Distributed Compressed Sensing Based Channel Parameter Estimation for MIMO-FBMC Communications

- For the sparse correlation between channels in multiple input multiple output filter bank multicarrier with offset quadrature amplitude modulation (MIMO-FBMC/OQAM) systems, the distributed compressed sensing (DCS)-based channel estimation approach is studied. A sparse adaptive distributed sparse channel estimation method based on weak selection threshold is proposed. Firstly, the correlation between MIMO channels is utilized to represent a joint sparse model, and channel estimation is transformed into a joint sparse signal reconstruction problem. Then, the number of correlation atoms for inner product operation is optimized by weak selection threshold, and sparse signal reconstruction is realized by sparse adaptation. The experiment results show that proposed DCS-based method not only estimates the multipath channel components accurately but also achieves higher channel estimation performance than classical orthogonal matching pursuit (OMP) method and other traditional DCS methods in the time-frequency dual selective channels

Abstract-For the sparse correlation between channels in multiple input multiple output filter bank multicarrier with offset quadrature amplitude modulation (MIMO-FBMC/OQAM) systems, the distributed compressed sensing (DCS)-based channel estimation approach is studied. A sparse adaptive distributed sparse channel estimation method based on weak selection threshold is proposed. Firstly, the correlation between MIMO channels is utilized to represent a joint sparse model, and channel estimation is transformed into a joint sparse signal reconstruction problem. Then, the number of correlation atoms for inner product operation is optimized by weak selection threshold, and sparse signal reconstruction is realized by sparse adaptation. The experiment results show that proposed DCS-based method not only estimates the multipath channel components accurately but also achieves higher channel estimation performance than classical orthogonal matching pursuit (OMP) method and other traditional DCS methods in the time-frequency dual selective channels. technology realizes the parallel transmission of high speed serial data through frequency division multiplexing, and it has better ability to resist multipath fading. Due to its technical characteristics and advantages, MIMO technology has been widely used in fourth generation (4G) and fifth generation (5G) networks after combining with OFDM technology, and has become one of the key technologies for the next generation mobile communications [1][2][3]. Although the traditional OFDM technology can achieve low complexity and high bandwidth efficiency, it is difficult to achieve strict synchronization and discontinuous band transmission when it is applied to more complex dynamic or multi-user networks in future mobile communication scenarios. Filter bank multicarrier with offset quadrature amplitude modulation (FBMC/OQAM) technology [4,5] can solve the above problems by using well time-frequency (TF) property filter banks. FBMC/OQAM, abbreviated as FBMC, provides a way to overcome the known limitations of OFDM. Firstly, FBMC is not strictly orthogonal, when the channel is not highly selective, it does not need cyclic prefix, and so it has higher spectrum efficiency [6]. Secondly, FBMC system can flexibly control the interference between adjacent subcarriers and make good use of the scattered spectrum resources. Finally, each subcarrier of the FBMC system processes channel estimation and synchronization separately, which makes it more suitable for uplink communication [4].  [11]. Compared with the SISO-FBMC system [12], more imaginary interference between the preamble symbols is existed in the MIMO-FBMC system, which leads to the low accuracy of the preamble-based CE [13].
[14], a CE method based on orthogonal matching pursuit (OMP) was proposed. Compared with the least square (LS) estimation method, the CS method in FBMC/OQAM can significantly improve the CE performance. In Ref. [15], the authors proposed a weak selection regularized OMP CE method based on Tanimoto sparsity, which has better bit rate ratio (BER) performance than the classical CS methods. For MIMO-FBMC systems, the authors in [16] proposed an approximate information transfer CS-based CE method. Ref. [17] proposed an effective sparse adaptive MIMO-FBMC system CE method. The above two CS methods have better CE performance than classical methods. Traditional greedy CS-based CE approach has high computational complexity.
Ref. [18] adopted an inner product operation optimization strategy to reduce the algorithm complexity, and proposed a low complexity sparse CE method for MIMO-FBMC.
Distributed compressed sensing (DCS) theory [19] pointed out that the inter-correlation of multiple signal sparse structures can be used to achieve joint reconstruction, which greatly improves the reconstruction efficiency. In Ref. [20], the authors proposed a CE scheme based on DCS theory, the proposed scheme can achieve higher estimation accuracy than traditional methods. It is found in literature [20][21][22]  The rest of this paper is organized as follows. Section 2 gives the system model, including MIMO-FBMC system and preamble-based channel estimation. In Section 3, compressed sensing channel estimation theory is analyzed, and the proposed distributed compressed sensing approach is given.
Channel estimation performance comparisons of traditional algorithms are given in Section 4. In Section 5, it gives the conclusions.

A. MIMO-FBMC System
Consider a tr NN  MIMO-FBMC/OQAM system, as shown in Fig

B. Conventional Preamble-Based CE
When the output is on the th r n receive antenna at the 0 th m subcarrier and 0 th n OQAM symbol, and noise is eliminated, the single is given as We can rewrite (7) as    It can be found clearly from (10) that, for a rt NN  spatial multiplexing MIMO system, at least t N number of nonzero pilot symbols is needed to estimate the channel frequency response matrix. Fig. 2 gives a classical preamble structure for a 2x2 MIMO-FBMC system.
For MIMO systems with well TF property filter banks, the inherent interference being mostly came from the first order FT neighbors. Then, we can get the conclusion that H η η HA η η (12) where A denotes the orthogonal matrix, with 11 11 The pilot 0 m c can be pre-calculated as in the SISO case. Therefore, the estimate of CFR matrix at the subcarrier 0 m can be given as    11 1,. , δ .. (22) Define the set  which contains the antennas,      Fig. 6 and Fig. 4, it is found that the performance curves of the five methods have more obvious floor effect due to the increase of multipath number.
In Fig. 7    Comparison of MSE performance in PA channel Comparison of BER performance in PA channel.

Figure 6
Comparison of MSE performance in EPA channel.

Figure 7
Comparison of BER performance in EPA channel.

Figure 8
Comparison of BER performance in VA channel.

Figure 9
Running time of CS methods under different SNR.