# A Full-Duplex MIMO System Based on CP-Free OFDM in Sensor Network

Authors: Hao Jiang; Hongming Chen
Journal: Journal of Sensors
 (2022)

---

## Abstract

Recently, results have shown that full-duplex (FD) system based on orthogonal frequency division multiplexing (OFDM) is potential for wireless sensor networks. However, extending FD to further improve spectral efficiency by removing cyclic prefix (CP) with optimal canceling self-interference (SI) remains a challenge. In this paper, we analytically study the conventional FD OFDM system and proposed a CP-free system on this basis. The key point of the proposed scheme is the symbols transmitted in a unit of two identical symbols without CP. To eliminate the intersymbol interference, the disturbed part are replaced by the repeated signal at the receiver, which has the same effect as CP. Finally, an SI cancellation is down to restore the transmitted symbols. As a key of analysis, a multiple-input multiple-output (MIMO) FD simulation model is carried to show that our proposed scheme is effectiveness in terms of the bit error ratio (BER).


---

## Body

## 1. Introduction

As the artificial intelligence (AI) advanced, AI techniques are further combined with Internet of Things (IoT), which emerges a technology, namely, AI IoT (AIoT). During the technology, the ability to continuously collect, elaborate data, and integrate with participatory sensing is needed [1]. Seasonably, the interactive and shareable wireless sensor network (WSN) system that can meet the above requirements has been the one of the basic factors of the technology [2].The basic function of WSN is to sense data in small to large networks through sensor nodes and collect information to process any application. It also has a wide range of different platforms, which corresponds to the application of IoT, with the result that WSN will be the best sensor interfacing device in the IoT environment [2]. However, the current sensor equipment and wireless communication technology are not complete [3], which make traditional WSN difficult to achieve the delay and minimize power consumption requirement of the next generation’s communication system. The full duplex (FD) makes this possible by improved uplink/downlink delay at WSN without an additional energy price. FD is capable of simultaneously transmitting and receiving signals at the same carrier frequency, and it can have twice as high spectral efficiency (SE) in theory in comparison to the traditional communications, which has the advantage of facing the shortage of wide continuous spectrum below 6 GHz [4]. Nevertheless, in widely FD orthogonal frequency division multiplexing (OFDM) systems, cyclic prefix (CP), the one in charge of eliminating the interference, decreases the SE [5]. Through the literature, several attempts have been made to enhance the SE, and [5–7] aim to reduce the CP without distortion. However, due to imposition of the local transmitter signal on the local receiver, the strong self-interference (SI) also blocks the SE [8], and none of the designs [5–7] managed to remove CP in FD systems. Therefore, our focus in this paper is to design CP-free FD system while limit the effect of SI.In this paper, we propose a CP-free OFDM FD multiple-input multiple-output (MIMO) system. Comparing with the conventional system, the scheme can further improve the spectral efficiency while digital SI can be optimally canceled, which makes WSN more in line with the requirements of next-generation communication. Additionally, the effect of multipath channel on the signal is also eased.


## 2. Conventional Full-Duplex OFDM Model

In this section, a full-duplex MIMO communication system based on OFDM is shown in Figure1, where discrete Fourier transform (DFT), radiofrequency (RF), and SI elimination modules compose the system. Without loss of generality, we consider a signal RF chain to illustrate the process. The baseband signal with inserted CP at the local transmitter of the base station (BS) can be written as
(1)Xk=1M∑m=0M−1xmej2πmk/M,k=−Ncp,⋯,M−1,where xm is the transmitted symbol at the mth subcarrier with M being the total number of subcarriers and Ncp is the length of CP.Figure 1
A system model of full-duplex OFDM transceiver.After transforms the digital symbolsXk into the time domain signal xt. Then, xt can be upconverted into the local RF transmit signal by mixing with the transmitter oscillator, and the RF signal x~t is obtained as
(2)X~1t=xtej2πfct,where fc denotes the carrier frequency.Before providing the model for the received signal, it should be noted that the RF signalX~1t is transmitted to the users while the antenna of the base station also receives the local RF signal, which is a strong SI signal for the receiver signal. Consequently, the received RF signal at BS consists of the imposing SI signal from local transmitter and the signal-of-interest (SoI) from the users. Then, it can be given as
(3)y~mt=∑s=1Nshs,r1t∗X~1t+hs,r21t∗X~21t+nt,where Ns is the number of antennas, hs,r1t is the SI channel between the sth transmit antenna and rth receive antenna, ∗ denotes the convolution, hs,r21t is the multipath SoI channels, X~21t is the time domain signal form users, and nt is the receiver circular symmetric complex Gaussian (CSCG) noise with zero mean and variance σ2.In the sequel,y~mt downconverted to the baseband, and it is defined as
(4)ymt=y~mte−j2πfct.Following downconversion, in order to restore the signal, CP is removed and DFT is performed on the signalymt, from which we can get the equation as
(5)Ymk=1M∑s=1NsHs,r1kX1k+MHs,r21xm21+Nk,where Hs,r1k=0M−1 are the SI channel frequency response, X1kk=0M−1 are digital symbols of the transmitter from the local BS, and xm21 are the symbols from the user. Correspondingly, Hs,r21 is the frequency domain SoI channel. Then, equation (5) can be rewritten as
(6)Ymk=YmSI+Hs,r21xm+Nk,where YmSI is the SI signal. Naturally, the SoI signal can be recovered as
(7)YmSoI=Ym−YmSI,where YmSoI is the digital frequency domain SoI symbol.


## 3. CP-Free Scheme

### 3.1. System Model

In this section, as is shown in Figure2, a CP-free scheme is introduced, which consists of several identical symbols. Without loss of generality, two identical symbols that are treated as a unit in this figure, we assumed, transmit at the same index of subcarrier, i.e., symbols at the mth subcarrier repeat transmission twice. It is obvious that CP is removed, which leads to the enhanced spectral efficiency.Figure 2
Structure of the proposed unit with two identical symbols.At the transmitter, the baseband transmitted signal of a unit can be written as(8)sk=1M∑m=0M−1xmej2πmk/M,k=0,⋯,2M−1.Obviously,sk is transmit without CP.Then, the transmitted signal is transformed into the time domain signalst by digital-analog converter and upconverted into the local RF signal by means of the oscillator, which is the same as the conventional scheme, and the RF signal can be given as
(9)S~1t=stej2πfct.At the receiver, the received signal also consists of the SI signal that is obtained byS~1t passing through the multipath channel directly and the SoI signal form the users. Then, the received time domain signal goes downconverted from the carrier frequency and it becomes
(10)r~t=∑s=1Nshs,r1t∗S~1t+hs,r21t∗S~21te−j2πfct+nt,where S~21t is the SoI signal. Then, with analog-to-digital converter, the analog signal r~t is transformed into digital signal r~k.As we know, CP is aimed at removing the interference which is caused by the multipath channel, without which a great increase of bit error ratio (BER) may happen. Therefore, to eliminate the effect of multi-path channel, in the proposed scheme, as shown in Figure3, the signal r~k, k=0,1,⋯,Ncp−1 is replaced by the signal r~k, k=M,1,⋯,M+Ncp−1. Then, the signal can be obtained as
(11)rk=r~k+M,ifk=0,1,⋯,Ncp−1,r~k,ifk=Ncp,Ncp+1,⋯,2M−1.Figure 3
Illustration of signal replacement to construct the circular convolution structure.We turn the SoI channel into the circular convolution structure which has the same effect as adding CP by (11). Later, carry out a 2M-point DFT on rk, and it is thus given as
(12)Ym0k=12M∑s=1NsH~s,r1kXm01k+2MH~s,r21xm021+N~k,where H~s,r1kk=02M−1 is the 2M-point DFT of the discrete SI channel, Xm01k=02M−1 is the SI digital symbols from the Node 1 with m0=2m, H~s,r21=∑k=02M−1hs,r21e−j2πlk/2M is the 2M-point of the lth tap SoI channel, and xm021 is the SoI symbol with m0=2m. It is obvious that 2M-point DFT change the subcarrier index of the symbols.Subsequently, the SoI signal can be restored after canceling the SI signal and is given as(13)Y~m0SoI=Y~m0−Y~m0SI=H~s,r21xm021+N~k.It should note that the received signalY~m0SoI contains the transmitted symbol at m0=0,2,⋯,2M−1th subcarrier. Therefore, the symbols can be restored by performing a 2-point downsampling on Y~m0SoI, and it is given by
(14)φm=Y~2mSoI,m=0,1,⋯,M−1.Finally, the SoI symbol can be restored by channel equation when channel is available at the receiver. The proposed CP-free scheme model is shown at the top this page.In the following content, we focus on the SI estimation. According (12), the matrix from of the received signal is given as
(15)ym0=∑s=1NsXFhs,r1+ym0SoI+n,where X=diagX0,X1,⋯,2M−1 is symbol matrix of the SI digital signal from Node 1, hs,r1=hs,r10,hs,r11,⋯,hs,r12L−1T is the SI channel impulse vector, ym0SoI=Y~2mSoI0,Y~2mSoI1,⋯,Y~2mSoI2M−1T is the SoI vector, n=N~0,N~1,⋯,N~2M−1T is the additive CSCG noise vector, and Fm,k=e−j2πmk/2M is a discrete fourier transform matrix. Note that ·T is transpose.According to [9], a weighted linear SI channel estimator can be given as
(16)h^s,r1=WXFhs,r1+Wym0SoI+Wn,where W is the weight matrix which is used for minimized the residual SI power. Then, the recovered SoI is obtained as
(17)y^m0SoI=ym0−XFh^s,r1.When the optimalh^s,r1 is obtained, the residual SI power can be further reduced. The system flow of the proposed scheme is shown in Figure 4.Figure 4
Block diagram of full-duplex CP-free scheme.


### 3.2. Noise Power

SinceN~k has a effect on BER, the correlation processing for the noise is addressed in detail.In (13), h^s,r1 is channel noise which is Gaussian vector with zero mean and variance σ2 after DFT. The noise can be expressed as
(18)N~=12M∑k=02M−1nke−2jπmk/2M.The mean ofN~ is given as
(19)EN~=E12M∑k=02M−1nke−2jπmk/2M=0,where E· stands for the expectation operation.Then, the variance ofN~ is given by
(20)VarN~=EN~2−EN~2=E12M∑k=02M−1nke−2jπnk/2M2=12ME∑k=0Ncp−1nk+M+∑k=Ncp2M−1nke−2jπnk/2M2.Since channel noisenk follows Gaussian distribution, the following equation can be rewritten according to that Enkn∗m=0 when k≠m [5], i.e.,
(21)VarN~=σ2+12ME∑k=0Ncp−1ηk+M2ej2πm/2+e−j2πm/2=σ2+2Ncpσ22Mcosπm.Finally, profiting from the above attributes, we can draw a conclusion thatN~ satisfies the complex Gaussian distribution with mean zero and variance σ2+Ncpσ2/Mcosπm.


## 3.1. System Model

In this section, as is shown in Figure2, a CP-free scheme is introduced, which consists of several identical symbols. Without loss of generality, two identical symbols that are treated as a unit in this figure, we assumed, transmit at the same index of subcarrier, i.e., symbols at the mth subcarrier repeat transmission twice. It is obvious that CP is removed, which leads to the enhanced spectral efficiency.Figure 2
Structure of the proposed unit with two identical symbols.At the transmitter, the baseband transmitted signal of a unit can be written as(8)sk=1M∑m=0M−1xmej2πmk/M,k=0,⋯,2M−1.Obviously,sk is transmit without CP.Then, the transmitted signal is transformed into the time domain signalst by digital-analog converter and upconverted into the local RF signal by means of the oscillator, which is the same as the conventional scheme, and the RF signal can be given as
(9)S~1t=stej2πfct.At the receiver, the received signal also consists of the SI signal that is obtained byS~1t passing through the multipath channel directly and the SoI signal form the users. Then, the received time domain signal goes downconverted from the carrier frequency and it becomes
(10)r~t=∑s=1Nshs,r1t∗S~1t+hs,r21t∗S~21te−j2πfct+nt,where S~21t is the SoI signal. Then, with analog-to-digital converter, the analog signal r~t is transformed into digital signal r~k.As we know, CP is aimed at removing the interference which is caused by the multipath channel, without which a great increase of bit error ratio (BER) may happen. Therefore, to eliminate the effect of multi-path channel, in the proposed scheme, as shown in Figure3, the signal r~k, k=0,1,⋯,Ncp−1 is replaced by the signal r~k, k=M,1,⋯,M+Ncp−1. Then, the signal can be obtained as
(11)rk=r~k+M,ifk=0,1,⋯,Ncp−1,r~k,ifk=Ncp,Ncp+1,⋯,2M−1.Figure 3
Illustration of signal replacement to construct the circular convolution structure.We turn the SoI channel into the circular convolution structure which has the same effect as adding CP by (11). Later, carry out a 2M-point DFT on rk, and it is thus given as
(12)Ym0k=12M∑s=1NsH~s,r1kXm01k+2MH~s,r21xm021+N~k,where H~s,r1kk=02M−1 is the 2M-point DFT of the discrete SI channel, Xm01k=02M−1 is the SI digital symbols from the Node 1 with m0=2m, H~s,r21=∑k=02M−1hs,r21e−j2πlk/2M is the 2M-point of the lth tap SoI channel, and xm021 is the SoI symbol with m0=2m. It is obvious that 2M-point DFT change the subcarrier index of the symbols.Subsequently, the SoI signal can be restored after canceling the SI signal and is given as(13)Y~m0SoI=Y~m0−Y~m0SI=H~s,r21xm021+N~k.It should note that the received signalY~m0SoI contains the transmitted symbol at m0=0,2,⋯,2M−1th subcarrier. Therefore, the symbols can be restored by performing a 2-point downsampling on Y~m0SoI, and it is given by
(14)φm=Y~2mSoI,m=0,1,⋯,M−1.Finally, the SoI symbol can be restored by channel equation when channel is available at the receiver. The proposed CP-free scheme model is shown at the top this page.In the following content, we focus on the SI estimation. According (12), the matrix from of the received signal is given as
(15)ym0=∑s=1NsXFhs,r1+ym0SoI+n,where X=diagX0,X1,⋯,2M−1 is symbol matrix of the SI digital signal from Node 1, hs,r1=hs,r10,hs,r11,⋯,hs,r12L−1T is the SI channel impulse vector, ym0SoI=Y~2mSoI0,Y~2mSoI1,⋯,Y~2mSoI2M−1T is the SoI vector, n=N~0,N~1,⋯,N~2M−1T is the additive CSCG noise vector, and Fm,k=e−j2πmk/2M is a discrete fourier transform matrix. Note that ·T is transpose.According to [9], a weighted linear SI channel estimator can be given as
(16)h^s,r1=WXFhs,r1+Wym0SoI+Wn,where W is the weight matrix which is used for minimized the residual SI power. Then, the recovered SoI is obtained as
(17)y^m0SoI=ym0−XFh^s,r1.When the optimalh^s,r1 is obtained, the residual SI power can be further reduced. The system flow of the proposed scheme is shown in Figure 4.Figure 4
Block diagram of full-duplex CP-free scheme.


## 3.2. Noise Power

SinceN~k has a effect on BER, the correlation processing for the noise is addressed in detail.In (13), h^s,r1 is channel noise which is Gaussian vector with zero mean and variance σ2 after DFT. The noise can be expressed as
(18)N~=12M∑k=02M−1nke−2jπmk/2M.The mean ofN~ is given as
(19)EN~=E12M∑k=02M−1nke−2jπmk/2M=0,where E· stands for the expectation operation.Then, the variance ofN~ is given by
(20)VarN~=EN~2−EN~2=E12M∑k=02M−1nke−2jπnk/2M2=12ME∑k=0Ncp−1nk+M+∑k=Ncp2M−1nke−2jπnk/2M2.Since channel noisenk follows Gaussian distribution, the following equation can be rewritten according to that Enkn∗m=0 when k≠m [5], i.e.,
(21)VarN~=σ2+12ME∑k=0Ncp−1ηk+M2ej2πm/2+e−j2πm/2=σ2+2Ncpσ22Mcosπm.Finally, profiting from the above attributes, we can draw a conclusion thatN~ satisfies the complex Gaussian distribution with mean zero and variance σ2+Ncpσ2/Mcosπm.


## 4. Simulation Results

In this section, simulations result under i.i.d complex normal noise are carried out to analyze the CP-free scheme, in terms of BER. An OFDM-modulated FD communication system is simulated withM=64 subcarriers in each OFDM symbols to carry binary phase shift keying (BPSK) data, and the carrier frequency Δf is set to 15 kHz. Therefore, the sample time is 1/Δf·M=1×10−6. Other parameters are set as follows: the OFDM CP Ncp=M/4=16 and the total transmit antennas Ns=64. To adapt to the typical attenuation value provided by the simulated cancellation [10], the SI channel’s Rician factors are set to 30 dB and the Rayleigh channel is considered with a power-delay profile of 0, -5, -10, -15, and -20 dB for delays of 0th, 1st, 2nd, 3rd, and 4-th taps.The BER is depicted in Figure5 under complex normal noise and the signal-to-noise ratio (SNR) is defined as SNR=1/N0, where N0 is the power of noise. The observations above have shown that the proposed CP-free OFDM suffer from some degradation compared to the conventional scheme. The reasons are summarized in the following. From (21), the power of noise increases due to the signal replacement. More precisely, the noise becomes correlated from i.i.d, which leads to the increase of noise variance.Figure 5
BER of the proposed CP-free scheme and the classical scheme.In summary, the proposed scheme eliminate the intersymbol interference and improved the spectrum efficient while it sacrifices BER.


## 5. Conclusion

In this paper, we concentrated on the CP elimination in a FD MIMO communication system based on OFDM. A novel CP-free scheme was designed in a way that the spectral efficiency is improved. By utilizing duplication and replacement symbol to construct the circular convolution structure of the transmitted signal and channels without interference at the receivers, the system could eliminate the effect of multipath channel as CP. All the CP are removed, which led to an increase in spectral efficiency. Monte Carlo simulation has been carried out to show the comparison with classical work in BER and verify the effectiveness of our proposed scheme.



---

*Source: 6888809-2022-07-11.xml*