3 OFDM-based precoding for FBMC waveforms
3.6 Filter Predistortion
For both waveforms, the received symbols are distorted by the frequency response of the filter as shown in (3.8) for FFT-FBMC et (3.27) for BF-OFDM.
Several options exist to deal with those coefficients. The first option consists in ignoring them. The filter-induced distortion will be estimated by the channel estimation and considered as part of the channel response.
The second option is to pre-compensate those coefficients at the transmitter side. Indeed, the coefficients can be pre-computed and a pre-distortion stage can be pre-pended to the transmission chain. The predistortion coefficient to be applied on the kth subcarrier of the pth subband (at all time instants) Pp,k[n] is given in (3.33) for the two schemes. As already mentionned, this coefficient does not depend neither on the subband index p nor on the time intant n.
Pp,k[n] = |G(k1 o)|2 for FFT-FBMC Pp,k[n] = G ∗(ko) |G(ko)|2 for BF-OFDM (3.33)
The impact of the filter predistortion on the transmitted spectrum is observed in Figure 3.13 for the two schemes. For each scheme, the 40-dB prototype filter defined in Table 3.4 is used.
The addition of filter predistortion stage at the transmitter side, as it flattens the in-band transmitted spectrum at the expense of a slightly weakened side lobe rejection. The receiver can thus operate without any knowledge on the filter- ing performed at the transmitter side. Such receiver is said to be ”transparent”. The transparency condition allows a straightforward multiple access for the up- link. Indeed, if the uplink users have different configuration (such as prototype filter parameters), the receiver can demodulate the different signals without any information on the transmitter filtering.
For FFT-FBMC, the filter predistortion stage is not interesting as it is assumed that the receiver also uses the Tx prototype filter. Considering a filter predistortion stage for FFT-FBMC would be interesting when different TX and Rx prototype filters are considered. This case is not addressed in this thesis. The predistortion will thus not be considered in FFT-FBMC in the proposed study.
-4 -2 0 2 4 −140 −120 −100 −80 −60 −40 −20 0 Frequency [MHz] PS D [d B/3kHz ]
without filter predistortion with filter predistortion
-4 -2 0 2 4 −140 −120 −100 −80 −60 −40 −20 0 Frequency [MHz] PS D [d B/3kHz ]
Figure 3.13: Impact of transmitter filter-predistortion for FFT-FBMC (left) and BF-OFDM (right).
It seems interesting noticing that the addition of the filter predistortion stage at the transmitter side has no impact of the SIR level after demodulation as it is verified for FFT-FBMC below. Same verification can be performed with BF- OFDM expression. SIR = 1 Npδ X k∈Ω σ2a P ǫ6=0 |G ∗(k+ǫN )G(k)|2 |G(k)|4 σ2a = 1 Npδ X k∈Ω |G(k)|4σ2 a P ǫ6=0|G∗(k + ǫN )G(k)|2σa2 (3.34)
3.7
Conclusion
In this section, the OFDM precoding for FBMC-based waveforms has been pro- posed to allow NPR in the complex field.
The proposed precoding can restore the complex orthogonality of a filter-bank based waveform. Indeed, it prevents the subband overlapping (without compro- mising the spectral efficiency) which is a source of interference in FBMC-based waveforms. However, to ensure complex NPR, the frequency localisation is thus relaxed with respect to the commonly used OQAM signaling (from subcarrier-wise to subband-wise). Besides, the spectral efficiency of the scheme has to be relaxed as well with the insertion of CP ans CS according to the Balian Low Therorem.
Two schemes results from this study, namely FFT-FBMC with a FBMC-based receiver and BF-OFDM with a simple OFDM-based receiver. The working con- ditions for the two schemes have been established for any FBMC rate factor δ. The two complex orthogonal schemes are thus very flexible (in terms of subband bandwidth and precoding alphabet size) so that they can be easily adapted to any system requirements. The flexibility of the schemes is even improved by the proposed prototype filter design methods which allow to ensure complex NPR for any symbol rate and spectrum requirements.
The proposed schemes thus benefit from both complex orthogonality and a subband filtering performed by a filter-bank. The schemes are thus interesting for future mobile technologies. On top of that, BF-OFDM relies on a 5G NR receiver which makes it highly appealing for beyond 5G NR technologies. That is why in the next chapter, the two schemes will be now adapted to 5G NR numerologies and their performance evaluated for the scenarios considered in Chapter 2.
3.7.1 Contribution
This chapter represents the major contributions of the research work. First, the BF-OFDM scheme has been detailed in [92]: D. Demmer, R. Gerzaguet, J.-B. Dor´e, D. Le Ruyet, and D. Kt´enas, “Block-Filtered OFDM: a novel waveform for future wireless technologies,” in Proc. IEEE International Conference on Commu-
nications (ICC), (Paris, France), May 2017. The prototype filter design methods
presented in Section 3.5.1 and 3.5.2 have been published in [93]: D. Demmer, R. Gerzaguet, J.-B. Dor´e, D. Le Ruyet, and D. Kt´enas, “Filter Design for 5G BF-OFDM Waveform,” in Proc. IEEE. European Conference on Networks and
Communications (EuCNC), (Oulu, Finland), June 2017. However, the filter de-
sign optimising both the interference and side lobe rejection has not been published yet.
A first performance evaluation of BF-OFDM has been done in [94]: R. Gerzaguet, D. Demmer, J.-B. Dor´e, and D. Kti´enas, “Block-filtered OFDM: A new promising waveform for multi-service scenarios,” in Proc. IEEE International Conference on
Communications (ICC), pp. 1–6, May 2017.
Then, the study has been extended to any FBMC rate factor δ in a collabo- rative work with the inventors of FFT-FBMC in [91]: D. Demmer, R. Zakaria, R. Gerzaguet, J.-B. Dor´e, and D. Le Ruyet, “Study of OFDM Precoded Filter- Bank Waveforms,” IEEE Transactions on Wireless Communications, pp. 1–1, 2018.