Pilot Sequence Assisted Channel Estimation in MIMO/SIMO/SISO-OFDM Systems

: For improving the communication system performance in multiple input multiple output-orthogonal frequency division multiplexing (MIMO-OFDM) system, single input multiple output-orthogonal frequency division multiplexing (SIMO-OFDM) system, single input single output-orthogonal frequency division multiplexing (SISO-OFDM) system, this paper introduces a pilot assisted channel estimation method. The proposed method is a combination of pilots and channel estimation based on known channel state information (CSI). First, the pilots are used to maintain the orthogonality characteristics of space time block coding (STBC). By designing the interference-free pilots we estimating the channel, and then with the pre-estimated channel characteristics data is decoded at the MIMO-OFDM system receiver. In this paper, we proposed four kinds of comb-type pilot sequences with interference-free pilots designing among consecutive subcarriers. The proposed pilot assisted channel estimation method in MIMO/SIMO/SISO-OFDM systems could be well adopted with different low and high order modulations. This flexible transmission mechanism can save pilot overhead and has strong anti-interference ability in dynamic channels. Moreover, high-order constellation modulation level will enhance the channel capacity in MIMO/SIMO/SISO-OFDM system. Therefore, it can be used as a candidate technology for 5G or 6G MIMO/SIMO/SISO-OFDM system.


Introduction
Orthogonal frequency division multiplexing (OFDM) system is characterized by its robustness to the multipath induced inter-symbol interference (ISI) [1], [2].Foschini et al. [3], [4] showed that antenna diversity can be exploited to significantly enhance spectral efficiency by using multiple antennas at both transmitter and receiver.Recently, space time block coding (STBC) has been proposed as an efficient way to achieve this capacity improvement for the multiple input multiple output (MIMO) channel.MIMO/ single input multiple output (SIMO)/single input single output (SISO)-OFDM systems are recognized as the promising technology for 5G and 6G mobile communications.
When MIMO is used with OFDM, such as STBC based transmit diversity, channel state information (CSI) [5] is required for coherent detection and decoding.CSI can be obtained in two categories.The first one is blind pilots, and the second one is based on pilots which are known beforehand at the receiver.In STBC MIMO-OFDM systems, different symbols are transmitted from different antennas simultaneously, and consequently, the received signal is the superposition of these signals.The designed pilot sequence (PS) must be orthogonal among transmit antennas [6].Optimal pilot sequences were first proposed in [7]- [10] for MIMO-OFDM systems.Chern et al. [11] proposed a prime PS to one transmit antenna.The sequences of other transmit antennas are phase shift in frequency domain, or cyclic shift in time domain, to the prime sequence.Del Peral-Rosado et al. [12] proposed an optimal placement of the pilot subcarriers with regard to the mean square error (MSE) of the least square (LS) channel estimation for SISO-OFDM systems.Younas et al. [13] proposed a classical MIMO transmission with pilot aided sequences based on adaptive LS channel estimation in a correlated time varying channel.It simplifies the LS channel estimation by utilizing the proposed pilot construction to avoid matrix inversion which causes great complexity of the receiver.LMMSE and SVD channel estimation methods are widely utilized in multi-user MIMO-OFDM systems [14]- [17], but they inevitably bring a large amount of matrix calculation in frequency domain.
For virtual multiple-input single-output (MISO)-OFDM systems, Wang et al. [18] proposed an efficient resource allocation method to provide high transmission throughput.The base stations (BS) can allocate subcarriers to transmit node with the highest magnitude of channel frequency response (CFR) on the subcarriers.Under time varying channels, Youssefi et al. [19] proposed a new approach to achieve optimal training sequences (OTS) in terms of minimizing the MSE for spectrally efficient MIMO-OFDM systems.The OTS are equal powered and spaced, and orthogonal positioned.
However, in practical OFDM based systems to avoid the transmitted data, being distorted by the low pass filter, the subcarriers that fall in the roll-off region of the filter transfer function are not used, which are often referred to as virtual subcarriers [20]- [23].The existence of virtual subcarriers breaks the equal spaced property of conventional pilot sequences and the system performance will be increased.Kenarsari-Anhari et al. [24] formulated the power allocation as linear programming (LP) problem in coded OFDM system.Wang et al. [25] proposed a low-complexity power allocation method in the cooperative OFDM networks and it can greatly improve the system throughput.The equivalent channel power gain can be calculated and the power among each subcarrier can be allocated through Lagrange optimization method.The complexity is linear in the number of subcarriers, which is attractive in practical application for OFDM networks.
In most STBC MIMO schemes, the interference between the two transmit braches degrades the performance of communication system severely.To improve communication performance and obtain diversity gains, the paper proposes a novel interlaced pilot sequence channel estimation method in STBC MIMO-OFDM systems which suppresses the ISI and inter-carrier interference (ICI) effectively.In addition, the total available bandwidth using the STBC pre-coder could provide high channel capacity in MIMO-OFDM systems.
This paper introduces an interlaced PS assisted channel estimation method in MIMO/SIMO/SISO-OFDM systems to combat the interference induced by Rayleigh fading channels.Simulation results show that the proposed channel estimation method based on interlaced PS could provide significant diversity gains in MIMO/SIMO/SISO-OFDM system under different modulation modes.
The remainder of this paper is organized as follows.The MIMO/SIMO/SISO-OFDM system models are presented in Section II.Section III introduces pilot assisted channel estimation.Section IV illustrates Rayleigh channel model.Simulation results and comparison analysis are presented in Section V. Section VI concludes the paper.

MIMO/SISO-OFDM System Model
Fig. 1 and Fig. 2 illustrate the MIMO-, and SISO-OFDM systems, respectively.In this paper, we consider the MIMO-OFDM system with the number of transmit and receive antennas 1 At the transmitter side, the input bits are grouped and mapped according to a pre-specified constellation modulation scheme.The SISO-OFDM and MIMO-OFDM systems could adopt different kinds of modulation patterns, such as binary phase shift keying (BPSK), quadrature phase shift keying (QPSK), 8 phase shift keying (8PSK), 16 quadrature amplitude modulation (16QAM) and 64 quadrature amplitude modulation (64QAM) [26].The higher order modulation mode, the more bits an OFDM symbol carries, the more information the MIMO-OFDM system transmits.Therefore, higher order modulation can improve the transmission efficiency of MIMO-OFDM.

MIMO-, SIMO-, SISO-OFDM System Model
After constellation modulation, the modulated symbols are sent to space-time encoder.According to Alamouti criterion, the space-time coded signals are allocated to two antennas.After STBC [2], the transmitted OFDM codeword could be expressed as: Correspondingly, the transmit OFDM symbols on the transmit antenna one could be represented as: (2) Similarly, the transmit OFDM symbols on the transmit antenna two could be represented as: 3) The received OFDM symbols Y are the superposition coming from transmit antenna one and two.After STBC in the transmitter, the comb-type pilots are inserted through the time domain by fixed intervals of subcarriers.Figs. 1 and 2 illustrate the system models of SISO-OFDM and MIMO-OFDM, respectively.As shown in Fig. 2, the inverse fast Fourier transform (IFFT) block is used to transform the data sequence 1 X and 2 X into time-domain signal x 1 and x 2 on the transmit antenna one, which can be shown as: on the receive antenna one and two could be represented as: where 1 () k W and 2 () k W are the frequency-domain AWGN.After removing the CP, the time-domain received OFDM symbols are transformed into frequency domain in two FFT blocks in the MIMO-OFDM systems.The received frequency-domain signals could be represented as: where 0,1, 2, , 1 kN  L represents the index of subcarriers and j e π N  2 is the twiddle factor of FFT.where y 1 and y 2 are the time-domain received OFDM complex value symbols after multipath fading and AWGN from receive antenna one and receive antenna two, respectively.Y 1 and Y 2 are the frequency domain received OFDM complex value symbols after multipath fading and AWGN from receive antenna one and receive antenna two, respectively.
In the receiver of MIMO-OFDM system, the frequency-domain symbols are decoded in the space-time block decoding (STBD).The signals at multiple receive antennas are decoded using CSI provided by the channel equalizer.Therefore, channel equalizer is a critical module of MIMO-OFDM systems supposing that the CSI is known to the MIMO-OFDM receiver.At last, the binary information bits are obtained after the BPSK, QPSK, 8PSK, 16QAM [26], and 64QAM constellation demodulation.

STBD IN MIMO-OFDM System Model
Diversity gains can be obtained by using STBC technology at the transmitter.In MIMO-OFDM systems, STBC is a key technology to improve the system performance.STBC technology is used to encode signals in the frequency domain.Alamouti code is a complex orthogonal STBC specially designed for two transmit antennas [1], [2].
According to the estimated CFR, the OFDM symbol after STBD in the receiver can be shown as: ˆˆˆˆˆˆˆˆˆ.
ˆˆˆˆˆˆˆˆˆ (10) where 1 X and 2 X are the 1st and 2nd STBD OFDM symbols, respectively.In MIMO-OFDM system, 11 Ŷ , 12 Ŷ , 21 Ŷ , and 22 Ŷ are the received symbols transmitted from transmit antenna one to receive antenna one, from transmit antenna one to receive antenna two, from transmit antenna two to receive antenna one, from transmit antenna two to receive antenna two, which could be represented as:  (11) where 11 Ŵ , 12 Ŵ , 21 Ŵ and 22 Ŵ are the frequency domain AWGN between transmit antenna one to receive antenna one, transmit antenna one to receive antenna two, transmit antenna two to receive antenna one, transmit antenna two to receive antenna two, respectively.11 H , 12 H , 21 H , and 22 H represent the estimated CFR between transmit antenna one to receive antenna one, transmit antenna one to receive antenna two, transmit antenna two to receive antenna one, transmit antenna two to receive antenna two, respectively.
For simplicity, the Eq. ( 10) could be represented as:

Y H Y H Y H Y H X | H | H | H | H | X Y H Y H Y H Y H | H | H | H | H |
(12)

Pilot Assisted Channel Estimation
In the MIMO-OFDM, SIMO-OFDM and 12  , 13  , 14  , , and 1 500  SISO-OFDM systems, the number of used subcarriers, data subcarriers, pilot subcarriers, and virtual subcarriers are 1001, 990, 11, and 1047, respectively.Correspondingly, the number of data subcarriers are 500, 750, 875, 950, 980, and 990, respectively.The number of pilot subcarriers are 501, 251, 126, 51, 21, and 11, respectively.To avoid the distortion of the low-pass filter at the transmitter, the subcarriers falling in the roll-off region of the transmitter filter are generally not used to transmit data or pilots, this part of subcarriers are defined as virtual subcarriers and the length of virtual subcarriers is 1047 in MIMO/SIMO/SISO-OFDM systems.
The interference caused by Rayleigh fading channel and AWGN could exist in the four quadrants in the complex plane.The pilots in the adjacent subcarriers should be set in different quadrants to avoid interference.In this paper, four kinds of PS are chosen to be utilized in the simulation.Under the pilot interval 2 n  , could be represented as: could be represented as: Under n  , 3 could be represented as: 1.5166 1.5166 1.5166 1.5166 1.5166 1.5166 1.5166 could be represented as: could be represented as: The number of pilot subcarriers for , and 100 n  is 1001.Because the number of pilots inserted into the system is limited, so it would not waste too much frequency resources.The proposed pilot assisted channel estimation method could save valuable bandwidth in the MIMO/SIMO/SISO-OFDM systems.The interference caused by Rayleigh fading channel and AWGN could exist in the four quadrants in the complex plane [10].The pilots in the adjacent subcarriers should be set in different quadrants to avoid interference caused by large-scale propagation and small-scale propagation.The coherent time in Rayleigh fading channel [27] of the MIMO-OFDM system could be represented as: where d f is the Doppler spread and can be represented as [28]: where υ is the mobile speed and λ is the wavelength.Under the condition of d 20Hz f  , according to (16), the coherent time .When the Doppler spread d f becomes large, the coherent time c T becomes short, the multipath channel undergoes deep time selective fading.The smaller value the coherence time c T , the more serious the complex transmitted signal decays.Fig. 3 illustrates large-scale propagation and small-scale propagation of the STBC MIMO-OFDM.When d f increases, it would induce time selective propagation, which is illustrated in Fig. 3.The time selective propagation includes large-scale propagation and small-scale propagation.To suppress the interference which is caused by small-scale propagation, the pilots are inserted in comb-type manner through the subcarriers in the frequency domain with different pilot intervals.
Fig. 4 illustrates SIMO-OFDM models utilized in micro-cell and macro-cell.According to the number of receive antennas, 12  SIMO-OFDM, 13  SIMO-OFDM, 14  SIMO-OFDM could be utilized in micro-cell and 15  SIMO-OFDM, 1 500  SIMO-OFDM could be utilized in macro-cell.The base station (BS) in the microcell/macro-cell could adjust the transmission power according to either the different modulation mode, such as BPSK, QPSK, 8PSK, 16QAM, 64QAM, or the transmission distance from BS to mobile station (MS).Fig. 4(a), (b), and (c) belong to micro-cell OFDM systems.As shown in Fig. 4(a), MS1 and MS2 could receive OFDM symbols from two antennas.As shown in Fig. 4(b), MS1, MS2, and MS3 could receive OFDM symbols from three antennas.As illustrated in Fig. 4(c), MS1, MS2, MS3, and MS4 could receive OFDM symbols from four antennas independently.Fig. 4(d), (e), (f), (g), (h), and (i) belong to macro-cell OFDM symbols.As illustrated in Fig. 4(d), ten antennas could receive OFDM symbols irrelevantly.It could be seen from Fig. 4(e), (f), (g), (h), and (i) that twenty, fifty, one hundred, two hundred, five hundred antennas could receive OFDM symbols irrelevantly.

Rayleigh Channel Model
The multipath fading channels obey Rayleigh distribution and the power distribution function (PDF) of transmit signals 1 x and 2 x obeys Rayleigh distribution, which could be represented as [29], [30]:  (28) where , ˆα β σ denotes the noise standard deviation from the transmit antenna α to receive antenna β .In the multipath fading environments, if there are light of sight (LOS) signals from transmit antenna to receive antenna, the transmit signals 1 x , 2 x could obey Rice distribution, which is where A is the peak value of the main signal amplitude and 0 () I  is the modified Bessel function of order zero with type one.When 0 A  , Ri 1 () f x and Ri 2 () f x would tend to Ra 1 () x and Ra 2 () f x .Under Rayleigh distribution, the PDF of the complex transmitted symbols Ra () f x could be represented as: ) Under Rice distribution, the PDF of the complex transmitted symbols Ri () f x could be represented as: Fig. 5 illustrates the Rayleigh distribution under different noise standard deviation., the value of () f x is small.Therefore, the value of pilots should be set in the interval of [1.4,1.6] .

Simulation Results and Comparison Analysis
This section presents the bit error rate (BER) performance comparisons between QPSK, 8PSK, 16QAM, 64QAM modulated MIMO-OFDM system under AWGN channel.The simulation is performed in static AWGN channel environments and adopts four kinds of constellation modulation modes of QPSK, 8PSK, 16QAM, and 64QAM, respectively.The interlaced PS is inserted in STBC MIMO-OFDM, SIMO-OFDM and SISO-OFDM systems by comb-type manner.The PS1, PS2, PS3, and PS4 are inserted in the proposed SISO/SIMO/STBC MIMO-OFDM systems.
The profiles for the MIMO/SIMO/SISO-OFDM systems are shown in Table 1.The length of CP occupies 512 subcarriers and the number of subcarriers is 2048 N  in the MIMO/SIMO/SISO-OFDM systems.The pilot insertion pattern is comb-type and the pilot value is -1.5166 and 1.5166.The pilot interval could be in MIMO/SIMO/SISO-OFDM systems, respectively.

Fig. 7 4 1 10 
represents the BER performances of22  STBC MIMO-OFDM system under one path Rayleigh fading channel.Fig.7(a) and (b) represent the BER performance of QPSK and 8PSK modulated STBC MIMO-OFDM system under 1 path Rayleigh fading channel.We can see from Fig. 7(a) that when SNR = 10dB , the BER value of d 20 Hz f  , and d = 60 Hz f becomes zero, but the QPSK BER value of d = 80 Hz f Fig. 7(b), at the target BER of 6 5 10   , the 8PSK BER curve of d = 60 Hz f outperforms the BER curve of d = 80 Hz f , and d = 20 Hz f about 0.4 dB and 0.8 dB SNR gains.Therefore, the interlaced PS1 and PS4 in QPSK and 8PSK modulated MIMO-OFDM systems could improve the accuracy of channel estimation at the receiver of MIMO-OFDM systems.Fig. 7(c) and (d) represent the BER performance of 16QAM and 64QAM modulated 22  STBC MIMO-OFDM system under one path Rayleigh fading channel.As can be seen from Fig. 7(c), because of the orthogonality of interlaced PS2 in MIMO-OFDM systems with two transmit antennas and two receive antennas, the 16QAM BER curves of d = 20 Hz f , d = 60 Hz f , and d = 80 Hz f almost have the same performance and at SNR = 15dB , the 16QAM BER value could reach the communication performance of STBC MIMO-OFDM system significantly.As shown in Fig. 7(d), when the BER is 3 , the 64QAM BER curves with d = 20 Hz f , d = 60 Hz f , and d = 80 Hz f almost have the same performance.At SNR = 20dB , the 64QAM BER value of the three curves is 4 5.6 10   .It could be concluded that the interlaced PS3 could resist the deep fading interference among different transmit antennas and receive antennas in one path Rayleigh fading channel.

Fig. 15
Fig. 15 represents the BER performance of 11  SISO-OFDM system under AWGN.Fig. 15(a) represents the BER performance of BPSK modulated SISO-OFDM system under AWGN inserted by PS1.At the target BER of 4 10  , the BPSK BER curves of 100 n  and 50 n  outperform the BPSK BER curves of 20 n  , 8 n  , 4 n  , and 2 n  about 0.2 dB, 0.6 dB, 1.05 dB, and 2.1 dB SNR gains, respectively.Fig. 15(b) illustrates the BER performance of 8PSK modulated 11  SISO-OFDM system under AWGN inserted by PS1.At the target BER of  STBC MIMO-OFDM system under AWGN inserted by PS1.At the target BER of 3 10  , respectively.
) represents the BER performance of BPSK modulated 12  STBC SIMO-OFDM system under AWGN inserted by PS2.At , 0.3 dB, 0.8 dB, 1.05 dB, 2.1 dB SNR gains, respectively.Fig.8(b) represents the BER performance of QPSK modulated 12  STBC SIMO-OFDM system under AWGN inserted by PS1.At the target BER of  about 0.07 dB, 0.21 dB, 1.35 dB, and 2.25 dB SNR gains, respectively.Fig.9represents the BER performances of 13  SIMO-OFDM system under AWGN.Fig.9(a)represents the BER performance of BPSK modulated 13  SIMO-OFDM system under AWGN inserted by PS2.At the target BER of  , the BPSK BER curves of  about 0.2 dB, 0.6 dB, 1.05 dB, and 2.1 dB SNR gains, respectively.Fig.15(b)illustrates the BER performance of 8PSK modulated 11  SISO-OFDM system under AWGN inserted by PS1.At the target BER of could provide about 0.1 dB, 0.2 dB, 0.7 dB, 1.1 dB, and 2.1 dB SNR gains, respectively.Fig.15(c) represents the BER performance of QPSK modulated SISO-OFDM system under AWGN inserted by PS3.At the target BER of  about 0.2 dB, 0.4 dB, 1.1 dB, 1.5 dB, and 2.15 dB SNR gains, respectively.Fig.16represents the BER performance of 11  SISO-OFDM system under AWGN.Fig.16(a)represents the BER performance of BPSK modulated SISO-OFDM system under AWGN inserted by PS3.At the target BER  about 0.1 dB, 0.2 dB, 0.5 dB, 1.1 dB, and 2.3 dB SNR gains, respectively.Fig.16(b) represents the BER performance of 64QAM modulated SISO-OFDM system under AWGN inserted by PS2.At the target BER of  about 0.4 dB, 0.6 dB, and 1.45 dB SNR gains, respectively.Fig.16(c) represents the BER performance of 64QAM modulated SISO-OFDM system under AWGN by inserted PS4.At the target BER of  about 0.2 dB, 0.26 dB, 1.12 dB, 1.78 dB, and 2.89 dB SNR gains, respectively.