max}\right|$ and the triangle inequality, the following relations can be obtained:

$$\begin{aligned} \left| \acute{S}^\mathrm {Ext}(f_{\mathrm {\nu }})\right| ^2 \le N_B^2 \left| S_{\mathrm {max}}\right| ^2 \left( \sum _{k=-\frac{N}{2}}^{\frac{N}{2}-1}\left| W(f_{\mathrm {\nu }}-k\varDelta f)\right| \right) ^2, \end{aligned}$$

(27)

which provide an upper-bound on the sidelobe level at the frequency $f_\mathrm {\nu }$. Compared to (5), this upper-bound is just a scaled version with the factor $N_B^2$. It can be easily shown that the average spectral power of the interference signal within its bandwidth also scales with $N_B^2$. Therefore, the sidelobe reduction requirement remains the same as in (6). In other words, the analysis using a single OFDM symbol is equivalent to that using multiple OFDM symols.