## 1 Introduction  
Even since its introduction, the IEEE 802.15.4 low rate wireless personal area network (LR-WPAN) standard has found wide application in low complexity, low cost, low power consumption, and low data rate wireless connectivity among inexpensive devices [1], e.g., the smart sensor node in pervasive Wireless Sensor Networks (WSNs) [2]. WSNs can be applied to home automation, precision agriculture, health care, consumer electronic, industrial wireless control, environmental monitoring, and data collecting in battlefield awareness [3]. The specifications of the physical (PHY) layer and the medium access control (MAC) layer for IEEE 802.15.4 are defined in [1]. Much focus on its MAC protocol and capacity analysis has been witnessed in recent years [3; 4; 5]. Specially, [PERSON] et al. detailedly analyzed the capacity of WSNs, where \(n\) nodes are located in a region of area 1 m\({}^{2}\). However, as we know, there is relatively less attention on the reliability issue in PHY layer, which is concerned in this paper. Specifically, the noncoherent signal detection algorithm for IEEE 802.15.4 WSNs is studied. A binary phase shift keying (BPSK) direct sequence spread spectrum (DSSS) scheme is required in 868/915/950 MHz bands as indicated in [1]. A noncoherent receiver is preferred as compared to a coherent one in IEEE 802.15.4 BPSK receivers. This is because carrier acquisition and tracking is not required at the receiver in the battery-operated sensor node, although the complexity simplification is achieved at the cost of a compromise in detection performance. This degradation is often directly manifested in terms of the required signal-to-noise ratio (SNR) for a given bit error rate (BER) or packet-error rate (PER) [6; 7]. _Bit-level_ single differential coherent detection (SDCD) is known to be more popular in IEEE 802.15.4 BPSK receivers because of its attractive performance [2; 8]. This follows that the _chip-level_ SDCD suffers from serious performance loss due to chip-error propagation [9], while the bit-level SDCD combines soft decision values of the chip samples for detection and compensates for the constant carrier frequency offset effect (CFOE) in statistics after differential decoding (DD) [2]. To the best of our knowledge, all available detectors classified into this category [2; 8; 10] employ a two-step approach referred to here as the bit-level SDCD (BSDCD) approach: Step 1 (postcompensation step) _estimates_ the residual CFOE based on a measurement derived from the whole preamble samples at the autocorrelator \(output\) and then feeds back a coherent reference to the following autocorrelation sample of the useful data; and Step 2 (decision step) _detects_ the data bit-by-bit. The idea in the first step seems to be economically attractive for WSNs because of its simple implementation. Furthermore, the second step combines the simplicity of the approach without any compensation, with the improved performance due to including some degree of simple phase rotation of the detection statistic after DD, i.e., the differential detector output. Hence, this unified _estimation-detection_ framework appears to offer a very reasonable trade-off between error performance and detection complexity. This unified heuristic configuration can be considered an inspiration from the idea of the Generalized Likelihood Ratio Test (GLRT) [11], yet the receiver has partial prior knowledge of the nuisance parameter (e.g., an unknown CFOE) from _known_ symbols (e.g., the preamble symbols). In principle, it can be interpreted as an approximation to the optimal coherent detectors [12]. The creative approximation is imperative for IEEE 802.15.4 WSNs where computation of the optimal detector is too difficult and uneconomical. It can also be classified into the data-aided (DA) noncoherent demodulation [13]. It is important to note that a similar approach was also introduced by [PERSON] et al. in [14] for \(M\)-ary phase shift keying (\(M\)-PSK) with single differential (SD) coding.