## 1 Introduction
In a dense sensor network deployment, where many nodes are periodically sending data to the sink, concurrent transmissions are highly probable. However, the probability of having a collision because of more than two concurrent transmissions is relatively low [18, 20], thanks to CSMA-CA. In such conditions, the performance of the receiver depends on the overall amount of interferer signal energy and does not change with the number of interferers [18, 21]. Hence, solely the impact of one interferer on the capture probability will be considered in the mathematical analysis. On the other hand, we believe this study can also contribute to the identification of signal reception models for network simulators. In particular, as shown in Table 1, most common network simulators use signal-to-noise ratio threshold (SNRT)- or bit error rate (BER)-based models in order to decide the correct reception of a packet. In SNRT-based models, the packet is correctly received if the signal-to-noise ratio (SNR) is larger than a given threshold, whereas, in BER-based models, the packet reception decision is based on the BER, which is determined probabilistically depending on the value of the SNR. These models are rather simple, but have some drawbacks. In particular, SNR-based models do not take into account the impact of interference. This latter effect can be considered, in principle, by BER-based models, but the impact of the waveform of the interferer signals should be carefully considered, as it plays a significant role. Typically, conventional interference models are based on the assumption that the disturbance can be modeled as a Gaussian random variable; unfortunately, this is not the case of IEEE 802.15.4 systems, where only a limited number of strong interferers is present. To counteract this problem, we mathematically analyze the impact of the waveform of the interferer on packet reception and obtain curves that are organized as specific look-up tables. Figures, such as those derived in Figures 4 and 6, can be used to provide accurate PHY models for network simulators. In that case, the conventional on-off behavior of SNRT-based models can be replaced by a probabilistic model, where the actual value of SIR leads to a given probability of packet loss. In other words, we provide a SIR-based signal reception model for the interference-dominant environments, where noise is not the serious cause of packet loss (_i.e.,_ enough transmit power is used or nodes are using the best links to reach the destinations in a dense sensor network deployment). Furthermore, Figure 7 shows that, in the case of non-coherent detection in an interferer-dominant environment, an on-off model can be also applied. In any case, behavior changes when thermal noise cannot be neglected. As a conclusion, the results of this paper on chip error rate (CER) and PRR (see Figures 6 and 7) can be used within network simulators in terms of look-up tables. That allows a fast characterization of the behavior of the PHY layer. The computational complexity of the model for the coherent detection is O(1) (in big O notation). This makes it usable without intensive computational effort. For the non-coherent case, we show that the performance curve has a step-like behavior with the threshold at 0 dB. This simple model can capture the behavior of the non-coherent case without any computational effort. The rest of the paper is organized as follows: Section 2 describes CSMA-CA and the 2.4 GHz PHY of the IEEE 802.15.4 Standard. Sections 3 and 4 evaluate CER for coherent and non-coherent offset quadrature phase shift keying (O-QPSK), respectively. Section 5, obtains PRR in concurrent transmission by finding an upper bound, which transforms CER to data symbol error rate (DSER). \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Simulator** & GloMoSim & ns-2 & OPNET \\ \hline
**Signal Reception** & SNRT-based, BER-based & SNRT-based & BER-based \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Signal reception models in network simulators [24].