Experimental Evaluation of Measurement-based SINR Interference Models

Experimental Evaluation of Measurement-based SINR Interference Models Wee Lum Tan, Peizhao Hu and Marius Portmann Queensland Research Lab, National ICT Australia (NICTA) School of ITEE, The University of Queensland, Australia Email: {weelum.tan, peizhao.hu, marius.portmann}@nicta.com.au Abstract In 82.11-based wireless networks, the ability to accurately predict the impact of interference via the use of an interference model is essential to better and more efficient channel assignment algorithms and data routing protocols. Recently, there have been several works that proposed new interference models utilizing the well-known concept of signalto-interference-plus-noise ratio (SINR). Using active measurements, these models construct a profile that maps either the measured received signal strength (RSS) or the computed SNR or SINR values at a receiver, to its packet delivery ratio (PDR) performance. The profile is then used by the models to predict the PDR performance in more complex scenarios involving multiple interferers. While comparison with other basic models (e.g. hop-based and distance-based) have been made in these works, there has as yet been no comprehensive comparison on the accuracy of these measurement-based SINR interference models. In this paper, we systematically evaluate the performance of three measurement-based SINR interference models in predicting the interference impact on the successful reception of packets. Our evaluations cover various interference scenarios with both 82.11 and non-82.11 interferers, in experiments carried out in both our conducted testbed and an over-the-air testbed. Our results show that an interference model that utilizes an SINR profile can accurately predict the PDR performance with a maximum root-meansquare error (RMSE) of 1.8% across all our evaluations. In contrast, interference models that rely on the SNR profile and the RSS profile perform poorly, with a maximum RMSE of 61.7% and 66.1% respectively. I. INTRODUCTION Interference in wireless networks such as 82.11-based wireless LAN, sensor and mesh networks, plays a major role in the deployment and operational strategies of these networks. Estimating interference and its impact on network performance is crucial to the design of numerous protocols and algorithms running in these networks, such as channel allocation [1], routing [2], and scheduling [3]. Being able to predict and quantify the impact of interference can help these algorithms to assign better channels, route data around high interference regions, and schedule concurrent transmissions, in order to optimize the overall network performance. In 82.11-based wireless networks, the effects of interference can be grouped into two types; (i) a drop in the maximum sending rate at the sender (termed as carriersensing interference) and (ii) a reduction in the achievable packet delivery ratio (PDR) or throughput at the receiver due to packet corruption (termed as receiver interference). In this paper, we focus our attention on the impact of receiver interference on the achievable PDR performance of a wireless link. In particular, we evaluate the performance of three wireless interference models utilizing the well-known signalto-interference-plus-noise ratio (SINR) concept to predict the interference effects of multiple 82.11 and non-82.11 interferers on the PDR performance of a wireless link. The PDR metric is defined as the ratio of number of packets received to the number of packets sent on the wireless link. An SINR model typically describes the relationship between the bit error rates of different modulation schemes and the SINR values as computed at the receiver. The SINR S ΣI+NF value is defined as, where S is the signal power of the sender, ΣI is the sum of interference power from multiple interferers transmitting at the same time as the sender node, and NF is the noise floor at the receiver. Generally, the SINR model is constructed based on theoretical models of RF signal propagation, path loss, and fading. In reality, wireless signal propagation, attenuation, and reception are often too complicated to be sufficiently characterized by theoretical models. As a result, recent works tend to use measurement-based approaches in constructing their interference models [4] [5] [3] [6] [7] [8]. In [4], active measurements are used to record the received signal strength (RSS) and PDR metrics of a traffic stream between a pair of sender-receiver. These measurements are used to construct an RSS profile that maps the RSS values to the PDR performance. The authors of [4] also manipulated the SINR model in a way that enables them to use the RSS profile to predict the PDR performance in more complex scenarios involving multiple interferers. The authors in [5] use the same measurement methodology as in [4] to construct a signal-to-noise ratio (SNR) profile that maps the SNR values to the PDR performance, where SNR is computed as the ratio of the received signal strength to the noise floor (NF) at the receiver. In [3], a slightly different measurement methodology is used where an interferer is added to interfere with the sender s traffic stream at the receiver. Measurements of RSS of the sender and interferer, and the NF at the receiver, are used to construct an SINR profile that maps the computed SINR values to the measured PDR performance of the senderreceiver link. In more complex scenarios with multiple interferers, these two models compute the SINR value at the 978-1-4673-1239-4/12/$31. c 212 IEEE

receiver, and lookup the SNR profile [5] or SINR profile [3] in order to predict the PDR performance. While comparisons with other simpler interference models (e.g. hop-based and distance-based) have been made [5] [3], there has as yet been no comprehensive comparison and evaluation on the accuracy of these measurement-based SINR interference models. Using a conducted testbed that allows us to control the propagation and attenuation of radio signals, we carry out a systematic evaluation on the interference prediction accuracy of three measurement-based SINR interference models that utilizes the RSS profile [4], SNR profile [5], and SINR profile [3] respectively. Our evaluations cover various interference scenarios with both 82.11 and non-82.11 interferers, in experiments carried out in both our conducted testbed and an over-the-air testbed. Results from our experiments show that an interference model that uses an SINR profile can accurately predict the PDR performance with a maximum root-mean-square error (RMSE) of 1.8% across all our evaluations. In contrast, interference models that rely on the SNR profile and the RSS profile perform poorly, with a maximum RMSE of 61.7% and 66.1% respectively. In addition, our investigations also reveal that an SINR profile that is constructed offline in the lab, can be used to predict the PDR performance of wireless links in over-the-air experiments. This indicates that the SINR profile is a characteristic of the radio card, and thus leads to an easy deployment strategy where the SINR profile can be first built offline, and then utilized in real operational networks. The remainder of this paper is organized as follows. We discuss related work in Section II, and describe our experimental setup in Section III. We provide a review on the three measurement-based SINR interference models that we investigate in Section IV, and present the performance comparison of these models in Section V. Finally, we summarize our key findings in Section VI. II. RELATED WORKS Common interference models, such as the hop-based model, distance-based model, and the protocol model [9], are simple binary-based interference models, and as such, cannot predict the degree of the impact of interference on the quality and performance of wireless links. It has been shown that simple theoretical models to predict the impact of interference in wireless networks, e.g. using simple path loss models, have very limited accuracy in realistic and relatively complex deployment scenarios [7] [1]. Consequently, there has been a trend towards measurementbased approaches. In [7], a measurement-based approach was presented to predict the impact of interference on the capacity of links in wireless multi-hop networks. The method requires O(n 2 ) measurements for a network of n nodes, and is limited to predicting pairwise interference, i.e. scenarios with only a single interferer. 5 L2 A4 L17 L18 L19 L16 A5 L13 4 A9 L14 A8 L15 L4 1 L3 A1 A3 L2 L1 A7 L12 L11 A6 A1 L9 3 L8 L7 L5 L6 L1 2 A2 (a) Configuration including attenuators. Figure 1: Conducted testbed and network topology (b) Photo of Figure 1: Wireless mesh testbed configuration for five no Experiments In [8], Niculescu further extended the measurement approach of [7] and proposed a model to predict the impact of multiple simultaneous interferers using only information from pairwise measurements. As in [7], this method does not scale very well, due to the measurement cost of O(n 2 ). Furthermore, our recent evaluation of this method using a conducted testbed has shown limitations in the prediction accuracy [11]. In particular, we demonstrated that some of the underlying linearity assumptions of the model do not hold. Halperin et al. [12] recently presented a method for predicting the packet delivery ratio of 82.11 OFDM links using Channel State Information (CSI). The presented model focusses on the issue of frequency selective fading and does not consider interference. Reis et al. [4] and Kashyap et al. [5] separately proposed measurement-based interference models that require only O(n) measurements. Their approaches are based on the traditional SINR model. Similarly, Maheshwari et al. [3] [6] also aim to predict the impact of interference via the use of a measurement-based SINR interference model. In these works, performance comparisons (via over-theair experiments) have been carried out with other simple interference models, like the hop-based and the distancebased models. However, as far as we know, there has not been any performance comparison of these measurementbased SINR interference models themselves. The presented testbed can be used to perform various experime performance of Wireless mesh devices. Here, only two examp are reported. In the first experiment the performance of variou schemes of 82.11 is compare using the testbed. The link is rate fixed attenuation starting at db and increasing to 63 db, thi real world path loss of 56 db to 12 db, corresponding to a link at full data rate and one which has no link at all. As it can be seen in Figure 2(a), each modulation rate (1M to 5 cut offs with respect to the path loss, which correspond to the noise ratio required for each modulation. The general pattern is t which transmit less information per symbol have the best resist saturate at a lower data rate. The higher rates all have decre which corresponds to retransmissions which occur due to certain In the right sideof Figure 2(a), the SNR ratio as measured by shown. Although the measured SNR value follow the level of modulation scheme gives a different relative SNR value. This sh value as reported by the radio card is accurate to 2 db. The c value, confirms the previous observation of each rate requiring a The second experiment concerns the network chain topology. T wireless nodes (often with two radios/antennas), receiving and sen a chain. In order to allow simultaneous sending and receiving, d are used for adjacent links. However, due to the close proximity each link, there can be self interference. This effect can be mode by combining the two radios with a corresponding isolation be the usual wireless connection. The throughput and the reductio interference is shown in Figure 2(b). III. EXPERIMENTAL SETUP The majority of the experiments reported in this paper are carried out on our conducted testbed [13], which has been designed and constructed to provide a controlled environment for our experiments. The conducted testbed not only allows us to control the propagation and attenuation of radio signals in the experiments, but also minimizes any external interference from other 82.11 networks or RF sources. This leads to a fully controllable setup and ensures repeatability of our experiments. Our conducted testbed and a logical representation of the network topology are shown in Fig. 1. There is a total of five 82.11 nodes, using the Wistron Neweb CM9 Atheros

82.11a/b/g mini-pci card with the AR5213A chipset. Coaxial cables are attached to the antenna port of each node s radio card so that RF signal propagation between the nodes occur only along the cables, rather than over the air. The five nodes are fully connected to each other via a combination of co-axial cables, programmable attenuators, fixed inline attenuators, combiners and splitters. The programmable attenuators (A1, A2,...) allow us to electronically control the quality of the wireless link between the nodes. By varying the attenuation on the RF attenuator from db to 63 db (in 1 db steps), we vary the link s quality from a perfectly connected link to a completely disconnected link. To minimize any external RF interference from other 82.11 networks to our experiments, the nodes are placed in RF shielding boxes that provide 85 db of isolation from the external environment. In addition to the five 82.11 nodes, our testbed also includes an RF white noise source/generator (NW6G-26-CS). We connect the noise source to a wide band amplifier in order to amplify its low output power. This noise source is used to provide controlled external interference (across the frequency range 1 MHz to 6 GHz) in some of our experiments. In our experiments, the nodes are running Linux kernel version 2.6.35, with the ath5k driver for the radio cards. Operating in the 82.11a mode, the nodes run the iperf tool to broadcast saturated traffic load (containing UDP packets of size 124 bytes) at a fixed physical transmission rate of 6 Mbps. Signal strength measurements are retrieved from the radiotap header attached to packet traces that are captured with tcpdump, while noise floor measurements are obtained from the output of the iw utility executed every second. Finally, experiment results are averaged over a measurement duration of 6 seconds. IV. MEASUREMENT-BASED SINR INTERFERENCE MODELS In this section, we provide a short overview of the three measurement-based SINR interference models that we investigate in this paper. We will describe their measurement approaches and the profiles that are constructed. We will also explain how the profiles are used to predict the impact of interference on the PDR performance of a wireless link. A. RSS Profile In [4], a measurement-based approach to interference modeling is proposed. In their model, measurements of tuples {PDR, RSS} between pairs of nodes are performed by having each node taking turns to broadcast packets, and every other node measuring the PDR and corresponding RSS. The PDR value is defined as the ratio of the number of packets successfully received to the number of packets sent, while the RSS values are retrieved from the captured packet traces at the receiving node. At every node, the set of these tuples is plotted to obtain an RSS profile for that node, Figure 2: Network topology for RSS profile construction Packet Delivery Ratio (%) 1 9 8 7 6 5 4 3 2 1-1 -95-9 -85-8 Received Signal Strength (dbm) Figure 3: RSS profile which can be interpreted as the probability of successful packet reception as a function of the measured RSS. In this paper, we construct the RSS profile for the model in [4] by configuring the sender-receiver network topology on our conducted testbed, as shown in Fig. 2. The sender S and receiver R are connected via an attenuator, and by varying the attenuation on the link, we vary the link quality and the signal strength of the sender s packets, as measured at the receiver. The sender broadcasts 124 bytes packets at a physical transmission rate of 6 Mbps. For every attenuation value, the tuples {PDR, RSS} are measured and plotted in Fig. 3, where we see that for RSS values less than - 98 dbm, the PDR is zero, while for RSS values higher than -95 dbm, the PDR is 1%. In between these two threshold RSS values, there is a narrow transition region of 3dB width where the PDR rapidly increases from % to 1%. Using this RSS profile, one can easily predict the PDR performance of a wireless link simply by measuring the RSS of packets received at the receiver, and looking up the corresponding PDR on the RSS profile. For example, looking at the RSS profile in Fig. 3, if the measured RSS is -97 dbm, then the predicted PDR is 58%. However, this PDR prediction is accurate only in interference-free scenarios. We have performed various experiments with different levels of interference and found that the RSS profile changes (shifts to the right) in scenarios with interference. This shows that the RSS profile is dependent on the environment in which it is constructed. In order to use the same RSS profile to predict the PDR performance of a sender-receiver link in the presence of 82.11 interferers, the model in [4] computes a hypothetical single-sender RSS that is equivalent to the RSS of the sender when concurrent transmissions from the interferers are oc-

curing. The authors in [4] are able to do this computation by manipulating the SINR model in a way that enables them to use the RSS measurements to predict the PDR performance as a function of interference. For further details, interested readers can refer to Sections 4.2 and 4.3 in [4]. In this paper, we summarize the computation of the hypothetical singlesender RSS as follows: RXsr ti = R sr δ r ( R tir Īr) (1) where RXsr ti is the hypothetical RSS of sender s at receiver r when interferers t i (i ) are also transmitting R sr is the mean RSS of sender s as measured at receiver r during the initial RSS profile construction phase R tir is the mean RSS of interferer t i as measured at receiver r during the initial RSS profile construction phase δ r is the SINR threshold at receiver r above which it can successfully decode a packet Īr is the average external interference at receiver r Note that in our conducted testbed, Ī r = since we eliminate all external interference through the use of the RF shielding boxes. In addition, Eqn. (1) is written in terms of mw. Finally, to predict the PDR performance when interferers t i are also transmitting, a lookup is performed on the RSS profile to find the PDR value that corresponds to the hypothetical RSS value, RXsr. t B. SNR Profile In [5], the authors utilized a similar measurement-based approach as in [4] to construct a profile. However, in addition to measurements of the tuples {PDR, RSS} between pairs of nodes, measurements of the noise floor (NF) at each node are also taken. The signal-to-noise ratio (SNR) value is then computed as the ratio of the RSS value to the NF value. At every node, the set of the tuples {PDR, SNR} is then plotted to obtain an SNR profile for that node. Similar to the RSS profile described earlier in Section IV.A, an SNR profile 1 depicts the relationship between the SNR values at a receiver, and the achievable PDR performance. In this paper, we use the same sender-receiver network topology in Fig. 2 to construct the SNR profile shown in Fig. 4. In [5], the authors have stated that the SNR profile does not change even when interference is present on the link (section 5.3 in [5]). In order to use the SNR profile to predict the PDR performance of a wireless link in the presence of interferers, one needs to first know the RSS of the individual interferers. This can be easily obtained from the initial measurements of RSS between pairs of nodes, during the SNR profile construction phase. The RSS values (in mw) i 1 The use of an SNR profile to predict link quality has also been proposed in [14] [15]. Packet Delivery Ratio (%) 1 9 8 7 6 5 4 3 2 1 5 1 15 2 25 SNR (db) Figure 4: SNR profile corresponding to the concurrent sender and interferers are then used as input into the equation where SINR = R sr i R tir + NF R sr is the mean RSS of sender s as measured at receiver r during the initial SNR profile construction phase R tir is the mean RSS of interferer t i as measured at receiver r during the initial SNR profile construction phase NF is the mean noise floor at receiver r Note that in Eqn. (2) above, the value computed is the SINR, due to the presence of the interferers. The computed SINR value is then used to lookup the SNR profile to determine the corresponding PDR value. C. SINR Profile In [3] [6], a slightly different measurement approach is proposed to construct an SINR profile. First, measurements of RSS between pairs of nodes are performed, similar to the approach in [4] [5]. Next, concurrent transmissions from a sender and an interferer are carried out, and the receiver records the number of packets it receives correctly from the sender. This is then used to compute the PDR of the sender-receiver link, in the presence of the interferer. The corresponding SINR value is computed in Eqn. (2), by using the values of the sender s and the interferer s RSS values, and the noise floor NF at the receiver. Different pairs of {sender, interferer} nodes are used to generate many tuples of {PDR, SINR}, which are then used to construct the SINR profile. Note that unlike the measurement approach in [4] [5] that requires only O(n) measurements for a network of n nodes, the measurement approach in [3] [6] to construct the SINR profile requires O(n 2 ) measurements. In this paper, we construct the SINR profile for the model in [3] [6] by configuring the network topology shown in Fig. (2)

Figure 5: Network topology with an 82.11 interferer for construction of SINR profile Figure 7: Network topology with single 82.11 interferer 1 1 Data Link Attenuation: 1dB 8 8 6 4 6 4 2 2-2 -15-1 -5 5 1 15 2 25 SINR (db) Figure 6: SINR profile 5, where a single 82.11 interferer is present. Note that the sender and interferer nodes are hidden terminals. In Fig. 5, the attenuation on the data link is fixed at 15 db, while the attenuation on the interferer link is varied to produce different levels of interference at the receiver. Tuples of {PDR, SINR} are collected and plotted in Fig. 6 as the SINR profile. Note that we fixed the attenuation on the data link at 15 db so as to allow us to collect a full range of PDR values from % to 1% as the attenuation on the interferer link is varied. In order to use the SINR profile to predict the PDR performance of a wireless link in the presence of interferers, we follow the same methodology that we described in Section IV.B, i.e. using the RSS values (in mw) of the individual sender and interferers in Eqn. (2) to compute the SINR value. A lookup is then performed on the SINR profile to determine the PDR value corresponding to the computed SINR value. V. PERFORMANCE EVALUATION In this section, we evaluate the accuracy of the three measurement-based SINR interference models described in the previous section. We compare the models prediction on the impact of receiver interference on the achievable PDR performance of a wireless link. We refer to the models utilizing the RSS profile [4], SNR profile [5], and SINR 5 1 15 2 25 3 35 4 45 5 Attenuation on Interferer Link (db) Figure 8: Comparison of measured PDR values and predicted model (for a network with a single 82.11 interferer) profile [3], as the RSS model, SNR model, and SINR model, respectively. Since we are focusing on receiver interference, in all our evaluation scenarios, the sender and interferer nodes are hidden terminals so that they are able to transmit concurrently. Evaluations are carried out on our conducted testbed, as well as on an indoor 82.11a wireless testbed. Finally, the three models prediction accuracy is compared in terms of the root-mean-square error (RMSE) metric. A. Interference from a single 82.11 interferer In this evaluation, we compare the accuracy of the three models in a scenario where a single 82.11 interferer is interfering with the packet transmissions on a sender-receiver link, as shown in Fig. 7. For every attenuation value on the data link, we measure the PDR on the data link as the attenuation value on the interferer link is varied. Using the RSS values corresponding to every attenuation value on the data and interferer links, we compute the hypothetical RSS value in Eqn. (1) and the SINR value in Eqn. (2), which are then used to lookup the three models respective profiles to determine the predicted PDR value. Rather than reporting the results for every combination of attenuation values on the data and interferer links, we show in Fig. 8, one result that is representative of the three

models prediction of the changes in the PDR of the data link as the attenuation value on the interferer link is varied. In Fig. 8, results are shown for the case where the attenuation on the interferer link is varied from db to 49 db, while the attenuation on the data link is fixed at 1 db. The differences in the prediction accuracy of the three models is particularly evident in the narrow transition region where the measured PDR rapidly increases from % to 1%. The results show that the RSS model [4] performs relatively poorly in its PDR prediction. As mentioned earlier, the RSS model uses a profile that is highly dependent on the environment in which it is constructed, and we believe that is the cause for its poor PDR prediction accuracy. The SNR model [5] performs slightly better, although there is still a 2-3 db gap between its PDR prediction plot and the measured PDR plot in the narrow transition region. We believe this prediction gap is due to the SNR model using a profile that is constructed in a topology that is devoid of interference. We speculate that when an interferer is present, the capture effect [16] (where the receiver can successfully receive a stronger packet even during a packet collision) has a significant impact on the PDR performance, especially in the narrow transition region where the packet signal strengths of the sender and interferer nodes are comparable. Therefore, we would expect that a model that utilizes a profile constructed in a topology where 82.11 interference is present, would perform better in its PDR performance prediction. This is confirmed by our results in Fig. 8 where we see the SINR model [3] accurately predicting the PDR performance on the sender-receiver link, even in the narrow transition region. In terms of the RMSE of the PDR predictions, the SINR model easily outperforms the other two models with an RMSE of 5.6%, compared to the SNR model s and RSS model s RMSEs of 2.1% and 29.% respectively. B. Interference from two 82.11 interferers We next evaluate the PDR prediction performance of the three models in a network topology with two 82.11 interferers, as shown in Fig. 9. We set the attenuation on the data link to a fixed value of 1dB, while varying the attenuation on the two interferer links. The PDR on the data link is measured for every combination of attenuation values on the two interferer links. In Fig. 1, we show the result for the case where the attenuation on interferer link 1 is set to 18 db, while the attenuation on interferer link 2 is varied from db to 4 db. The result shown in Fig. 1 is representative of the three models prediction of the changes in the PDR of the data link, as the attenuation on the two interferer links are varied. Note that with 18 db attenuation on interferer link 1, there is still interference from interferer node I1 on the data link (even when the other interferer link 2 is disconnected due Figure 9: Network topology with two 82.11 interferers 1 8 6 4 2 Data Link Attenuation: 1dB; Interferer Link 1 Attenuation: 18dB 5 1 15 2 25 3 35 4 Attenuation on Interferer Link 2 (db) Figure 1: Comparison of measured PDR values and predicted model (for a network with two 82.11 interferers) to its attenuation being set to a high value like 4 db). This can be seen through the measured PDR values on the data link that only reaches a maximum of 98% (never reaching 1%) in Fig. 1. We see in Fig. 1 that the SINR model performs the best in predicting the PDR performance on the data link, compared to the SNR model and the RSS model. The RMSE for the PDR prediction of the SINR model is a low 2.5%, compared to an RMSE of 18.6% for the SNR model, and an RMSE of 37.3% for the RSS model. C. Interference from three 82.11 interferers In this evaluation, we construct a network topology with three 82.11 interferers, as shown in Fig. 11. The attenuation on the data link is set to 1 db, while the attenuation on interferer link 1 is set to 18 db. We vary the attenuation values on interferer links 2 & 3, and measure the corresponding PDR values on the data link. In Fig. 12, we show the result for the case where the attenuation on interferer link 3 is set to 18 db, while the attenuation on interferer

Figure 11: Network topology with three 82.11 interferers 1 8 6 4 2 Data Link Attenuation: 1dB; Attenuation on Interferer Link 1 & 3: 18dB 5 1 15 2 25 3 35 4 Attenuation on Interferer Link 2 (db) Figure 12: Comparison of measured PDR values and predicted model (for a network with three 82.11 interferers) link 2 is varied from db to 4 db. Again, this result is representative of the three models prediction of the changes in the PDR of the data link as we vary the attenuation values on interferer links 2 & 3. Fig. 12 shows that the measured PDR values never reach 1% even when interferer link 2 is disconnected (due to its attenuation being set to a high value, e.g. 4 db). The maximum measured PDR in Fig. 12 is only 91%. This is due to the existing interference from the two interferer nodes I1 and I3, with the attenuation on their links set to 18 db. We wish to point out that even when interferer link 2 is disconnected, the resulting PDR value cannot be directly compared to the corresponding PDR value for a network topology with two 82.11 interferers shown in Fig. 9. For example, we see in Fig. 12 that the measured PDR is 91% when interferer link 2 is disconnected. When this happens, the logical network topology is basically the same as in Fig. 9 (with the attenuations on interferer links 1 & 2 equal to 18 db). However, Fig. 1 shows that the measured PDR in this case is 96%. This discrepancy is because the physical characteristics of each interferer link in our conducted testbed are not the same, due to the different connectors and length of cables used on the links. This means that even though the programmable attenuator on interferer link 3 in Fig. 11 and interferer link 2 in Fig. 9 may be set to the same value of 18 db, the received signal strengths of packets received at receiver R from the interferer nodes I3 and I2 are not necessarily the same. As such, the measured PDR values may differ for two instances of network topologies that are similar. Fig. 12 shows that the SINR model performs the best in predicting the PDR performance on the data link, compared to the SNR model and the RSS model. The RMSE for the PDR prediction of the SINR model is 9.1%, compared to high RMSEs of 61.7% and 66.1% for the SNR model and the RSS model respectively. Note that for the RSS model, the predicted PDR values are % for all values of attenuation on interferer link 2. This is because when the RSS values (in mw) corresponding to the sender S and interferer nodes I1, I2, I3, are used in Eqn. (1), the resultant hypothetical singlesender RSS value (in mw) is less than. For negative RSS values (in mw), we take the predicted PDR value to be %. D. Interference from a single 82.11 interferer and white noise generator In Fig. 13, we construct a network topology with an 82.11 interferer and a white noise generator. By fixing the attenuation on the link connecting the white noise generator to the receiver R at 8 db, the interference signal from the white noise generator results in an approximately 2 db increase in the noise floor at the receiver R. We also vary the attenuation on the data and interferer links. We measure the PDR performance on the data link for every combination of attenuation values on the data and interferer links. We show in Fig. 14 a representative result of the combined effects of 82.11 interference and white noise interference on the PDR performance of the data link. Fig. 14 shows the result for the case where the attenuation on the data link is set to 1 db, and the attenuation on the interferer link is varied from db to 4 db. We see that even when the interferer link is disconnected (due to its attenuation value being set to a high value, e.g. 4 db), the measured PDR on the data link can only reach a maximum of 86%. This is due to the existing interference from the white noise generator. We also see that the SINR model performs the best in predicting the PDR performance on the data link, with an RMSE of 4.3%. In comparison, the SNR model and the RSS model perform poorly, with RMSEs of 43.5% and 17.5% respectively. The results in this

Figure 15: Indoor 82.11a wireless testbed 1 Tx Power at Sender Node: 9dBm Figure 13: Network topology with a single 82.11 interferer and white noise interference 1 Data Link Attenuation: 1dB; White Noise Link Attenuation: 8dB 8 6 4 8 2 6 4 2 18 16 14 12 1 Tx Power at Interferer Node (dbm) Figure 16: Comparison of measured PDR values and predicted model, in over-the-air experiments 8 6 4 2 5 1 15 2 25 3 35 4 Attenuation on Interferer Link (db) Figure 14: Comparison of measured PDR values and predicted model (for a network with a single 82.11 interferer and white noise interference) scenario with combined 82.11 and white noise interference are consistent with the results from our other experiments in the conducted testbed, i.e. the SINR model outperforms the other two models (SNR and RSS models) in predicting the PDR performance of a wireless link in the presence of interference. E. Over-the-air experiment Thus far, all the reported experiments have been carried out on our conducted testbed. In this section, we report the results of an experiment performed over-the-air in an indoor 82.11a wireless testbed, shown in Fig. 15. We operate the nodes in the testbed on a 5 GHz channel that is unoccupied by other 82.11 networks. Using three nodes S3, R and S4 on this testbed, we construct a network topology equivalent to the one shown in Fig. 7, i.e. a network with a single 82.11 interferer. Node S4 acts as the sender, while node S3 is the interferer. Fixed attenuators of 1 db and 5 db are attached to the antenna ports of the radio cards in the sender and interferer nodes respectively in order to reduce their transmission power. In addition to that, we also configure the transmission power levels at the sender and interferer nodes such that both nodes are hidden terminals, while at the same time being able to send packets to the receiver in the middle. The sender and interferer nodes are deemed to be hidden terminals if, when concurrently transmitting, they can transmit packets at the same maximum rate as when they are individually transmitting. The transmission power at the sender is varied from 1 dbm to 9 dbm, while the transmission power at the interferer is varied from 1 dbm to 19 dbm, both in steps of 1 dbm. At the receiver, we first measure its noise floor and the RSS of the sender and interferer nodes when they are individually transmitting. These measurements will be used to compute the hypothetical single-sender RSS and SINR values in Eqn. (1) and Eqn. (2) respectively. Then, with both sender and interferer nodes concurrently transmitting, we measure the PDR value on the data link. The measured PDR values are compared with the predicted PDR values from the three models in Fig. 16, where the transmission power at the sender is set to 9 dbm and the transmission power at the interferer is decreased from 19 dbm to 1 dbm. This result is representative of the three models prediction of the changes

in the PDR of the data link, as the transmission powers are varied at the sender and interferer nodes. Fig. 16 shows that the SNR model and the RSS model perform poorly in their PDR prediction, with RMSEs of 32.9% and 53.5% respectively. In contrast, the SINR model performs a lot better in predicting the PDR value on the data link, with an RMSE of 1.8%. This observation suggests that even though the profile used in the SINR model is constructed from an experiment in the conducted testbed, it can be used to predict the PDR performance in an overthe-air experiment. Since we use the same type of radio cards (Wistron Neweb CM9 Atheros 82.11a/b/g mini-pci card with the AR5213A chipset) in the nodes in both our conducted testbed and the indoor wireless testbed, this indicates that the SINR profile is a characteristic of the radio card, and is the same for all radio cards of the same model/type [14]. This also means that we only need to build the SINR profile once offline in the lab, and can then use it in actual network deployments. VI. CONCLUSION In this paper, we have systematically evaluated the accuracy of three measurement-based SINR interference models in predicting the impact of receiver interference on the PDR performance of a wireless link. Using different measurement methodologies to construct profiles that map the measured RSS or the computed SNR or SINR at the receiver to its measured PDR performance, these models utilize the SINR concept and the constructed profiles in order to predict the PDR performance of a wireless link in more complex scenarios involving multiple interferers. We have compared the accuracy of the three SINR interference models in various experiments carried out in both our conducted testbed and an indoor wireless testbed, incorporating multiple 82.11 interferers, and a non-82.11 interferer in the form of a white noise generator. Across all our evaluations, the results show that an interference model that uses an SINR profile consistently performs the best in predicting the PDR performance of a wireless link, with a maximum root-mean-square error (RMSE) of 1.8%. In constrast, interference models that use an SNR profile or an RSS profile perform poorly, with maximum RMSEs of 61.7% and 66.1% respectively. The performance difference in the three interference models that we evaluated is particularly evident in the narrow transition region where the PDR rapidly increases from % to 1%. In this transition region, the interference model utilizing the SINR profile easily outperforms the other two models using the SNR profile and the RSS profile. An interference model that can accurately capture the performance of a wireless link in the transition region has the potential to significantly improve the performance of channel allocation and transmission scheduling schemes. REFERENCES [1] A. Subramanian, H. Gupta, S. R. 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