Wireless Communications and Mobile Computing

Volume 2019, Article ID 5409612, 26 pages

https://doi.org/10.1155/2019/5409612

## A New Multiple-Symbol Differential Detection Strategy for Error-Floor Elimination of IEEE 802.15.4 BPSK Receivers Impaired by Carrier Frequency Offset

^{1}School of Information Engineering, Henan University of Science and Technology, Luoyang, China^{2}Key Laboratory of Middle Atmosphere and Global Environment Observation, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China^{3}National Key Laboratory of Science and Technology on Communications, University of Electronic Science and Technology of China, Chengdu, China^{4}Independent Researcher, Xi’an, China

Correspondence should be addressed to Gaoyuan Zhang; moc.361@704nauyoaggnahz and Congzheng Han; nc.ca.pai.liam@nah.c

Received 22 July 2019; Revised 10 October 2019; Accepted 22 October 2019; Published 26 November 2019

Academic Editor: Xianfu Lei

Copyright © 2019 Gaoyuan Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In this paper, we pay our attention towards the noncoherent demodulation aspect of binary phase shift keying (BPSK) receivers for IEEE 802.15.4 wireless sensor networks (WSNs), and a carrier frequency offset invariant as well as error-floor free multiple-symbol differential detection (MSDD) strategy is proposed over the flat fading channel. This detector is an alternative to the multiple-symbol detector that has been considered almost exclusively in the past. In this new configuration, the receivers do not perform chip-level precompensation as in conventional scheme but bit-level postcompensation. That is, the bit-level autocorrelation operation is first implemented with the “raw” chip sample, and then the carrier frequency offset effect (CFOE) embedded in the achieved statistic is compensated. Correspondingly, the cumulative error in the detection metric is decreased so much that the pervasive error floor for the conventional MSDD scheme is suppressed. Also, complexity efficient estimators for the MSDD scheme are reinvestigated, analyzed, and summarized. Simulation results demonstrate that this new detection strategy may achieve rather more encouraging gain from differential and spread spectrum coding than the conventional single differential coherent detection (SDCD) scheme. The pervasive error floor is also eliminated as compared with conventional MSDD scheme even if the most simple estimator is configured under large bit observation length. Then, much transmitting energy may be saved for each chip symbol, which is practically desired for transmit-only nodes in WSNs.

#### 1. Introduction

Recent years have witnessed much concentration on pervasive wireless sensor networks (WSNs), especially because of its wide application potentiality in the future “Internet of Things (IoT)” for the “edge access” [1–5]. In particular, more attention is attracted on WSNs with transmit-only nodes. The typical application includes intravehicular sensor network, industrial automation, wireless body area networks (WBANs), telemetry in precision agriculture, and household activities inference [1]. Simply reporting sensed data to the sink reliably and periodically within one hop is now the ultimate and critical goal of dense distributed sensor nodes. Namely, star WSN topologies are necessary to be implemented, and any external control is not needed in this context. For these end-point nodes, it is not necessarily equipped with the high-energy-consuming receiver module [1]. The function-reduced transmit-only nodes can not only achieve improved energy efficiency but also provide excellent support for these applications [6, 7].

The IEEE 802.15.4 binary phase shift keying (BPSK) physical layer (PHY) has found appropriate and wide range of application in WSNs [8, 9]. Previous works pay much attention towards developing single differential coherent detection (SDCD) strategy under the condition that the receiver is impaired by carrier frequency offset (CFO) [10–12]. The reader can refer to [12] for a detailed discussion.

Motivated by the aforementioned observations and also to achieve much more performance improvement from differential encoding and then energy saving for the transmit-only node [13, 14], in this work, we restrict our attention towards developing a multiple-symbol differential detection (MSDD) scheme for the receiver in the sink node. A preliminary work and result for an initial idea on this issue were presented in [15]. Unfortunately, only the pure additive white Gaussian noise (AWGN) channel is considered in [15]. Furthermore, when we equip the receiver in the sink node with a low-complexity estimator, undesired error floor is observed especially for large bit observation length. This follows from the fact that the decision metric is achieved by summation, and the error in each term will be accumulated. Moreover, the number of the summation terms grows rapidly with the observation length . Therefore, we further turn all our attention towards the MSDD scheme without error floor under both pure AWGN and fading channels in the presence of CFO. It should be mentioned that CFO and spread spectrum coding are not considered in these pioneering works [12, 13]. For a detailed discussion and an extensive list of references of MSDD, the authors suggest [13, 15].

Apparently, the MSDD scheme is much more complex than SDCD. However, it is obviously feasible and essential for both present and future WSNs. Five important reasons are the following:(i)As shown in [16], the sink node may be integrated into the higher-level system, and thus has less limited energy resources. Motivated by this observation, an augmented receiver for coded offset quadrature phase shift keying (O-QPSK) was introduced with the aid of iterative decoding in [16]. The performance gain is significant because of the combination of encoding, interleaving, and iterative decoding. Especially in future IoT, much computing resource will move towards the edge network to supplement the traditional remote cloud center [17–19]. Increasing computational power in the sink node continues to open the door to more sophisticated algorithms. Then, it will be completely both implementation feasible and energy unlimited for a more complex noncoherent receiver in the sink node.(ii)Although the MSDD scheme is time consuming, the typical refresh rate for some critical WSN applications such as condition is mandated in the order of minutes or hours [20]. Thus, the MSDD scheme is particularly well suited to these delay-tolerant but performance-sensitive WSNs, which have quite relaxed requirement on latency.(iii)Without sacrificing the quality of service (QoS), further reduction in energy that is distributed for each chip symbol may be achieved in the transmit-only terminal node. The reason behind this is the fact that our proposed augmented detector can yield rather encouraging reduced packet-error rate (PER). Therefore, it is clearly desirable in terminal devices for energy saving and then maximum service life of WSNs.(iv)Our proposed augmented detector outperforms the detection schemes for uncoded O-QPSK given in [21–24]. Then, it is particularly well suited to latency-tolerant but error-intolerant applications, such as remote sensing of environment, farming monitoring systems, and smart power meters.(v)Our proposed MSDD scheme may also exhibit its advantage in standard WSN systems with full-fledged transceivers. Because of giving feedback in the automatic repeat request (ARQ) mechanism [8], the traditional detection scheme can be classified as the close-loop technique [25]. However, no feedback may be required owing to further reliability improvement of our MSDD scheme [26], which can be classified as the open-loop technique [25]. In this context, the transceivers in both ends benefit from the less energy that will be consumed by retransmissions, and further energy can be saved by not sending and listening to automatic acknowledgements at all.

In this work, the main contribution is that a simple and robust MSDD scheme without error floor is improved for BPSK receivers in sink nodes of WSNs. Especially, we are extending and modifying the previous work [15] mainly in four aspects as follows:(i)We have assumed in [15] that the desired signal was constant in amplitude and not subject to fading due to multipath propagation or blockage. We now examine this constraint, and the detection is clarified in more detail under *fading together with AWGN channels.*(ii)In [15], we turn our attention towards the performance and implementation of an efficient estimator to lowering the error floor of the detection scheme. However, in this work, a new detection strategy to be compatible with the estimation scheme is proposed. In this new case, no error floor is exhibited even if the most simple estimator is configured in the receiver and the bit observation length is increased to 8. Note, however, that serious error floor is observed in [15] when the most simple estimator is implemented and the observation length is set to be 4.(iii)We develop a more general estimation scheme for CFO effect (CFOE) under slow fading channel. The estimator developed in [15] can be easily integrated into this configuration.(iv)We evaluate and analyze the detection performance extensively with further simulation study. To show the energy-efficient characteristic of the proposed algorithm to the transmit-only node, we also analyze the transmission energy consumption in a real sensor node platform, namely, the Atmel AT86RF212B [27]. Finally, to verify the robustness of the detection algorithm to carrier phase offset (CPO), the performance evaluation result of the proposed MSDD scheme in the presence of random changing CPO is also investigated with simulation.

It is pointed out that we pay all our attention towards uncoded binary differential phase shift keying (DPSK) modulation. The extension to the coded case is straightforward but not pursued here. Moreover, the ensuing analysis is not tailored uniquely for WSN, and thus the results of this paper may be easily extended to include any binary DPSK communication system impaired by both CPO and CFO. Finally, the proposed MSDD scheme may also be easily tailored for uncoded or coded *M*-ary DPSK receivers. Such analyses, however, will be under investigation in our future work.

The remainder of this work takes the following structure. The signal model over the fading channel is given in Section 2. In Section 3, we propose a new strategy to remove the error floor of the conventional multiple-symbol noncoherent detection scheme given in [15] under fading channel. In Section 4, we summarize some estimators, which can be easily developed from conventional tailored schemes for SDCD. In Section 5, we propose a more general estimation scheme under slow fading channel. Section 6 concentrates on the numerical results, while finally Section 7 offers some conclusions and future works.

#### 2. System Model

Although we have described similar system models over the AWGN channel in reference [15], for the reader’s convenience and also integrity of this work we will repeat it here. Assuming no intersymbol interference and perfect knowledge of timing synchronisation at the receiver over a fading channel, for the *m*th bit , we model the complex, baseband, received chip sequence as follows:

Here, the multiplicative fading is expressed as . The *k-*th bipolar BPSK modulated chip in the *m-*th bit interval is represented as . and are arbitrary modulo-2*π*-reduced CFO and CPO in radians, respectively. is the chip duration, is a discrete-time, circularly symmetric, zero-mean complex AWGN, and is the length of the pseudorandom number (PN) sequence [8].

Note that the normalized complex Gaussian process implies a Rayleigh distribution for when the mean . In addition, represents a Rician distribution when the mean . For simplicity and clarity in describing both estimations and detection schemes, a slow fading channel is considered. In particular, we focus on the case where , , and across a packet transmission. All nuisance parameters are assumed to be unknown for the receivers in this paper unless otherwise specified.

#### 3. Eliminating the Error Floor of Conventional MSDD by Postcompensation

As shown in [15], in conventional MSDD algorithm, CFOE is marginalized out with chip-level compensation with an external estimator prior to the bit-level autocorrelation operation. This external estimator is activated only once before each packet detection, and then it can provide an initial estimate of the unknown CFOE. Using this estimate as if it is the true value, the standard perfect-CFO detection scheme given in [28, 29] is implemented. Therefore, in this paper, we name conventional MSDD algorithm in [15] as “a chip-level precompensation-based strategy”. In order to reduce the detection error floor, an estimator with error to be small enough must be utilized. Consequently, in [15], a new estimation scheme is also proposed in view of the fact that all of the conventional estimation schemes are not compatible. In other words, conventional chip-level compensation-based detection algorithm is an estimator-selective scheme, and the external estimator must be as reliable as possible. Otherwise, the terrible error floor is unavoidable. In the sequel, we will give “a bit-level postcompensation-” based detection strategy, which is error-floor free as well as estimator-nonselective.

The realization that the effect of the CFO can also be wiped out posterior to the bit-level autocorrelation operation is the starting point of our new strategy. That is, we note that the data detection and CFOE compensation process can be swapped. The advantages of this configuration may be twofold. First, in the conventional scheme, the residual estimation error embedded in “each precompensated” chip sample will “accumulate” in each term of equation (6) in [15] by means of the -term summation operation. The simple idea of our configuration to overcome or weaken this limitation is that we “wholly postcompensate” the CFOE after the bit-level autocorrelation operation. Second, the aforementioned accumulated error will be seriously “amplified” in terms of summation operation as shown in equation (5) of [15], especially when the bit observation length is large. That is, the ultimate error in the detection metric will be improved as the bit observation length increases, and the irreducible error floor may be exhibited. Yet, this limitation is not observed in our new configuration. All of these qualitative observations will be supported by the quantitative results in Section 6. The main implementation process of this new scheme is given in the sequel.

First, we process the “raw” chip sample to obtain a statistic as follows:where represents the sample number. and are the delayed number of the bit interval, and the superscript is the complex conjugate. Then, reverse modulation is performed after the aforementioned bit-level autocorrelation operation to obtainwhere the estimated CFOE is expressed as

Here, the measurement is given by

Here, is the preamble bit observation length, and [8]. is the autocorrelation sample number, , and represents an integrated noise term. Note that although is purposely left generic here, its design is one of the important objectives of the paper. The computation of this estimator will be discussed in Sections 4 and 5. The implementation structure of is given in Figure 1. For , , and then we have, .