On the Use of Precoding in FBMC/OQAM Systems

Linear precoding can be applied to multicarrier systems to minimize the effect that a deep fade in one of the subchannels can have on the overall bit error ratio when the transmitter does not have channel state information (CSI). But for filterbank multicarrier (FBMC) systems, which were proposed to overcome the poor spectral characteristics and bandwidth/energy waste caused by the use of the cyclic prefix, there are very few proposals of precoded systems in the literatur e. This paper proposes a precoded SISO (single-input single-output) filterbank multicarrier system with zero-forcing (ZF) and minimum mean square error (MMSE) equalization. Results show that in a well-equalized system, the Monte Carlo simulation results match the ones provided by the BER approximation presented in this paper. However, in systems with residual interference, the Monte Carlo results drift from the approximation at high SNR values, with the error performance from precoded FBMC systems being more affected by the unequalized interference. I. I NTRODUCTION Modern wireless communication systems require ever increasing transmission rates; these systems have to transmi t and receive data through heavily multipath communication channels, which cause severe intersymbol interference (IS I) in the received data stream. Multicarrier systems have been proposed to overcome the inherent difficulty of equalizing the received data through these channels. If the transmitte r has knowledge of the channel state information (CSI) in a multicarrier system, adaptive coding and modulation can be employed to transmit more data on the subcarriers with the highest SNR, discarding the ones who are not fit to transmit data with a low error probability. However, this knowledge c an be hard to acquire precisely, since the channel in a wireless environment changes rapidly. For the situations when the transmitter does not have the CSI, linear precoding [1] can be employed to minimize the effect that a deep fade in one of the subchannels can have on the overall bit error ratio. Precoding proposals for wireless multicarrier systems wit h only one antenna in the transmitter and in the receiver (SISO ) can be found in [2], [3], but they need CSI at the transmitter. The single carrier system with cyclic prefix (SC-CP) [4] is a DFT-based transceiver with a channel independent unitary linear precoding matrix. It can be seen as a precoded OFDM system with the DFT matrix as a precoder. Precoded multicarrier systems are also being used for the uplink in multius er systems (as a modified form of OFDMA, called SC-FDMA This work has been partially sponsored by National Council f or Scientific and Technological Development (CNPq) and CAPES/COFECUB pro ject (544/07). [5]), due to its lower PAPR properties and lower sensibility for (sub)carrier frequency offset. OFDM/QAM systems, which are the widely used multicarrier ones, use a rectangular window to separate their subcha nnels. This window has poor spectral and time characteristic s, often requiring post-filtering to conform to a spectral mask and making the use of a cyclic prefix mandatory to eliminate the ISI. These drawbacks can be eliminated with the usage of pulses better localized in time and in frequency to separate the subchannels. The system using these filters, called Filterb ank Multicarrier with Offset QAM (FBMC/OQAM) [6] is more efficient spectrally and can discard the cyclic prefix, gaini ng more efficiency in bandwidth and power. The only proposal so far in the literature for a precoded FBMC system in the literature can be found in [7]. In this proposal, classical multicarrier, precoded multicarrier and pure single carrier transmissions can be done simultaneously, e ach in its group of subchannels, due to the high subchannel selectivity inherent to the FBMC systems. This paper presents a precoded SISO filterbank multicarrier system, using linear zero-forcing (ZF) and minimum mean square error (MMSE) equalization. We provide an BER approximation for the best-case scenario and compare it with Monte Carlo simulations from FBMC systems in different situations. The paper is divided in the following sections. Section II presents an introduction to filterbank multicarr ier systems. The following section presents an analysis on the error behaviour for precoded multicarrier systems. Simula tion results for FBMC systems and a comparison with the BER approximation provided earlier in the paper are presented i n Section IV and the concluding remarks in Section V. II. F ILTERBANK MULTICARRIER SYSTEMS A computationally efficient way to implement a large number of well conformed in time and frequency filters to separat e the subchannels is the usage of a filterbank, which can be implemented through the filters’ polyphasic decomposition associated with the fast Fourier transform (FFT). This way, the synthesis (SFB) and the analysis (AFB) filterbanks implemen t the systems’ modulator and the demodulator, respectively. The synthesis filterbank associates the polyphase network (PPN ), which is the set of the so-called prototype filters, with the inverse fast Fourier transform (IFFT) to divide the bandwid th in M subchannels for transmission. The inverse operation in reversed order is realized in the receiver by the analysis filterbank to recover the transmitted data. The 7th International Telecommunications Symposium (ITS 2010) However, the usage of these efficient filters to separate the subchannels instead of the rectangular window imposes the u se of a real modulation to maintain the orthogonality between subcarriers, since the transmultiplexer’s impulse respon e is non-unitary due to interference from the neighboring subch annels and time instants. Thus, the FBMC system has to transmit a real symbol every half OFDM symbol duration, yielding to the so-called FBMC/OQAM system. The baseband discrete signal at a time instant k at the output of a synthesis filterbank in a FBMC/OQAM system is expressed by