A Design of NLOS Communication Scheme Based on SC-FDE with Cyclic Suffix for UAV Payload Communication

Abstract

Non-line-of-sight (NLOS) communication with severe loss always leads to performance degradation in unmanned aerial vehicle (UAV) payload communication. In this paper, a UAV NLOS communication scheme based on single-carrier frequency domain equalization with cyclic prefix and cyclic suffix (CP/CS-SC-FDE) is designed. First, the reasons behind the generation of later intersymbol interference (LISI) in UAV NLOS communication are investigated. Then, the frame structure of conventional single-carrier frequency domain equalization with cyclic prefix (CP-SC-FDE) is improved, and the UAV NLOS communication frame structure based on cyclic prefix (CP) and cyclic suffix (CS) is designed. Furthermore, a channel estimation algorithm applicable to this scheme is proposed. The numerical results show that this UAV communication scheme can eliminate intersymbol interference (ISI) in NLOS communication. Compared with the conventional CP-SC-FDE system, this scheme can achieve excellent performance in the Rayleigh channel and other standard NLOS channels. In the CP/CS-SC-FDE system, the BER result is similar to that under ideal synchronization.

1. Introduction

Unmanned aerial vehicles (UAVs) have recently become research hotspots because they are widely applied not only in battlefields but also in commerce, industry, and public safety [1]. Wireless communication of UAV is a basic necessity and is normally categorized into control and non-payload communication (CNPC) as well as payload communication (PC) [2]. The former refers to communications between the UAV and ground base station (GBS) to ensure safe and reliable flight operation, which typically includes command and data, air traffic control data, and avoid data for UAV. The latter refers to all mission-related information transmission between UAV and GBS, such as aerial images, high-speed video, and data packets for relaying. Clearly, UAV CNPC desires high reliability, while UAV PC prefers a high data rate [3]. Single-carrier frequency-domain equalization (SC-FDE) is a technology commonly used in UAV payload communication. Compared with Orthogonal Frequency Division Multiplexing (OFDM), SC-FDE has the advantages of low peak-to-average ratio [4] and low transmission complexity [5], less sensitivity to frequency offset [6], and more energy efficiency [7], which is suitable for UAV communication. When combined with FFT processing and the use of a cyclic prefix (CP), SC-FDE can eliminate intersymbol interference (ISI) caused by multipath effects [8,9].

As a wireless communication system, the UAV PC must be affected by the multipath effect, which leads to performance degradation [10]. Multipath channel consists of line-of-sight (LOS) path and multiple non-line-of-sight (NLOS) path [11]. The LOS path is the direct path between the receiver and the transmitter. The NLOS path is the path reached by reflection and scattering. When the UAV flies at low altitude, the LOS path between the UAV and the ground station is easily blocked by buildings and trees, leading to non-line-of-sight (NLOS) communication [12,13,14]. There are significant differences between NLOS communication and LOS communication. In contrast to LOS communication, the power of the signal arriving through the LOS path in NLOS communication is very low and may even be zero. This means that the power of signals reached by other paths in NLOS communication accounts for a large proportion of the total signal power [15]. Then, the multipath effect of UAV NLOS communication is more significant, and the UAV communication performance degrades more seriously.

As is well known, the most common UAV channel model for LOS communication is the Ricean channel. For the NLOS case, the Rayleigh channel model typically provides a better fit [16,17,18]. A distinctive feature of the Rayleigh channel is that its path with maximum power (PwMP) may not be the first arrival path (FAP), which will cause time offset during synchronization and later intersymbol interference (LISI). The interpretation of LISI is that the decision of the current symbol is interfered with by later symbols. Experiments show that LISI will lead to a significant increase in the UAV communication bit error rate (BER). In a LOS channel, there is only preceding intersymbol interference (PISI), i.e., the decision of the current symbol is interfered with only by preceding symbols. PISI is known as ISI.

Inspired by the elimination of ISI, i.e., PISI, through CP, this paper eliminates LISI through cyclic suffix (CS). In [19,20,21], CS is applied to the super-Nyquist technology to eliminate interblock interference (IBI). These references did not analyze the principle of the CS and clarify the relationship between the CS and NLOS communication. Since PISI and LISI exist in NLOS communication, the SC-FDE NLOS communication scheme based on CP and CS for UAV PC is proposed in this paper. The main contributions of our work are given as follows.

(1)

We investigate the reason behind the generation of LISI in UAV NLOS communication. Moreover, the frame structure of conventional SC-FDE with CP (CP-SC-FDE) is improved, and we design an NLOS communication scheme based on SC-FDE with CP and CS (CP/CS-SC-FDE) for UAV PC. In addition, the scheme can be compatible with both LOS and NLOS communication.

(2)

A channel estimation algorithm applicable to this scheme is proposed, which can eliminate the ISI in UAV NLOS communication. Compared with the conventional CP-SC-FDE system, this scheme can achieve excellent performance in Rayleigh channel simulation. Moreover, the scheme does not need to eliminate the time synchronization offset but can achieve the same performance as the ideal synchronization.

The rest of the paper is organized as follows. Section 2 introduces the related works. Section 3 introduces the system model of CP-SC-FDE in UAV LOS communication. Section 4 presents the NLOS communication scheme based on CP/CS-SC-FDE for UAV PC. Numerical results are given in Section 5, and conclusions are given in Section 6.

2. Related Work

In [22], recognizing the fact that the maximal power path is not always the first path in channel impulse response (CIR), that is, there are paths with earlier arrival time but with weaker power, which results in ISI if the FFT window is not set ahead of them, it is suggested to bring forward the estimated time index by some amount. In order to eliminate the time synchronization offset, the key is to search for the FAP after capturing the PwMP. Existing methods can generally be classified into four categories [23]: Maximum Likelihood (ML) approaches [24], Matched Filter (MF)-based detectors [25,26], energy-based detectors [27,28,29] and machine learning-based approaches [30,31,32].

In [33], multipath components of measured waveforms are detected using a Maximum Likelihood (ML) detector. The ML estimator is theoretically asymptotically efficient, but its high computational complexity makes it challenging to implement. In [34], a three-step MF detection-based algorithm is proposed. First, the search region for FAP detection is determined; then, a rough detection of FAP is made by a threshold that is dynamically set using the MF output; last, a refined search process is carried out to obtain the precise location of the FAP. However, MF cannot perform satisfactorily in the low signal-noise ratio (SNR) region. In [28], to estimate the time of arrival in impulse radio ultra wideband ranging under harsh environments, the rank test is adopted in the study to detect the FAP in a dense multipath with energy detection receiver. In [35], the machine learning-based approaches are used to identify LoS and NLoS. They generally consist of data collection, feature extraction, model training and regression, which may have extremely high computational demand when the training data size becomes large. However, none of these methods can guarantee the accurate search of the first path; that is, they cannot completely eliminate the synchronization offset. Moreover, these methods add complexity to the system. Since LOS communication does not require searching FAP, computing resources will be wasted to be compatible with LOS communication.

In addition, to realize the communication in the NLOS scenario, UAV relay technology [36,37] and reconfigurable intelligent surfaces (RIS) technology [38,39] are also adopted. These two technologies require additional hardware to implement and are therefore not considered.

3. The System Model of CP-SC-FDE in UAV LOS Communication

The transceiver structure of CP-SC-FDE in UAV LOS communication is shown in Figure 1. At the transmitting end, the CP is appended before the preambles and data symbols, respectively. Then, in the framing module, they are grouped into a block. The receiver consists of modules for synchronization, channel estimation, and equalization. The synchronization module only considers time synchronization relevant to this study.

Let us consider a CP-SC-FDE system where preambles and data symbols, represented by vectors $\mathbf{p}={[p_0,\dots ,p_{M-1}]}^T$ and $\mathbf{x}={[x_0,\dots ,x_{N-1}]}^T$ respectively, are grouped into a block. M and N represent the length of the preambles and data symbols, respectively. Moreover, a CP of length C is appended to $\mathbf{x}$ and $\mathbf{p}$. Thus, a block can be represented as $\mathbf{s}=[p_{M-C},\dots ,p_{M-1}, p_0,\dots ,p_{M-1},$$x_{N-C},\dots ,x_{N-1}, x_0,\dots ,x_{N-1}{]}^T$, as shown in Figure 2. The preambles are used to perform time synchronization and channel estimation.

Assume that the multipath channel is $\mathbf{h}={[h_0,\dots ,h_{L-1}]}^T$, through which the resulting block is transmitted. L represents the length of the multipath channel and $h_i$ is the i-th path of the multipath channel. Moreover, the received signal is expressed as

$$r_n=\sum _{i=0}^{L-1}{h}_i{s}_{n-i}+v_n,n=0,\dots ,M+N+2C-1,$$

(1)

where $v_n$ is discrete thermal noise. At the receiver of UAV communication system, the local preambles are used to perform a sliding correlation with the received signal to complete the time synchronization. The sliding correlation result, with $v_n$ not considered, is represented as

$$\begin{array}{cc}\hfill u_n& =\sum _{j=0}^{M-1}{p}_j{r}_{n+j}\hfill \\ \hfill & =\sum _{j=0}^{M-1}{p}_j\sum _{i=0}^{L-1}{h}_i{s}_{n+j-i}\hfill \\ \hfill & =\sum _{i=0}^{L-1}{h}_i\sum _{j=0}^{M-1}{s}_{n+j-i}{p}_j,n=0,\dots ,N+2C-1.\hfill \end{array}$$

(2)

When $C\le n\le C+L-1$, $u_n$ can be represented as

$$\begin{array}{cc}\hfill u_n& =u_{C+l}\hfill \\ \hfill & =\sum _{i=0}^{L-1}{h}_i\sum _{j=0}^{M-1}{s}_{C+l+j-i}{p}_j\hfill \\ & =\sum _{i=0}^{L-1}{h}_i\sum _{j=0}^{M-1}{p}_{l+j-i}{p}_j\hfill \\ \hfill & =\sum _{\begin{array}{c}i=0\\ i\ne l\end{array}}^{L-1}{h}_i\sum _{j=0}^{M-1}{p}_{l+j-i}{p}_j+h_l\sum _{j=0}^{M-1}{p}_j{p}_j,0\le l\le L-1.\hfill \end{array}$$

(3)

If it is LOS communication, the PwMP of the multipath channel is the first path, i.e.,

$$h_0=max\left\{h_l|0\le l\le L-1\right\}.$$

(4)

According to the correlation property of the preambles, the correlation peak is

$$\begin{array}{cc}\hfill u_{max}& =max\left\{u_n|C\le n\le L-1+C\right\}=u_C,\hfill \end{array}$$

(5)

which corresponds to the start of the preambles. According to it, the CP is removed. Due to the CP, the discrete time-domain linear convolution is converted to discrete-time cyclic convolution, i.e.,

$$\begin{array}{cc}\hfill y_n& =\sum _{i=0}^{L-1}{h}_i{p}_{\left(n-i\right)modM}+v_n\hfill \\ \hfill & =h_n\otimes p_n+v_n,n=0,\dots ,M-1.\hfill \end{array}$$

(6)

It can be expressed as a matrix

$$\begin{array}{c}\hfill \mathbf{y}=\mathbf{Gp}+\mathbf{v},\end{array}$$

(7)

where $\mathbf{G}$ denotes the cyclic convolution matrix

$$\begin{array}{c}\hfill \mathbf{G}={\left[\begin{array}{cccccc}{h}_0\hfill & 0& \dots & 0& h_{L-1}& \dots \\ \dots \hfill & h_0& 0& \dots & 0& h_{L-1}\\ h_{L-1}\hfill & \dots & h_0& 0& \dots & 0\\ 0\hfill & h_{L-1}& \dots & h_0& 0& \dots \\ \dots \hfill & 0& h_{L-1}& \dots & h_0& 0\\ 0\hfill & \dots & 0& h_{L-1}& \dots & h_0\end{array}\right]}_{M\times M}.\end{array}$$

(8)

$\mathbf{G}$ is a right-circulant matrix [40], and each of its row vectors is a right-circulant shift of the previous row vector. The first column corresponds to the channel vector $\mathbf{h}$. In addition, according to the properties of the right circulant matrix, $\mathbf{G}$, $\mathbf{G}$ can be decomposed into

$$\mathbf{G}={\mathbf{F}}^H\mathbf{HF},$$

(9)

where ^H denotes the Hermitian transpose, $\mathbf{F}$ is the Discrete Fourier Transform (DFT) matrix, and $\mathbf{H}$ is a diagonal matrix with its eigenvalues given by

$$\mathbf{H}=diag\left(\mathbf{F}{[{\mathbf{h}}^T,{\mathbf{0}}_{1\times \left(M-L\right)}]}^T\right).$$

(10)

If the influence of noise is not considered, the time domain result of channel estimation using the preambles is ${[{\mathbf{h}}^T,{\mathbf{0}}_{1\times \left(M-L\right)}]}^T$.

4. The NLOS Communication Scheme Based on CP/CS-SC-FDE

4.1. CP-SC-FDE VS CP/CS-SC-FDE

In this subsection, the reason behind the generation of LISI in UAV NLOS communication is shown. Figure 3 shows the FFT regions of channel estimation and equalization in the LOS channel and the NLOS channel based on CP-SC-FDE. As is shown in part 2 of Figure 3, through a multipath channel, the received signal is a delayed superposition of the transmitted signal. In UAV LOS communication, corresponding to the blue CIR in part 1 of Figure 3, the PwMP of the multipath channel is the first path. As is shown in part 3 of Figure 3, $u_{max}=u_C$. Moreover, the FFT regions for channel estimation and equalization contain only information from the preambles, i.e., the preambles and the multipath channel satisfy cyclic convolution. Therefore, the receiver can achieve channel equalization correctly.

However, in UAV NLOS communication, corresponding to the red CIR in the part 1 of Figure 3, the PwMP of the multipath channel is not the first path. Assume that

$$h_1=max\left\{h_l|0\le l\le L-1\right\}.$$

(11)

Then,

$$u_{max}=u_{C+1},$$

(12)

which is shown in part 3 of Figure 3. In UAV NLOS communication, time synchronization occurs with an unavoidable time offset (TO). Moreover, the FFT region for channel estimation will introduce ISI from the later symbols of preambles, i.e., LISI, causing the preambles and the multipath channel not to satisfy the cyclic convolution. The channel equalization will be wrong.

Therefore, for UAV NLOS communication, we design a communication scheme based on CP/CS-SC-FDE, the block of which is shown in Figure 2. Figure 4 shows the FFT regions of channel estimation and equalization in the LOS channel and NLOS channel based on CP/CS-SC-FDE. As is shown in part 2 of Figure 4, even if the time synchronization occurs with an unavoidable TO in UAV NLOS communication, the channel estimation region will not introduce LISI as long as the length of the CS is larger than the TO. So, the preambles and multipath channel still satisfy the cyclic convolution. Moreover, the channel equalization will be right.

4.2. The Channel Estimation Algorithm of CP/CS-SC-FDE for UAV PC

In a CP/CS-SC-FDE system, assume that the length of the CS is D. Moreover, assume that in the multipath channel, the number of symbol intervals between the PwMP and the first and last path are E and F, respectively. C, D, E, and F satisfy

$$\left\{\begin{array}{c}C+D\le M\hfill \\ C\ge F\hfill \\ D\ge E\hfill \end{array}\right.$$

(13)

Then, $\mathbf{s}=[p_{M-C},\dots ,p_{M-1},p_0,\dots ,p_{M-1},p_0,\dots ,p_{D-1},x_{N-C}$$,\dots ,x_{N-1},x_0,\dots ,x_{N-1},x_0,\dots ,x_{D-1}{]}^T$. When $C\le n\le$$L+C-1$,

$$\begin{array}{cc}\hfill u_n& =u_{C+l}\hfill \\ \hfill & =\sum _{i=0}^{L-1}{h}_i\sum _{j=0}^{M-1}{s}_{C+l+j-i}{p}_j\hfill \\ \hfill & =\sum _{\begin{array}{c}i=0\\ i\ne l\end{array}}^{L-1}{h}_i\sum _{j=0}^{M-1}{p}_{l+j-i}{p}_j+h_l\sum _{j=0}^{M-1}{p}_j{p}_j,0\le l\le L-1.\hfill \end{array}$$

(14)

And,

$$\begin{array}{c}\hfill h_E=max\left\{h_l|0\le l\le L-1\right\}.\end{array}$$

(15)

Then,

$$\begin{array}{c}{u}_{max}=max\left\{u_n|C\le n\le L-1+C\right\}=u_{C+E},\hfill \end{array}$$

(16)

which corresponds to the start of the preambles. According to it, the CP and CS are removed. Due to the CP and CS, the discrete time-domain linear convolution is converted to discrete-time cyclic convolution, i.e.,

$$\begin{array}{c}\hfill {y^{\prime }}_n=\sum _{i=0}^{L-1}{h}_i{p}_{\left(n+E-i\right)modN}+v_n,n=0,\dots ,M-1.\end{array}$$

(17)

It can be expressed as a matrix

$$\begin{array}{c}\hfill {\mathbf{y}}^{\prime }={\mathbf{G}}_c\mathbf{p}+\mathbf{v},\end{array}$$

(18)

where the cyclic convolution matrix $\mathbf{G}$ of (7) becomes ${\mathbf{G}}_c$, i.e.,

$$\begin{array}{c}\hfill {\mathbf{G}}_c={\left[\begin{array}{ccccccccc}{h}_E\hfill & h_{E-1}& \dots & h_0& 0& \dots & 0& h_{L-1}& \dots \\ \dots \hfill & h_E& h_{E-1}& \dots & h_0& 0& \dots & 0& h_{L-1}\\ h_{L-1}\hfill & \dots & h_E& h_{E-1}& \dots & h_0& 0& \dots & 0\\ 0\hfill & h_{L-1}& \dots & h_E& h_{E-1}& \dots & h_0& 0& \dots \\ \dots \hfill & 0& h_{L-1}& \dots & h_E& h_{E-1}& \dots & h_0& 0\\ 0\hfill & \dots & 0& h_{L-1}& \dots & h_E& h_{E-1}& \dots & h_0\\ h_0\hfill & 0& \dots & 0& h_{L-1}& \dots & h_E& h_{E-1}& \dots \\ \dots \hfill & h_0& 0& \dots & 0& h_{L-1}& \dots & h_E& h_{E-1}\\ h_{E-1}\hfill & \dots & h_0& 0& \dots & 0& h_{L-1}& \dots & h_E\end{array}\right]}_{M\times M}.\end{array}$$

(19)

${\mathbf{G}}_c$ can be decomposed into

$$\begin{array}{c}\hfill {\mathbf{G}}_c={\mathbf{F}}^{\mathrm{H}}{\mathbf{H}}_c\mathbf{F},\end{array}$$

(20)

where ${\mathbf{H}}_c$ is a diagonal matrix with its eigenvalues given by

$$\begin{array}{c}\hfill {\mathbf{H}}_c=diag\left(\mathbf{F}{[h_E,\dots ,h_{L-1},{\mathbf{0}}_{1\times \left(M-L\right)},h_0,\dots h_{E-1}]}^T\right).\end{array}$$

(21)

If the influence of noise is not considered, the time-domain result of the channel estimation using the preambles is ${[h_E,\dots ,h_{L-1},{\mathbf{0}}_{1\times \left(M-L\right)},h_0,\dots ,h_{E-1}]}^T$, which is the cyclic shift of $\mathbf{h}$.

By determining that $E-i=-j$ in Formula (17), we obtain

$$\begin{array}{cc}\hfill {y^{\prime }}_n& =\sum _{j=0}^{L-1}{h}_{\left(E+j\right)modL}{p}_{\left(n-j\right)modM}+v_n\hfill \\ \hfill & =h_{n+E}\otimes p_n+v_n,n=0,\dots ,M-1.\hfill \end{array}$$

(22)

Moreover, it is converted to the frequency domain through a DFT, denoted by

$$\begin{array}{c}\hfill {Y^{\prime }}_k=H_k{P}_k+V_k,k=0,\dots ,M-1,\end{array}$$

(23)

where ${Y^{\prime }}_k$, $P_k$, $H_k$ and $V_k$ stand for the DFT of ${y^{\prime }}_n$, $p_n$, $h_{n+E}$ and $v_n$ respectively. In this CP/CS-SC-FDE system, the channel estimation algorithm is based on the frequency domain Least Square (LS) algorithm. Then,

$$\begin{array}{c}\hfill {\widehat{H}}_k={\displaystyle \frac{{Y^{\prime }}_k}{P_k}},k=0,\dots ,M-1,\end{array}$$

(24)

which is converted to the time domain through an inverse DFT (IDFT), denoted by

$$\begin{array}{c}\hfill {\widehat{h}}_n={\displaystyle \frac{1}{M}}\sum _{k=0}^{M-1}{\widehat{H}}_k{e}^{j2\pi {\displaystyle \frac{nk}{M}}},n=0,\dots ,M-1,\end{array}$$

(25)

Once the channel estimation for the preamble position is obtained, the channel estimation for the data position is calculated through an interpolation algorithm, i.e.,

$$\begin{array}{c}\hfill {\widehat{\mathbf{h}}}_d={[{\widehat{h}}_0,\dots ,{\widehat{h}}_{C-1},{0_1}_{\times \left(N-C-D\right)},{\widehat{h}}_{M-D},\dots ,{\widehat{h}}_{M-1}]}^T.\end{array}$$

(26)

Let ${[{\widehat{\mathbf{h}}}_d]}_n$ denote the n-th element of ${\widehat{\mathbf{h}}}_d$. The pseudocode of the channel estimation algorithm is shown in Algorithm 1.

Algorithm 1 Channel estimation algorithm of CP/CS-SC-FDE

Input: ${y^{\prime }}_n$, $P_k$;

Output: ${\widehat{\mathbf{h}}}_d$;

1: Perform an M-point DFT transformation on ${y^{\prime }}_n$;

2: Obtain the channel frequency response Using LS estimation ${\widehat{H}}_k={\displaystyle \frac{{Y^{\prime }}_k}{P_k}}$;

3: Obtain ${\widehat{h}}_n$ by performing an M-point IDFT transformation on ${\widehat{H}}_k$;

4: Set ${[{\widehat{\mathbf{h}}}_d]}_n=0,n=0,\dots ,N-1$;

5: for all $n=0,1,\cdots ,N-1$ do

6:  if $n\le C-1$ then

7:   ${[{\widehat{\mathbf{h}}}_d]}_n={\widehat{h}}_n$;

8:  else if $n\ge N-D$ then

9:   ${[{\widehat{\mathbf{h}}}_d]}_n={\widehat{h}}_{M-\left(N-n\right)}$;

10:  end if

11: end for

12: return ${\widehat{\mathbf{h}}}_d$.

5. Numerical Results

5.1. Simulation Results of Time Synchronization Offset and Channel Estimation in LOS and NLOS Channels

In the first simulation, we evaluate the impact of the LOS and NLOS channels on the time synchronization offset, as well as the results of channel estimation in CP/CS-SC-FDE.

Table 1. Simulation parameters.

Parameters	Settings
Modulation type	QPSK
Preambles type	Zadoff–Chu Sequences
The length of preambles (M)	128
The length of data (N)	1024
FFT Size	128/1024
The length of CP (C)	64
The length of CS (D)	0 or 64
Channel Model	Rice/Rayleigh fading channel with 8 non-zero taps
$E_b/N_0$	20 dB

contains the parameters and respective settings of the simulations.

The channel considered includes a LOS UAV channel and two NLOS UAV channels, corresponding to channels 1, 2, and 3, respectively. The LOS UAV channel is an outcome of the Rice fading channel. The two NLOS UAV channels are outcomes of the Rayleigh fading channel. The channel is assumed constant during a transmission block in all the results. The CIRs of three channels are shown in Figure 5. As seen from Figure 5, each of the three channels has 8 non-zero taps. Channel 1 is the LOS channel, whose PwMP is the first path. Channel 2 and channel 3 are NLOS channels whose PwMPs are the middle and last paths, respectively. The selection of three channels is very representative. Moreover, the key parameters of these three channels are shown in

Table 2. Simulation parameters.

Parameters	Channel 1	Channel 2	Channel 3
E	0	28	60
F	51	32	0
$u_{max}$	$u_C$	$u_{92}=u_{C+28}$	$u_{124}=u_{C+60}$

.

The sliding correlation values for time synchronization under these three channels are presented in Figure 6. As shown in Figure 6, in channel 1, the correlation peak is $u_C$, which corresponds to the synchronization point $C=$ 64, and there is no TO. Under channels 2 and 3, the correlation peak is $u_{C+E}$, which corresponds to the synchronization point $C+E=$ 92 and 124, and there is a TO, which is equal to E. The results of $u_{max}$ are also shown in Table 2. Therefore, there is no TO under the LOS UAV channel, whereas there is a TO with the value E under the NLOS UAV channel.

Figure 7 shows the channel estimation results in a CP-SC-FDE system. Due to the TO in the CP-SC-FDE system, the FFT region of channel estimation and equalization will introduce LISI. Comparing Figure 5 and Figure 7, it can be seen that there is an error in the channel estimation in the CP-SC-FDE system. As a comparison, Figure 8 shows the channel estimation result in a CP/CS-SC-FDE system. We can observe that the channel estimation is the cyclic shift of the channel in Figure 5 as deduced in Section 3. In channel 1, E = 0, and the channel estimation result has no cyclic shift. In channel 2, E = 28, and the channel estimation result corresponds to a 28-point cyclic shift. In channel 3, E = 60, and the channel estimation result corresponds to a 60-point cyclic shift.

5.2. BER in Several Classes of NLOS Channels

In the second simulation, we first assess the performance of CP/CS-SC-FDE compared with CP-SC-FDE in the Rayleigh fading channel. The simulation parameters are shown in Table 1. The value of $E_b/N_0$ is from 0 to 18 dB. The simulation result is shown in Figure 9. As a reference, the curve of ideal synchronization is also shown. Ideal synchronization means that although PwMP is not the FAP, the synchronization offset caused by NLOS will be manually eliminated. This is equivalent to an accurate search for FAP. Since the FAP searching algorithms in [28,33,34,35] cannot search the FAP accurately, the BER performance of these algorithms must not be as good as that of ideal synchronization. The optimal performance can be achieved under ideal synchronization, so the performance of CP-SC-FDE and CP/CS-SC-FDE systems is investigated and compared with the curve of ideal synchronization in this simulation. According to the above theoretical analysis, CP/CS-SC-FDE can still achieve the same performance as ideal synchronization without eliminating TO. As seen in Figure 9, when the channel is a Rayleigh channel, due to the LISI caused by TO, the BER is poor in the CP-SC-FDE system. On the contrary, in the CP/CS-SC-FDE system, since LISI is eliminated, the BER result is similar to that under ideal synchronization.

Then, we assess the performance of CP/CS-SC-FDE compared with CP-SC-FDE in the COST207-BU channel with 12 non-zero taps and TDL-C channel with 24 non-zero taps, respectively. The COST207-BU channel represents the bad urban scenario from the COST 207 channel model standard [41]. The TDL-C channel represents the bad NLOS scenario from the 3GPP channel model standard [42]. The COST207-BU channel and TDL-C channel are NLOS channels, where the PwMP is not the FAP. The simulation parameters are shown in Table 1. The value of $E_b/N_0$ is from 0 to 33 dB. The simulation result is shown in Figure 10. The BER curves of ideal synchronization in COST207-BU and TDL-C channels are also shown as a reference. As seen in Figure 10, the BER is poor in the CP-SC-FDE system. On the contrary, in the CP/CS-SC-FDE system, the BER result is similar to that under ideal synchronization.

6. Conclusions

To improve the performance of NLOS communication for UAV payload communication, we design an NLOS communication scheme based on CP/CS-SC-FDE. We first investigate the reason behind the generation of LISI in NLOS communication. The simulation shows that under the NLOS channel, there is a time offset with the value E, i.e., the number of symbol intervals between the PwMP and the first path, which causes the LISI in NLOS communication. Then, the frame structure of conventional SC-FDE with CP (CP-SC-FDE) is improved, and the UAV NLOS communication scheme based on CP/CS-SC-FDE is designed. Furthermore, a channel estimation algorithm applicable to this scheme is proposed. The numerical results show that this communication scheme can eliminate the ISI in NLOS communication. Compared with the conventional CP-SC-FDE system, this scheme can achieve excellent performance in the Rayleigh channel, COST207-BU channel, and TDL-C channel. In the CP/CS-SC-FDE system, the BER result is similar to that under ideal synchronization. Therefore, this NLOS communication scheme based on CP/CS-SC-FDE can be applied to UAV payload communication in an NLOS scenario where the LOS path is blocked.