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Research Article | Open Access

Volume 2021 |Article ID 6641192 | https://doi.org/10.1155/2021/6641192

Gaoyuan Zhang, Haiqiong Li, Congzheng Han, Congyu Shi, Hong Wen, Dan Wang, "Multiple-Symbol Detection Scheme for IEEE 802.15.4c MPSK Receivers over Slow Rayleigh Fading Channels", Security and Communication Networks, vol. 2021, Article ID 6641192, 19 pages, 2021. https://doi.org/10.1155/2021/6641192

Multiple-Symbol Detection Scheme for IEEE 802.15.4c MPSK Receivers over Slow Rayleigh Fading Channels

Academic Editor: Savio Sciancalepore
Received14 Oct 2020
Revised09 Nov 2020
Accepted03 May 2021
Published20 May 2021

Abstract

Although the full multiple-symbol detection (MSD) for IEEE 802.15.4c multiple phase shift keying (MPSK) receivers gives much better performance than the symbol-by-symbol detection (SBSD), its implementation complexity is extremely heavy. We propose a simple MSD scheme based on two implementation-friendly but powerful strategies. First, we find the best and second-best decisions in each symbol position with the standard SBSD procedure, and the global best decision is frozen. Second, for the remaining symbol positions, only the best and second-best symbol decisions, not all the candidates, are jointly searched by the standard MSD procedure. The simulation results indicate that the packet error rate (PER) performance of the simplified MSD scheme is almost the same as that of the full scheme. In particular, at PER of , no more than 0.2 dB performance gap is observed if we just increase the observation window length to 2. However, the number of decision metrics needed to be calculated is reduced from 256 to 2. Thus, much balance gain between implementation complexity and detection performance is achieved.

1. Introduction

With the widespread application of new information and communication technologies such as the Internet of Things (IoT), cloud computing, and big data, smart cities have developed rapidly in recent years. They have penetrated into all aspects of people’s lives and greatly meet the modern people’s pursuit of convenient, fast, and high-quality life [17]. Reliable and effective transmission of the sensing data is obviously important for the construction of the new smart city [8]. The IEEE 802.15.4c protocol provides the physical layer specification of the low-power short-distance IoT for China [9, 10]. The multiple phase shift keying (MPSK) is provided in IEEE 802.15.4c. This mainly follows from the fact that MPSK modulation is the most able to provide high reliability as well as data rate for sensing data transmission. Therefore, it is important to study robust detection technology of MPSK signal in line with the characteristics of wireless IoT. This paper focuses on the multiple-symbol detection (MSD) of IEEE 802.15.4c MPSK receiver.

Although the MSD scheme has excellent detection performance, its implementation complexity increases exponentially with the increase of the observation window length [11, 12]. In recent years, many concentrations have been achieved on complexity reduction of MSD. Stephen et al. studied the maximum likelihood detection (MLD) based on information symbol blocks. The corresponding block signal is used to limit only a part of the possible signal decisions, which will reduce the complexity of the receiver. However, there is a partial performance loss [13]. LoRici proposed a suboptimal receiver based on Viterbi algorithm. The complexity of the receiver increases in polynomial form of . However, the performance of the algorithm is related to the memory length of continuous phase modulation signal. For continuous-phase frequency-shift keying (CPFSK) signal , its detection performance is seriously degraded [14, 15]. Several low-complexity MSD algorithms are also proposed by Fischer and Wang Xin, but their performance is far behind that of the traditional MSD algorithm [16, 17].

In this work, we propose a simple MSD scheme for IEEE 802.15.4c MPSK receivers. Unlike the traditional receivers that were equipped with full MSD scheme with high complexity to achieve the best possible reliability, we pay our full attention to the simple design to balance the complexity and reliability. We summarize our main contributions as follows: (i)The optimal MSD scheme for IEEE 802.15.4c MPSK receivers based on the maximum likelihood criterion can give excellent results in the case of both slow fading and pure additive white Gaussian noise (AWGN) channels. However, the implementation is relatively complex and unachievable for IEEE 802.15.4c MPSK receivers. As an implementation achievable benchmark, a full MSD scheme based on compensation is proposed.(ii)As for the proposed full MSD scheme, more than two-hundred-decision statistic should be calculated before making final decision even if we set the observation window length to 2. Thus, we propose a new MSD algorithm, which greatly simplifies the full scheme.(iii)In order to verify the desirable properties we obtained from this simple scheme, the characteristics of the receiver are studied from many aspects with extensive simulations.

The rest of this paper is organized as follows: Section 2 focuses on the signal model under the slow fading Rayleigh channel. Section 3 describes the full MSD scheme, and Section 4 introduces the proposed simplified MSD scheme. Section 5 concentrates on frequency offset estimation. The simulation results are discussed in Section 6. Finally, some conclusions and future work are provided in Section 7.

2. System Model

According to the IEEE 802.15.4c protocol [18], the specific data modulation process for the MPSK physical layer is shown in Figure 1. From the binary data of the physical layer protocol data unit (PPDU), in each symbol period, four information bits form a symbol, which is used to select one of 16 orthogonal spreading sequences. The chips in the sequence are MPSK-modulated onto the carrier. For more details on the mapping rules, please refer to Table 1 in [19].

Ideal carrier synchronization is assumed at the receiver. Specifically, for the th symbol , the received complex baseband chip sequence can be expressed aswhere represents multiplicative fading, is the th chip of the th pseudorandom (PN) sequence , and Table 1 shows the detailed correspondence. represents the carrier frequency offset (CFO) in radians, and represents the residual CFO in Hz. represents the carrier phase offset (CPO) in radians, and represents the spreading chip period. is a discrete, cyclic symmetric, complex Gaussian random variable with zero mean and variance , and represents the length of the PN sequence [18].




We assume that a piecewise constant approximation is made to the multiplicative fading, CFO, and CPO [20]. That is, , , and . In addition, the receiver does not have any prior information about the CPO; that is to say, the uniform distribution in the interval is assigned to . The normalized complex Gaussian process follows Rayleigh distribution; that is, the mean . The CFO follows a symmetrical triangular distribution.

3. The Full MSD Scheme

Following the idea in [21], we can easily develop the optimal MSD scheme for IEEE 802.15.4c MPSK receivers based on MLD. However, the implementation complexity is extremely heavy as shown in [22], which limits its application in smart cities. Here, we consider a heuristic configuration. The specific detection process is as follows.

First, the baseband chip sample after carrier frequency offset effect (CFOE) compensation can be expressed aswhere denotes the estimated CFOE. The estimation of CFOE should be carefully developed and will be described in detail in Section 5. Please note that we assume that the effect of redundant parameter on is completely eliminated after compensation. In addition, the information is embedded in the carrier phase but not in the carrier amplitude. Therefore, there is no need to estimate and compensate for the multiplicative fading even if serious fading of the received signal strength may be exhibited.

Secondly, we divide the whole compensated chip sequence into block, and each block contains symbols. The detection metric for the th block can be then expressed as [23]whereand represents complex conjugate operation. Note that, for , (3) reduces to the symbol-by-symbol detection (SBSD) scheme. From (3), we can also see that the multiplicative fading has no effect on the final decision, and there is no need to estimate and compensate for the fading coefficient .

Finally, the decision rule can be expressed as follows:

After demapping, we can obtain the final detection result. This detection scheme is based on [23] but is different from [23]. The signal model in [23] only considers phase offset. In this work, we further considered CPO, spread spectrum, and slow Rayleigh channel. Therefore, we summarize the detailed process of the complete MSD program.

As shown in (3), based on an exhaustive search, 256 detection metrics need to be calculated for the full MSD even if we set the observation window length to 2. This is clearly complexity-heavy. In order to make MSD easy for hardware implementation, we consider two simple strategies, which parallels Wilson’s approach in [15]. First, we find the best and second-best decisions in each symbol position with the standard SBSD procedure characterized by (3) and freeze the global best decision. Second, for the remaining symbol position, only the best and second-best symbol decisions, not all the candidates, are jointly searched by the standard MSD procedure. Here, a qualitative explanation for this configuration is as follows. Apparently, the detection metric given in (3) can partly reflect the reliability of the decision result in each symbol position. Therefore, it is reasonable that the global best decision with the standard SBSD procedure characterized by (3) is the most reliable and can be frozen especially for high signal-to-noise ratio (SNR). Moreover, under high SNR, only searching the best and second-best symbol decision for the remaining symbol position is also feasible. In Section 6, we will further verify its rationality through quantitative simulations.

4. The Proposed Detection Scheme

For each symbol position, with the standard SBSD procedure characterized by (3), we can easily obtain two local metrics, that is, the best metric and second-best metric. Then, we froze the decision result corresponding to the most reliable symbol position, which is achieved by searching all the local best metric. For the remaining symbol position, the number of symbols to be searched is truncated. That is to say, only the symbols corresponding to the local best and second-best metrics are considered as the candidates. In this context, for observation window length , we have reduced the number of the metrics given in (3) to be calculated from 256 to 2. However, the simulation results in Section 6 show that the performance loss is very small. The specific implementation process is detailed as follows.

For the th block, the decision metric for each symbol position is first calculated asHere, , which is the complex cross-correlation function.

Secondly, the best and the second-best metrics for the th symbol in the th block can be given as follows:where and , respectively, represent the estimated value of the index for the PN sequence corresponding to the best and second-best metrics of the th symbol. For example, we can see that, as shown in Figure 2, a compensated baseband chip sequence passes through decision block 1 to generate decision set , and the best and second-best metrics in the decision set are recorded as and , respectively.

Furthermore, find the global best metric, and freeze the detection result:that is, let the detection result of the th symbol be . Figure 2 gives the implementation structure.

Finally, the data in the remaining symbol periods are jointly determined as follows:where and are given by (8). Figure 3 is a structural diagram of this joint decision.

Algorithm 1 introduces the detailed implementation step of proposed MSD scheme. For simple implementation, we only selected the most and second-most reliable symbols here. More metrics can also be involved, which, however, are complexity-intensive and not suitable for our purposes. In essence, when 16 metrics are selected, we arrive at the full MSD. Furthermore, the simulation results in Section 6.2 show that excellent performance has been exhibited even if we only equip the MSD scheme with the most and second-most reliable metrics.

Input:
: baseband samples of the th bit
  : PPDU payload length
  : sample num ber of the th symbol in the preamble
  : length of the PN sequence
  : the maximum chip delay number
  : observation window length
: preamble length
 In order to simplify the detection process, is set 4 in this algorithm.
Output:
and : detect the spread spectrum sequence of the actual data.
(1)initial
(2) to eliminate the influence of
(3)for for
(4) for for
(5)  
(6)  end for
(7)end for
(8)for do
(9) for do
(10)  for do
(11)   
(12)  end for
(13) end for
(14)
(15)
(16)end for
(17)The quantization function of frequency offset estimator , where
(18)for
(19) for
(20)  for
(21)