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In filter bank multicarrier with offset quadrature amplitude modulation (FBMC/OQAM) systems, a large pilot overhead is required due to the existence of the imaginary interference. In this paper, we present an approach to reduce the pilot overhead of channel estimation. A part of pilot overhead is used for transmitting data, and compensating symbols are required and designed to remove the imaginary interference. It is worthwhile to point out that the power of compensating symbols can be helpful for data recovery; hence, the proposed approach decreases the overhead of pilots significantly without the cost of additional pilot energy. In addition, the proposed scheme is extended into multiple input multiple output systems without the performance loss. Compared with the conventional preamble consisting of

Currently, filter bank multicarrier with offset quadrature amplitude modulation (FBMC/OQAM) has been considered as a potential alternative [

Unlike in OFDM, channel estimation in FBMC/OQAM is not a straightforward mission, which is related to that the waveform synthesis and analysis of FBMC/OQAM are not same as that of OFDM. Since the orthogonality condition only is met in real field [

To avert the imaginary interference, a direct method is to disable the symbols surrounding the pilots, which results in a reduced spectral efficiency. By applying the following method, this spectral efficiency loss could be avoid [

In this paper, we present an approach to reduce the pilot overhead of channel estimation in FBMC/OQAM systems. Compared with the conventional pilot structures, a part of pilot overhead is used for transmitting data, and compensating symbols are required and designed to eliminate the imaginary interference from data. Note that it is proven that the power of compensating symbols can be helpful for data recovery; hence, the proposed approach decreases the overhead of pilots significantly without the cost of additional pilot energy. Compared with the conventional methods with

The rest of this paper is organized as follows. The IAM method is briefly introduced in Section

As depicted in Figure

The FBMC/OQAM system diagram.

Following Figure

where

Then, the signal at the receive antenna is obtained

where the sign

Then, demodulations at the receiver can be written as

Then, an operator of taking real part is required.

Note that channel estimation is necessary in the FBMC/OQAM system under the multipath channel.

In [

where

with the maximum channel delay spread of

with

And the noise term

Then, the IAM channel estimation is written as [

Figure

The conventional preamble and the proposed preamble in FBMC/OQAM.

The conventional 3-column preamble structure of IAM

The preamble structure of POP

The POP method is another preamble-based channel estimation method in [

Suppose

where

Then, the channel coefficients have been estimated. This approach does not require any knowledge of the prototype function and could be adopted as preamble-based method and also as a scattered-based channel estimation method.

Figure

The proposed pilot structure in FBMC/OQAM.

where

Then, it is obtained as

It should be noted that (

It is proven that

Thus, it can be concluded that

In addition, define

In this subsection, it is proven that the CPS is helpful for data recovery of ADS. Therefore, the ADS has the similar ability to fight against the noise compared with data symbols as we can see below.

According to (

where

According to (

Let

When the channel noise vanishes, we have

In this section, the proposed scheme in Section

The MIMO-FBMC system model.

Without loss of generality,

Proposed preamble in MIMO-FBMC systems.

Conventional preamble structure in MIMO-FBMC

Proposed preamble structure in MIMO-FBMC

At the receiver, the demodulation of the

where noise

As mentioned above, the imaginary interference between antennas can be removed completely. Then, for the proposed preambles in Figure

Accordingly, the channel estimation in MIMO-FBMC systems can be obtained as

Then, the simple linear interpolation is performed on

In this section, we evaluate the performance of the proposed channel estimation approaches that are presented in this paper through computer simulations. The FBMC/OQAM system employs the PHYDYAS filter [

Subcarrier number: 2048

Sampling rate (MHz):

Path number:

Delay of path (

Power delay profile (dB): 0, -5, -10

Modulation: 4QAM

Channel coding: convolutional coding [

For comparison, we also give the performance of POP [

Figures

MSE of the proposed scheme.

BER of the proposed scheme.

Figure

BER of the proposed scheme in MIMO-FBMC with 2 transmit antennas and 2 receive antennas.

In this paper, an approach was presented for the pilot overhead reduction in the channel estimation of FBMC/OQAM systems. Compared with the conventional methods with

From (

In addition, let

denote an

Note that

Based on the equations

Then,

Finally, we can obtain that

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was financially supported in part by the National Science Foundation of China with Grant number 62001333, Nature Science Foundation of Southwest University of Science and Technology with Grant number 18zx7142, and the Scientific Research Fund of Beijing Information Science and Technology University with Grant number 2025018.