Optimizing the performance of non-fading and fading networks using CSMA with joint transmitter and receiver sensing
© Kaynia and Øien; licensee Springer. 2012
Received: 1 August 2011
Accepted: 28 July 2012
Published: 23 August 2012
We consider a mobile ad hoc network where packets belonging to specific transmitters arrive randomly in space and time according to a 3-D Poisson point process, and are upon arrival transmitted to their intended destinations using the carrier sensing multiple access (CSMA) MAC protocol. A packet transmission is considered successful if the received SINR is above a predefined threshold for the duration of the packet. A simple fully-distributed joint transmitter-receiver sensing scheme is proposed for the CSMA protocol to improve its performance in both non-fading and fading networks. The outage probability of this enhanced version of CSMA is derived and optimized with respect to the sensing thresholds. In order to derive a mathematical expression for the optimal sensing thresholds, the inherent hidden and exposed node problems of CSMA are considered and efficiently balanced. The performance of this improved CSMA protocol is compared to the other flavors of CSMA, and shown to bring about significant performance gain.
Medium access control (MAC) layer design is commonly applied to address the problem of allocating scarce resources in a wireless network. Various MAC protocols are proposed in order to share the communication channel in the most efficient manner, in order to minimize the destructive interference. One such protocol that has gained great popularity is carrier sensing multiple access (CSMA). This protocol is successfully employed in the IEEE 802.11 standard family, and many enhancements have been proposed and implemented in order to minimize the inherent hidden and exposed node problems [1–3]. Nevertheless, there is still room for improvement, in particular in networks with high density of simultaneous transmissions. This provides the motivation behind our study.
Numerous studies have evaluated the performance of the CSMA protocol, evaluating its performance in terms of throughput and bit error rate [4–6]. Much of this study confirms CSMA’s superiority over other protocols, such as ALOHA, with natural tradeoffs in other domains such as transmission rate and delay [1, 6]. Also, many extensions have been proposed to improve the performance of CSMA [7–9]. However, the conventional model used in most of these studies assumes that the topology of the network is known, and that multiple links cannot communicate simultaneously. Such assumptions are not realistic for mobile ad hoc networks (MANETs). The closest model to a real-life ad hoc network is that used in [10, 11], where users are assumed to be Poisson distributed in space and each transmitter communicates with its own receiver using ALOHA, while allowing for simultaneous communication between links. This model was embraced in , and is also applied in our study.
Choosing the right value for CSMA’s sensing threshold (which the backoff decision is based on) is of great importance for the performance of this protocol. Many studies have proposed various adaptation schemes to find the optimal carrier sensing threshold of CSMA to enhance the throughput and the transmission reliability in dynamically changing networks [13–15]. In , a novel analytical model was introduced for determining the optimal carrier sensing range in ad hoc networks by minimizing the sum of the hidden and exposed terminal areas. The optimization is done in terms of aggregate throughput, yielding that the optimal carrier sensing range is approximately equal to the interference range. The study of  further improves the carrier sensing capability of CSMA by adding fairness to the equation, while retaining the throughput performance. The shortcoming of this study is that only six node pairs are considered in the performance evaluation, limiting the applicability of the results to a randomly distributed ad hoc network with high density of simultaneous transmissions. Moreover, it is shown in  that the optimal algorithm is for the senders to keep the product of their transmit power and carrier sensing threshold equal to a constant. However, this algorithm is not distributed, and is dependent on the estimation of signal powers. Another algorithm for maximizing the throughput is to decrease the sensing range as long as the network remains sufficiently connected . An improved carrier sensing threshold adaptation algorithm was proposed in , where each node chooses the sensing threshold that maximizes the number of successful transmissions in its neighborhood. The drawback of this technique is that it relies on the collection of information over a period of time, which entails higher complexity, and introduces delays. Zhu et al. derive in  the optimal sensing threshold of the conventional CSMA protocol to be β t =ρ(1 +β1/α) α , where ρ represents the transmitted signal strength, α is the path loss exponent, and βis the minimum required signal-to-interference-plus-noise ratio (SINR) threshold for correct reception of packets. The optimized CSMA protocol was evaluated on a real test-bed in .
In , a new version of the CSMA protocol is proposed, denoted CSMARX, where the receiver (as opposed to the transmitter in CSMATX) performs the channel sensing and makes the backoff decision. The sensing thresholds of both CSMATX and CSMARXare optimized in a non-fading ad hoc network. It is shown that for lower densities, applying a sensing threshold may not provide any improvement compared to having no sensing at all. For higher densities, however, significant reduction in the outage probability can be obtained by setting the sensing threshold of the transmitter in CSMATX, β t , or of the receiver in CSMARX, β r , equal to the communication threshold, β, i.e., .
Having considered the performance of CSMATXand CSMARX, a natural question then becomes: Can we improve the performance of CSMA further if we allow both the transmitter and its receiver to sense the channel, and subsequently let them collectively decide whether or not to initiate transmission of each packet? And moreover, what are the optimal sensing thresholds that minimize the outage probability of this new flavor of CSMA both in the absence and presence of fading?
Hence, in the following, we will analyze the impact of a joint backoff decision making on the performance of the CSMA protocol. Following the same style of notation as in , we refer to this modified flavor of CSMA as CSMATXRX. The analytical framework used in the present study is inspired from , with the addition of allowing for a joint backoff decision making mechanism, and adding fading effects to the network model. The concept of a joint backoff decision making was first introduced in , where only a non-fading network was considered, and the MAC protocols did not allow for multiple backoffs and retransmissions, something that simplified the analysis significantly. Not only is the analysis of the present article useful for future improvements made to CSMA, it also provides us with a fundamental understanding of the hidden and exposed node problems, which are the main sources of imperfection of this protocol. This in-depth understanding is used to derive the optimal sensing thresholds of CSMATXRX, something that would otherwise be too complicated to achieve. The hidden node problem occurs whenever a new node is unable to detect an ongoing transmission, so that it initiates its transmission and thereby causes outage for an already active packet. The exposed node problem is characterized by transmissions being prevented even though they could have taken place without harm to other ongoing transmissions. A decrease in one of these two problems, results in an increase in the other, and vice versa. Choosing optimal values for the sensing thresholds β t and β r will provide a balance between the hidden and exposed node problems, thus improving the network performance.
where we have used: . Replacing by a fixed value R yields the error expression we use in our analyses and thereby confirms that our assumption on the fixed transmitter-receiver distance does not impact the lower bound outage probability analysis significantly. Also, it is worthwhile noting that the whole network with a fixed R could be viewed as a snapshot of a multi-hop wireless network, where R is the bounded average inter-relay distance. For more details on this 3-D model, please refer to .
Our traffic model has the following main attributes, which will be significant in our derivations;
Our network is highly mobile, meaning that different and independent sets of nodes are observed on the plane from one slot (of duration T) to the next.
The waiting time between each retransmission attempt, t wait , is by design ensured to be more than T. Because of the high mobility assumption, new channel instances are observed between transmission attempts, and thus there are no temporal correlations between retransmissions.
Upon retransmission of a packet, it is treated as a new packet arrival and placed in a new location, resulting are no spatial correlations between retransmission attempts.
where r i is the distance between the node under observation and the i th interfering transmitter; h00represents the fading effects between the receiver under observation, RX0, and its designated transmitter; h0i is the fading coefficient between RX0 and the i th interfering transmitter. The summation is over all active interferers on the plane at a given time instant t.
The channel access is driven by the CSMATXRXprotocol. This protocol operates as follows: When the transmitter has a packet to transmit, it performs physical carrier sensing of the interference power, Pint, in the channel (i.e., the radio measures the energy received on its available radio channel). Based on this measurement, and its knowledge on the distance R to its own receiver, the transmitter calculates the expected received SINR by using Equation (2), where the denominator is replaced by the measured Pint. If this expected received SINR is below the required threshold β t , the channel is considered busy and the transmitter refrains from transmission. If it is above β t , a request-to-send (RTS) signal is sent to the receiver, which then performs a similar channel sensing of the interference power around itself. If this measured SINR at the receiver is below the required sensing threshold β r , it informs its transmitter to cancel the transmission; if the measured SINR is above β r , a clear-to-send (CTS) signal is sent to the transmitter, which then initiates the packet transmission.
Once a transmission is initiated, there is still a probability that the packet is received in error at its destination, i.e., the received SINR is below βat some t∈(0,T). In this case, the packet is retransmitted. Each packet is given M backoffs and N retransmissions before it is dropped and counted to be in outage.
Note that the main difference between the proposed CSMATXRX protocol and the CSMA/CA protocol used in the IEEE 802.11 standard is that in the latter, all nodes hear the RTS and CTS signals, whereas in CSMATXRX, the communication of control signals occurs between a transmitter and its own receiver only (e.g., by using coding or separate frequency bands). Such isolated signaling scheme has a few benefits: (a) collision between the control signals is avoided, (b) delays in the decision-making stage are reduced, and (c) the situation where nodes unnecessarily decide to back off due to the detected RTS/CTS signal (even though their packets would have been received correctly at their own receivers) is mitigated.
where b is the average rate that a successful packet achieves, with units [bits/s/Hz per packet]. The unit of is [bits/s/Hz/m2]. In the following sections, we derive the outage probability of CSMATXRXboth in the absence and in the presence of fading. In Section 5, the sensing threshold of the transmitter, β t , and that of the receiver, β r , are both optimized.
Performance in the absence of fading
In this section, we assume no fading effects in the channel, i.e., the signal degradation is due to path loss only, as described in Section 2. First, we explain the method of analysis as well as the key steps of the mathematical derivations, before the result of the analysis is presented in Subsection 3.2.
Method of analysis
Now, given the packet transmission of TX0-RX0 is initiated and it is not in error at the start of its transmission, there is a probability that a new interferer, TX i , enters the plane at some t∈(0,T), is located inside B(RX0,s), and thus causes error for the packet of RX0. Since TX i would back off if it or its receiver detect the transmission of TX0, this means that in order for TX i to cause outage for RX0, it must be placed inside , while its receiver RX i is located outside of B(TX0,s r ). This probability is denoted as Pduring, and is given in the following subsection.
where P b is the backoff probability, Prt 1is the probability that the packet is received in error at its first transmission attempt, and P rt is the probability that the packet is received erroneously in a retransmission attempt. The reason we distinguish between Prt 1 and P rt is that due to the backoff decision making stage, the area where there is a probability of detecting an active interferer during a transmission is smaller in the first transmission than in the following retransmissions.
Outage probability in non-fading networks
Based on the above derivations, we are now able to mathematically express the outage probability of CSMATXRX in a non-fading network. This is given by the following theorem.
where A ol (s t ,s r )is given by Equation (6).
with Arx|active(s t ,s r ,s)given by Equation (7).
For more details on the derivation of Equations (10) and (14), please refer to . Optimization of the sensing thresholds is carried out in Section 5, and comparison between CSMATXRXwith the other CSMA versions is performed in Section 6.
Performance in the presence of fading
In this section, we add fading effects to the path loss attenuation, as described in Section 2. Due to the independence of the channel fading coefficients on distance, we can no longer operate with the closest interferer for the derivation of the outage probability. Instead, we must consider the dominant interferer, which is a single interferer whose received interference power (affected by the distance and the random channel coefficients) alone is strong enough to result in outage for the packet under observation.
Similar to Section 3, we first explain the method of analysis as well as the key steps of the mathematical derivations, before the result of the analysis is presented in Subsection 4.2.
Method of analysis
which is inserted back into Equation (20).
Inserting this expression back into Equation (17), yields the backoff probability of CSMATXRX.
Once a transmission has been initiated, there is a probability that the packet is in error at the start of its first transmission attempt. This is denoted by Prx|active(h00,h0i). Using geometry again, this probability is given as the probability that an active interferer already exist on the plane inside B(RX0,s f ), that was not detected during the backoff decision-making stage. That is, the interferer TX i must be located inside , which is shown as the darkly shaded area in Figure 2 and is approximated by Equation (7).
Outage probability in fading networks
Based on the derivations given above, we arrive at the following theorem.
where is given by Equation (18).
Optimization of the sensing thresholds is carried out in the next section, and comparison between CSMATXRXwith the other CSMA versions is performed in Section 6.
Optimizing the sensing thresholds
In order to find the optimal sensing thresholds of CSMATXRX, , and , such that the outage probability is minimized, we must in principle differentiate the outage probability expressions given in Theorems 1 and 2 with respect to s t and s r , and set each equal to 0. However, because of the complexity of our equations, this turns out to be a nontrivial task. Hence, we attack our optimization problem from another angle; we evaluate the total outage probability of CSMATXRXbased on the change in the exposed and hidden node problems.
The exposed node problem is a direct consequence of the transmitter making the backoff decision.
Optimization in the absence of fading
For 2Π λcsmas2<1, we have that , indicating convexity. Hence, we may conclude that for low enough values of the density (where our approximate expressions are more accurate), Perror (and thereby Pout(CSMATXRX)) is a convex function of s.
where P rt =P rx + (1−P rx ) Pduring. The optimal value for s t is then the solution to , which must be solved numerically.
First set s t to be a fixed value (e.g., s t =0as in ). We know from  that the optimal s r that minimizes the outage probability of CSMARXis , which corresponds to . The intuition behind this is as follows:
●For s r <s⇒B(RX0,s r )<B(RX0,s)⇒lower probability of backoff ⇒higher probability that outage occurs during an active transmission. Note that the reduction in the backoff probability does in fact not result in a reduction in the probability that outage occurs during a transmission, because even though B(RX0,s r )<B(RX0,s), any active transmissions inside B(RX0,s)upon the arrival of TX0-RX0 will contribute to the outage. Hence, if s r <s, the total outage probability will be higher than its minimum value.
●For s r >s⇒B(RX0,s r )>B(RX0,s)⇒higher probability of backoff ⇒lower probability that outage occurs during an active transmission. However, this decrease is less than the increase in the backoff probability, because the change in the area of B(RX0,s r )is larger than the decrease in the circumference of the circle around TX i where RX i can be located. Hence, the total outage probability increases as s r increases beyond s.
The point where the outage probability is decreasing at its highest rate, i.e., the minimum point of , occurs for s t =s−R b . This corresponds to β t =(β1/α−1) α . For this value of β t , B(RX0,s) covers B(TX0,s t ) completely, meaning that the transmitter sensing of CSMATXRXintroduces no additional exposed node problems, while at the same time providing some protection for its receiver, thus reducing the hidden node problem. That is, for s>R, s t can be increased up to (s−R)without introducing any exposed node problems, meaning that in CSMATXRX it is always valid that .
Optimization in the presence of fading
In the case of fading, the optimization problem becomes more complicated, as we can no longer translate it to a distance problem. Intuitively, we would expect CSMATXRXto yield an optimal performance when β r =βand β t =0. The reason for this is as follows:
If β r >β, the exposed node problem is increased, while the hidden node problem is not reduced (this is partly because we do not consider the aggregate interference power in our derivations). On the other hand, if β r <β, there is no exposed node problem, but the hidden node problem is higher than when β r =β. Hence, .
Next, we evaluate the benefit that the transmitter sensing of CSMATXRXprovides. Since the channel coefficient from TX i to TX0 is independent from the channel coefficient from TX0 to RX i , the decision-making of the TX i based on its own channel does not provide much benefit for the packet reception at its receiver (in terms of the hidden node problem). In fact, the transmitter’s decision to back off from transmission when its receiver wishes to activate it, is only adding to the exposed node problem. Hence, .
Second, we observe that as the density increases, so does the outage probability, until the network reaches a point of saturation, where Pout≈1. By increasing the number of backoffs and retransmissions, significant performance gain can be obtained. For low densities with (M,N)=(2,1), the outage probability is up to 10 times lower than when (M,N)=(1,0). Thirdly, the addition of transmitter sensing in CSMATXRXdoes not appear to provide any improvement compared to CSMARX. In fact, CSMARX outperforms CSMATXRX by up to 20% in non-fading networks and up to 50% when fading is present. This is due to the exposed node problem caused by the transmitter sensing in CSMATXRX. That is, when M is small, the protection that the transmitter sensing provides does not counterbalance the backoff probability increase it generates.
In this article, we improve the performance of CSMA in wireless ad hoc networks by introducing joint transmitter-receiver sensing and simultaneously optimizing the sensing thresholds of both the transmitter and the receiver. This protocol is denoted as CSMATXRX. Within a Poisson distributed ad hoc network, approximate analytical expressions are derived for the outage probability of CSMATXRXwith respect to the transmission density and the sensing thresholds. The optimal sensing thresholds for both the transmitter and receiver are obtained both in non-fading and fading networks, and an understanding is provided for how these optimal thresholds balance between the hidden and exposed node problems of CSMA. It is shown that using optimal sensing thresholds can provide significant performance gain for all transmission densities. Moreover, when multiple backoffs are allowed, CSMATXRX outperforms CSMARX, which was previously shown to provide the best performance in unslotted systems, e.g., when M=4, this improvement is 40%.
For future study, we wish to improve the performance of CSMA by investigating more efficient use and exchange of channel information between each transmitter and its receiver. Other possible extensions are to apply adaptive rate and power control to further improve the performance of CSMA in wireless ad hoc networks.
aThis protocol was evaluated in . We assume low density of transmissions, where the outage probability expressions are good approximations.bThis assumes that s>R, which is the case in most networks, as it ensures that the receiver can detect its own transmitter.
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