1. Introduction
Driven by the explosive surge of Internet of Things (IoT) services for sixth-generation (6G) mobile communications systems, different new 6G use cases have been proposed and are under intensive research discussion recently, such as IoT industry automation, maritime machine-type communication networks, and other applications [
1,
2]. As one of the key technologies to achieve the vision of the Internet of Everything, UAVs have been widely used to perform diversified tasks [
3,
4,
5] due to their low cost and flexible deployment.
There has been a recent surge of studies on the use of UAVs for IoT communication [
6,
7,
8], such as data collection [
9,
10] and mobile edge computing [
11]. However, with the dramatic increase in the number of connected machines, the number of IoT devices deployed worldwide is expected to grow to 75.4 billion by 2025 [
12]. There is a growing demand for low complexity and high power efficiency in UAV-aided IoT communication due to the limited payload of the devices.
Continuous phase modulation (CPM) is suitable for power- and bandwidth-limited systems because of its good spectral efficiency and its higher power efficiency relative to linear modulations with comparable spectral efficiency. Moreover, the constant envelope property of CPM allows the nonlinear power amplifier (PA) to be operated at a high efficiency, which further increases the power efficiency of the system [
13]. For battery-powered IoT nodes and UAVs, energy efficiency and cost are key factors because these devices are difficult to recharge or recycle once depleted. Therefore, CPM is one of the preferred modulation schemes in UAV-aided IoT communications systems due to its favorable low power consumption, which can greatly increase the life of terminal devices.
However, CPM transmission over multipath fading channels is a challenging task due to the high computational complexity in the receiver. If the design of the waveform is poor, it will reduce the overall power of the communications systems, even offsetting the increased power efficiency achieved by the PA. Therefore, we focus our attention on the receiver design at the physical layer for CPM over frequency-selective channels employing low data rates and short bursty transmissions, which is a fundamental tool to implement UAV-aided IoT. In general, the main contributions of this paper include the following:
We combed the literature related to CPM and summarized it in the
Table 1.
To meet the demands of low data rates and short-burst transmission scenarios of the UAV-aided IoT system, a short burst structure of CPM is designed in this paper, and a link-level simulation platform of the communications system is established on this basis.
A low complexity approach for soft-input soft-output (SISO) blind equalization is proposed to achieve a fast and accurate blind equalizer in the UAV-aided IoT system. The first step utilizes the soft-output Lazy Viterbi algorithm instead of the Viterbi algorithm to perform the expectation step and obtain a low complexity expectation–maximization Lazy Viterbi algorithm (EMLVA), while the second step applies the BCA method to establish a set of initializers, denoted as the BCA initializers, which achieves a high global convergence probability.
The blind turbo equalization for short-burst CPM is proposed based on the new SISO blind equalization with iterative detection, where the blind equalizer and decoder exchange extrinsic information in the form of log-likelihood ratios (LLRs). To further improve the convergence of iteration and reduce the average iteration number, the decision-aided (HDA) algorithm based on weighted extrinsic information exchange is proposed.
The blind turbo equalization based on EMLVA is proposed and evaluated on a link-level simulation platform. Simulation results show that EMLVA can obtain a good trade-off between complexity and BER performance. When the HDA with weighted extrinsic information is applied, the convergence of iterative detection and real-time performance can be further improved.
The rest of this paper is organized as follows.
Section 2 provides related work on the channel estimation and equalization of CPM transmission over frequency-selective channels. In
Section 3, the burst structure, communications system, and channel model are designed and formulated for typical UAV-aided IoT communications scenarios. The new low-complexity blind equalization based on EMLVA, as well as the turbo scheme are introduced and described in
Section 4. The performances of the proposed turbo blind equalizer are evaluated and analyzed based on the link-level simulation platform in
Section 5. In
Section 6, we discuss the application prospects of reflecting intelligent surfaces (RISs) in UAV-aided IoT communications systems. Finally, the paper is concluded in
Section 7.
2. Related Work
In practical communications, the signals are transmitted over the fading channel and the channel response is unknown. In [
14], a generalized pilot symbol-aided demodulation method based on the idea of inserting data-dependent symbols periodically was proposed for CPM in a flat Rayleigh fading channel. An optimal front-end filter was developed based on the mean-squared error (MSE) in the channel estimation process. Then, the channel estimates generated by the interpolation filter, together with the received signal, are input into a coherent CPM demodulator using the Viterbi algorithm. In frequency-flat fast-fading channels, Ref. [
15] provided a data-aided channel estimation algorithm with local B-splines, and the results showed that there exists a minimum sampling interval proportional to the normalized fading rate for pilot insertion. However, when short bursts are considered, the data-aided channel estimation method can significantly increase the overhead-to-payload ratio. Similarly, low-complexity frequency-domain equalization for CPM [
27,
28,
29] requires the addition of a cyclic prefix or unique words, which can also increase the overhead-to-payload ratio for short bursts.
As an alternative, blind channel equalization can recover the signal directly, without a training sequence. The author in [
16] applied the Tong–Xu–Kailath algorithm to CPM by extracting the second-order statistics of the signal for channel estimation. The eigenvector method was used to identify the channel from a fourth-order cross-cumulant matrix under the GSM channel in [
17], combined with turbo estimation. However, when applied to a low number of symbols, the statistical moments did not provide accurate channel estimation. In [
18,
30], the author developed a nonlinear signal model for GMSK rather than the conventional finite impulse response model. The information symbols were obtained by Bayesian inference based on Markov chain Monte Carlo (MCMC) with implicit channel estimation.
CPM and the multipath channel can construct a joint trellis, which can be represented by a finite state machine (FSM). Therefore, a forward adaptive SISO (FA-SISO) [
19], which considers the channel correlation in only one direction, was proposed for MSK, which replaces the unknown channel by the least-mean-squared error for each hypothesis branch symbol. Then, due to the high complexity of FA-SISO, the author in [
20] proposed various reduced-state A-SISO (RS-A-SISO) algorithms for complexity reduction at the same time. The thresholds of the RS-A-SISO algorithms were obtained by the density evolution technique in [
21]. Another structure is the forward/backward adaptive algorithm. An exact expression for the soft metrics was derived when the unknown parameter was modeled as a Gauss–Markov process in [
22], which can be estimated iteratively by the Kalman filter. The author in [
23] employed the concept of bidirectional estimation in [
22] and derived a generalized a posteriori probability of soft branch metrics.
The FSM can also be described by a hidden Markov model (HMM), and the Baum–Welch (BW)/EM algorithm allows for great likelihood estimation of the unknown parameters in the HMM. The batch-BW (BBW) algorithm, as well as two variants were proposed by Carles [
24] for time-invariant channels. One is to split the received signal into several sub-blocks, producing different channel estimates in each, called the segmented batch-BW (SBBW) algorithm. However, the variant needs to avoid over-fragmentation because of a poor estimate from fewer data. An alternative algorithm called time-dependent BW (TDBW) was derived by introducing some linear constraints emerging from a linear FIR hypothesis on the channel. The author in [
25] proposed an improved Baum–Welch algorithm to directly estimate the channel parameters, avoiding over-parameterization in the estimation problem. In [
26], an algorithm for joint channel estimation and equalization by applying the Viterbi algorithm within an EM iteration was introduced, which was used to implement the E-step. However, the major drawbacks among the works cited above are relatively poor convergence with an inappropriate initializer and high complexity.
CPM serves as one of the preferred modulation schemes for the transmission of low data rates in the IoT uplink, suffering from the high complexity and poor convergence of the channel estimation at the receiver. Therefore, the paper proposes a low-complexity blind equalization algorithm for short-burst CPM signals based on the HMM. The proposed blind equalizer significantly outperforms the traditional one in complexity, while keeping a similar BER performance, which helps the device achieve online real-time detection. In general, as the spectrum resources are limited and the number of connected devices is increasing day by day, CPM is a promising modulation scheme, which is suitable for battery-powered devices and is expected to play an important role in the physical layer design of UAV-aided IoT communications.
4. EMLVA for Blind Channel Equalization
4.1. EM Algorithm
The EM algorithm is divided into two steps, one of which is the expectation step (E-step) and the other is the maximization step (M step). For a blind equalization problem, the observations and transmitted symbols can be written as a new data vector . The EM algorithm then consists of the following iteration.
E-step: Compute the mean log-likelihood function:
where
represents a conditional probability density.
M step: Compute new estimates of parameters:
4.2. VA and Its Variants
The Viterbi algorithm (VA) was proposed in 1967 for maximum likelihood (ML) detection of convolutional codes, searching for the ML paths by dynamic programming. At each symbol duration, the path metrics of all paths entering the current state are compared by the VA, and the path with the largest metric is selected for that state, called the survivor path. Finally, the VA outputs the information bits corresponding to the survivor path, which is named the ML path. Thus, the computational complexity of the VA is , where M is the number of states of the finite-state machine, L is the memory length, and N is the length of the sequence. When the number of states in the trellis is too large, searching on the original full trellis for ML paths requires a large number of computational resources. It is not always necessary to traverse the full trellis when only the ML path is searched, especially in the case of a high signal-to-noise ratio.
Before the VA, sequential decoding algorithms are used in decoding the convolutional code, which are essentially greedy algorithms. They only search for branches that are possible to become the ML path, which has low complexity, but cannot guarantee finding the ML path. Therefore, a variant of the VA algorithm, the Lazy VA algorithm [
35,
36], was developed. A priority queue (PQ) data structure is introduced to ensure finding ML paths. Compared to the standard VA, the Lazy VA is far better than the Viterbi algorithm in complexity and no worse than the VA in the worst case. For the ease of writing, the VA and Lazy VA are denoted as Viterbi-like algorithms in this paper, and the Lazy Viterbi algorithm is summarized in Algorithm 1.
Algorithm 1 Lazy Viterbi algorithm [36]. |
- 1:
The trellis is set to empty, and the PQ contains the initial node with initialized cumulative metric . - 2:
Pop the top node of PQ. - 3:
if is the same as some node of the trellis then - 4:
Discard - 5:
else if with the smallest metric in the PQ then - 6:
Output as the current node - 7:
else if is not the last node then - 8:
Insert its successors into PQ, and return to Step 2 - 9:
else - 10:
Trace back the ML path and output hard/soft decision bits - 11:
end if
|
4.3. The EMVA/EMLVA Blind Equalizer
With these definitions in mind, the Lazy VA in Algorithm 1 is used to implement the E-step for the EM algorithm. The resulting algorithm is denoted as the expectation–maximization Lazy VA (EMLVA) soft blind equalizer, and it can be found in Algorithm 2, which can be implemented as follows:
Algorithm 2 The EMVA/EMLVA blind equalizer. |
- 1:
Input: the received signal - 2:
Set the maximum estimated number of iterations S - 3:
Initialization: - 4:
for to S do - 5:
With the current initializer to run Viterbi or Lazy Viterbi in Algorithm 1 - 6:
Calculate the probability of each path by (18) - 7:
Compute the expectation of the logarithmic likelihood function by (19) - 8:
Maximize the expectation and compute the estimated parameters by (21) and (22) - 9:
end for - 10:
Output: the soft information corresponding to the ML path
|
(1) Set the initializer and , the maximum number of inner iterations S, which is the iterations of EMLVA starting with zero.
(2) A set of Q survivor paths is obtained by using the Viterbi-like algorithm with current initializer
. The probability of the
qth survivor path can be computed:
where
is the path metric for the
qth survivor path,
is a constant to prevent these metrics from becoming too large, which is usually selected as the minimum path metric, and the normalizing factor
satisfies
.
(3) Obtain the complete data expected log-likelihood function:
where
d is a constant independent of the estimated parameter
.
(4) Maximize the likelihood function for
:
where
(5) With the values obtained after the EMV algorithm, make soft decisions as to which sequence of channel symbols or output soft information in input into the decoder.
Similarly, the standard VA used to implement the E-step for the EM algorithm is referred to as EMVA. A block diagram of the EMLVA/EMVA equalizer is included in
Figure 4, where the grey boxes represent the initializer.
4.4. BCA Method and Convergence Criterion
Since the EM algorithm is sensitive to the initializer and the channel is different in any two different bursts, a single fixed initializer has a poor convergence, which falls into an initial value trap, making it difficult to track the channel. Therefore, a set of initializers based on the BCA method [
37] is used in this paper. For complex channel response, global convergence is ensured with a high probability if the initializer contains only one nonzero unit real-valued tap and one nonzero unit purely imaginary tap, located at the appropriate locations. Therefore, for a complex channel response of length
l, there are
initializers for a set, and the number is reduced to
for a real-valued channel. The set of initializers is denoted as the BCA initializer, and the other is called a single initializer.
When the set of initializers has been traversed, a set of estimated parameters is obtained, and then, the optimal estimated parameters need to be selected. For the
kth initializer, the EMV equalizer converges to
, and the evaluation of the likelihood function can be expressed as
where
The best estimated parameters can be selected by maximizing
, i.e.,
4.5. The Turbo EMLVA Blind Equalizer and Positive Feedback
Figure 4b shows that the detector can further improve performance through turbo equalization in
Section 3.1, which can effectively improve the bit error rate performance and convergence of the algorithm. A turbo equalization EMV algorithm based on the BCA initializer is presented in Algorithm 3. To distinguish the iteration of turbo equalization from the iteration of the EM algorithm, the turbo equalization between CPM-SISO and Decoder-SISO is denoted as the outer iteration, and the iteration of the EM algorithm is called the inner iteration. The algorithm is as follows:
Algorithm 3 The EMLVA blind turbo equalizer (T-EMLVA). |
- 1:
Input: the received signal - 2:
Set the maximum outer iteration equalization times T - 3:
for to T do - 4:
With the current initialization to , run Algorithm 2 - 5:
Compute an estimate to the extrinsic LLRs . Feed to the channel decoder - 6:
From the channel decoder per-bit soft-output, recompute LLRs for each symbol - 7:
end for - 8:
Output: Output the soft decision output detection results
|
(1) A set of initializers , and select the kth initial value .
(2) Set the maximum iteration number of turbo equalization , with the initial outer iteration ; set the maximum iteration number of iterations of the EM algorithm with the initial inner iteration .
(3) With the current initializer , the received signal r and the a priori information returned by the convolutional code (initially 0), run Algorithm 2 to obtain the Q survivor paths , the path metric , and the soft information of each path.
(4) After traversing all the initializers, the optimal estimated parameter is selected by the convergence criterion in Equation (
27) for the blind equalization, and the corresponding soft symbol information
is demapped and deinterleaved to obtain the soft information
of the information bits, which is input into the channel decoder as a priori information.
(5) When , an extrinsic LLR on the coded bits is mapped and interleaved again and delivered back to the CPM blind equalization as the updated a priori probability. Steps 3 to 5 are repeated for a given maximum number of iterations .
For turbo equalization, the inner iteration using different Viterbi algorithms is denoted as T-EMVA and T-EMLVA, respectively. It should be noted that under the condition of a short burst, the coded CPM system exhibits positive feedback in the process of outer iteration and convergence to a suboptimal solution by directly exchanging extrinsic information. Therefore, extrinsic information exchange methods play an important role in the convergence of the outer iteration, and the performance of equalization can be further improved by superior extrinsic information exchange methods.
4.6. Complexity Analysis
The computational complexity of the EMV based on the BCA initializer mainly comes from the Viterbi-like algorithm of the E-step. Only considering this part, the complexity of the EMVA is , and the complexity after adding the outer iteration of turbo equalization is , where D is the channel memory length, is the lengthin terms of the symbol time, L is the memory length of the CPM frequency pulse, M is the base number of CPM, S is the maximum number of inner iterations, T is the maximum number of external iterations, and N is the sequence length.
To reduce the calculation amount, the EMLVA can be implemented by applying the Lazy VA in the E-step. In the best case, the complexity can be reduced to
, and T-EMLVA has complexity of
. After adding the iteration stopping criterion, the number of outer iterations can be further reduced and the decoding delay can be effectively reduced. The average number of iterations of turbo equalization after adding the stopping criterion can be denoted as
, and the computational amount is
. A detailed comparison of the complexity of the T-EMVA and the T-EMLVA is included in
Table 2.
6. Discussion
In this paper, we focused our attention on the physical layer design of a UAV-aided IoT communications system. In recent years, an emerging and revolutionizing technology, RIS, can significantly improve communication performance by smartly reconfiguring the wireless propagation environment [
38].
In the non-LOS scenarios of UAV-aided IoT, the RIS can be applied to maximize the received power of the user to keep the connection. In the presence of eavesdroppers, the reflected signal by the RIS can be tuned to cancel out the signal from the sensors node at the eavesdropper by smartly adjusting the reflection coefficients [
39]. Apart from this, when the RIS is applied in the UAV-aided IoT communications system, the structure of the transmitter and receiver can be simplified, further meeting the requirements of low power and cost [
40]. Predictably, the application of the RIS to future UAV-aided IoT communications systems will fundamentally change their architecture and significantly improve their performance.