Effective Carrier Sensing in CSMA Networks under Cumulative Interference

In the literature, most studies on carrier sensing (e.g., [10, 8, 13, 11, 9, 12]) are based on the pairwise interference model. For a link under the pairwise interference model, the interferences from the other links are considered one by one. If the interference from each of the other links on the link concerned does not cause a collision, then it is assumed that there is no collision overall. Ref. [8] established the carrier-sensing range required to prevent hidden-node collisions in CSMA networks under the pairwise interference model. The resulting carrier-sensing range is too optimistic and can not eliminate hidden-node collisions if the more accurate cumulative interference model is adopted instead.

A number of recent papers studied the CSMA networks under the cumulative interference model (e.g., [14, 15, 16, 17]). An earlier unpublished technical report of ours [17] derived the safe carrier-sensing range under the cumulative interference model. The technical report, however, did not include the IPCS realization presented in this paper. Neither did Ref. [14, 15, 16] address the implementation of a carrier-sensing range based on power detection. Ref. [14] studied the asymptotic capacity of large-scale CSMA networks with hidden-node-free designs. The focus of [14] is on “order” result rather than “tight” result. For example, if $\gamma_{0}=10dB$ and $\alpha=4$, the safe carrier-sensing range derived in [14] is $8.75d_{\max}$. In this paper, we show that setting the safe carrier-sensing range to $5.27d_{\max}$ is enough to prevent hidden-node collisions.

The authors in [15, 16] attempted to improve spatial reuse and capacity by tuning the transmit power and the carrier-sensing range. Although the cumulative interference model is considered in [15, 16], spatial reuse and capacity are analyzed based on carrier-sensing range. In particular, they assumed that the transmitters of concurrent transmission links can be uniformly packed in the network. As discussed in this paper, such uniform packing can not be realized using the current 802.11 carrier-sensing mechanism. Therefore, the results in [15, 16] are overly optimistic without an appropriate carrier-sensing mechanism. IPCS fills this gap so that the theoretical results of [15, 16] remain valid. We summarize the key related models and results in the literature in Table I^***This paper focuses on the incremental-power carrier-sensing (IPCS) mechanism under the cumulative interference model. But IPCS proposed in this paper can also deal with the pairwise interference model..

The rest of this paper is organized as follows. Section II presents the cumulative interference model and the carrier sensing mechanism in the current 802.11 protocol. Section III derives the safe carrier-sensing range that successfully prevents the hidden-node collisions under the cumulative interference model. Section IV presents the IPCS mechanism. Section V evaluates the performance of IPCS in terms of spatial reuse and network throughput. Section VI concludes this paper.

We represent links in a wireless network by a set of distinct and directed transmitter-receiver pairs $\mathcal{L}=\{l_{i},1\leq i\leq{\left|\mathcal{L}\right|}\}$. Let $\mathcal{T}=\{T_{i},1\leq i\leq{\left|\mathcal{L}\right|}\}$ and $\mathcal{R}=\{R_{i},1\leq i\leq{\left|\mathcal{L}\right|}\}$ denote the set of transmitter nodes and the set of receiver nodes, respectively. A receiver decodes its signal successfully if and only if the received Signal-to-Interference-plus-Noise Ratio (SINR) is above a certain threshold. We adopt the cumulative interference model, where the interference is the sum of the received powers from all transmitters except its own transmitter. We assume that radio signal propagation follows the log-distance path model with path loss exponent $\alpha>2$. The path gain $G(T_{i},R_{j})$ from transmitter $T_{i}$ to receiver $R_{j}$ follows a geometric model:

where $d(T_{i},R_{j})$ is the Euclidean distance between nodes $T_{i}$ and $R_{j}$.

In 802.11, each packet transmission on a link $l_{i}$ consists of a DATA frame in the forward direction (from $T_{i}$ to $R_{i}$) followed by an ACK frame in the reverse direction (from $R_{i}$ to $T_{i}$). The packet transmission is said to be successful if and only if both the DATA frame and the ACK frame are received correctly. Let $\mathcal{L}^{\prime}$ ($\mathcal{L}^{\prime\prime}$) denote the set of links that transmit concurrently with the DATA (ACK) frame on link $l_{i}$. Under the cumulative interference model, a successful transmission on link $l_{i}$ needs to satisfy the following conditions:

and

where $P_{t}$ is the transmit power, $N$ is the average noise power, and $\gamma_{0}$ is the SINR threshold for correct reception. We assume that all nodes in the network use the same transmit power $P_{t}$ and adopt the same SINR threshold $\gamma_{0}$. For a link $l_{j}$ in $\mathcal{L}^{\prime}$ or $\mathcal{L}^{\prime\prime}$, $S_{j}$ represents the sender of link $l_{j}$, which can be either $T_{j}$ or $R_{j}$. This is because either DATA or ACK transmission on link $l_{j}$ will cause interference to link $l_{i}$.

If there exists a link $l_{i}\in\mathcal{L}$ such that not both (1) and (2) are satisfied, this means there is collision in the network. In 802.11, carrier sensing is designed to prevent collision due to simultaneous transmissions that cause the violation of either (1) or (2). In this paper, we assume carrier sensing by energy detection. Consider a link $l_{i}$. If transmitter $T_{i}$ senses a power $P^{CS}(T_{i})$ that exceeds a power threshold $P_{th}$, i.e.,

then $T_{i}$ will not transmit and its backoff countdown process will be frozen. This will prevent the DATA frame transmission on $l_{i}$.

In most studies of 802.11 networks, the concept of a carrier-sensing range $CSR$ is introduced. The carrier-sensing range $CSR$ is mapped from the carrier-sensing power threshold $P_{th}$:

Consider two links, $l_{i}$ and $l_{j}$. If the distance between transmitters $T_{i}$ and $T_{j}$ is no less than the carrier-sensing range, i.e.,

then $T_{i}$ and $T_{j}$ can not carrier sense each other, and thus can initiate concurrent transmissions between them. The pairwise relationship can be generalized to a set of links $\mathcal{S}^{CS}\subseteq\mathcal{L}$. If the condition in (4) is satisfied by all pairs of transmitters in set $\mathcal{S}^{CS}$, then all links in $\mathcal{S}^{CS}$ can transmit concurrently.

Setting an appropriate carrier-sensing range is crucial to the performance of 802.11 networks. If $CSR$ is too large, spatial reuse will be unnecessarily limited. If $CSR$ is not large enough, then hidden-node collisions may occur. The underlying cause of hidden-node collisions are as follows. A number of transmitters transmit simultaneously because condition (4) is satisfied by all pairs of the transmitters. However, there is at least one of the links does not satisfy either (1) or (2). As a result, collisions happen and the carrier sensing mechanism is said to have failed in preventing such collisions.

We now define a safe carrier-sensing range that always prevents the hidden-node collisions in 802.11 networks under the cumulative interference model.

For analysis simplicity, we assume that the background noise power $N$ is small compared with interference and thus can be ignored. We will consider Signal-to-Interference Ratio (SIR) instead of SINR.

In the current 802.11 MAC protocol, given the safe carrier-sensing range Safe-$CSR_{\text{\emph{cumulative}}}$, the carrier-sensing power threshold $P_{th}$ is set as

Before transmitting, a transmitter $T_{i}$ compares the power it senses, $P^{CS}(T_{i})$, with the power threshold $P_{th}$. A key disadvantage of this approach is that $P^{CS}(T_{i})$ is a cumulative power from all the other nodes that are concurrently transmitting. The cumulative nature makes it impossible to tell whether $P^{CS}(T_{i})$ is from one particular nearby transmitter or a group of far-off transmitters [18]. This reduces spatial reuse, as illustrated by the example in Fig. 3.

There are four links in Fig. 3, with Safe-$CSR_{\text{\emph{cumulative}}}$ set as in (6). In Fig. 3, the distance $d(T_{1},T_{2})$ is equal to Safe-$CSR_{\text{\emph{cumulative}}}$. From (II-B), we find that $T_{1}$ and $T_{2}$ can not carrier sense each other, thus they can transmit simultaneously.

First, consider the location requirement of the third link $l^{\prime}_{3}$ that can have a concurrent transmission with both $l_{1}$ and $l_{2}$, assuming that each transmitter can perfectly differentiate the distances from the other transmitters. Suppose that the third link is located on the middle line between $l_{1}$ and $l_{2}$. Based on the carrier-sensing range analysis, the requirements are $d(T^{\prime}_{3},T_{1})\geq\text{\emph{Safe-}}CSR_{\text{\emph{cumulative}}}$ and $d(T^{\prime}_{3},T_{2})\geq\text{\emph{Safe-}}CSR_{\text{\emph{cumulative}}}$. So the third link can be located in the position of $l^{\prime}_{3}$, shown in Fig. 3. Furthermore, as the number of links increases, a tight packing of the concurrent transmitters will result in a regular equilateral triangle packing with side length Safe-$CSR_{\text{\emph{cumulative}}}$. The “consumed area” of each transmitter is a constant given by $A=\frac{\sqrt{3}}{2}\emph{Safe-}CSR_{\text{\emph{cumulative}}}^{2}$.

Now, let us consider the location requirement of the third link $l_{3}$ under the carrier-sensing mechanism of the current 802.11 protocol. In order to have concurrent transmissions with both $l_{1}$ and $l_{2}$, the cumulative power sensed by $T_{3}$ due to transmissions of both links $l_{1}$ and $l_{2}$ should be no larger than $P_{th}$, i.e.,

where $P_{th}$ is given in equation (8). So the minimum distance requirement on $d(T_{3},T_{1})$ and $d(T_{3},T_{2})$ is

as shown in Fig. 3. Since $2^{\frac{1}{\alpha}}$ is always greater than $1$, the requirement of the separation between transmitters is increased from $\text{\emph{Safe-}}CSR_{\text{\emph{cumulative}}}$ (i.e., $d(T_{1},T_{2})$) to $2^{\frac{1}{\alpha}}\text{\emph{Safe-}}CSR_{\text{\emph{cumulative}}}$ (i.e., $d(T_{1},T_{3})$ and $d(T_{2},T_{3})$). The requirement on the separation between transmitters will increase progressively as the number of concurrent links increases, and the corresponding packing of transmitters will be more and more sparse. As a result, spatial reuse is reduced as the number of links increases.

Another thing to notice is that the order of the transmissions of links also affects spatial reuse in the conventional carrier-sensing mechanism. Consider the three links, $l_{1}$, $l_{2}$ and $l_{3}$ in Fig. 3 again. If the sequence of transmissions is $\{l_{1},l_{2},l_{3}\}$, as discussed above, $T_{1}$, $T_{2}$ and $T_{3}$ sense a power no greater than $P_{th}$, and thus $l_{1}$, $l_{2}$ and $l_{3}$ can be active simultaneously. If the sequence of transmissions on these links is $\{l_{2},l_{3},l_{1}\}$, however, both $T_{2}$ and $T_{3}$ sense a power no larger than $P_{th}$. But the cumulative power sensed by $T_{1}$ in this case is

Therefore, $T_{1}$ will sense the channel busy and will not initiate the transmission on $l_{1}$. The spatial reuse is unnecessarily reduced because there would have been no collisions had $T_{1}$ decide to transmit⁸⁸8This corresponds to the exposed-node phenomenon..

We propose an enhanced physical carrier-sensing mechanism called Incremental-Power Carrier-Sensing (IPCS) to solve the issues identified in section IV-A. Specifically, the IPCS mechanism can implement the safe carrier-sensing range accurately by separating the detected powers from multiple concurrent transmitters.

There are two fundamental causes for collisions in a CSMA network. Besides hidden nodes, collisions can also happen when the backoff mechanisms of two transmitters count down to zero simultaneously, causing them to transmit together. Note that for the latter, each of the two transmitters is not aware that the other transmitter will begin transmission at the same time. Based on the power that it detects, it could perfectly be safe for it to transmit together with the existing active transmitters, only if the other transmitter did not decide to join in at the same time. There is no way that the carrier-sensing mechanism can prevent this kind of collisions. This paper addresses the hidden-node phenomenon only. To isolate the second kind of collisions, we will assume in the following discussion of IPCS that no two transmitters will transmit simultaneous³³3Collisions due to simultaneous countdown-to-zero can be tackled by an exponential backoff mechanism in which the transmission probability of each node is adjusted in a dynamic way based on the busyness of the network. In WiFi, for example, the countdown window is doubled after each collision. The probability of this kind of collisions can be made small with a proper design of the backoff mechanism. Conceptually, we could imagine the random variable associated with backoff countdown to be continuous rather than discrete, which means that the starting/ending of one link’s transmission will coincide with the starting/ending of another link’s transmission with zero probability.

The key idea of IPCS is to utilize the whole carrier-sensing power history, not just the carrier-sensing power at one particular time. In CSMA networks, each transmitter $T_{i}$ carrier senses the channel except during the time when it transmits DATA or receives ACK. The power being sensed increases if a link starts to transmit, and decreases if a link finishes transmission. As a result, the power sensed by transmitter $T_{i}$, denoted by $P_{i}^{CS}(t)$, is a continuous function of time $t$.

In IPCS, instead of checking the absolute power sensed at time $t$, the transmitter checks increments of power in the past up to time $t$. If the packet duration $t_{packet}$ (including both DATA and ACK frames and the SIFS in between) is a constant for all links, then it suffices to check the power increments during the time window $[t-t_{packet},t]$⁴⁴4This assumption is used to simplify explanation only. In general, we could check a time window sufficiently large to cover the maximum packet size among all links.. Let $\{t_{1},t_{2},\cdots,t_{k},\cdots\}$ denote the time instances when the power being sensed changes, and $\{\Delta P_{i}^{CS}(t_{1}),\Delta P_{i}^{CS}(t_{2}),\cdots,\Delta P_{i}^{CS}(t_{k}),\cdots\}$ denote the corresponding increments, respectively. In IPCS, transmitter $T_{i}$ will decide the channel to be idle at time $t$ if the following conditions are met:

where $P_{th}$ is the carrier-sensing power threshold determined according to $CSR$; otherwise, the channel is deemed to be busy. Since $\Delta P_{i}^{CS}(t_{k})$ is negative if a link stops transmission at some time $t_{k}$, we only need to check the instances where the power increments are positive.

By checking every increment in the detected power, $T_{i}$ can separate the powers from all concurrent transmitters, and can map the power profile to the required distance information. In this way, IPCS can ensure the separations between all transmitters are tight in accordance with Theorem 1.

Let us use Fig. 3 again to show how IPCS can implement the safe carrier-sensing range successfully. We set the carrier-sensing power threshold $P_{th}$ as in (10). We will show that the location requirement of the third link under IPCS is the same as indicated by the safe carrier-sensing range (location $l^{\prime}_{3}$ in Fig. 3). The transmitter of the third link will only initiate its transmission when it senses the channel to be idle. Its carrier-sensed power is shown in Fig. 4. Without loss of generality, suppose that link $l_{1}$ starts transmission before $l_{2}$. The third transmitter detects two increments in its carrier-sensed power at time instances $t_{1}$ and $t_{2}$ which are due to the transmissions of $T_{1}$ and $T_{2}$, respectively. In the IPCS mechanism, the third transmitter will believe that the channel is idle (i.e., it can start a new transmission) if the following is true:

Substituting $P_{th}$ in (10) to (11), we find that the requirements in (11) are equivalent to the following distance requirements:

So the third link can be located at the position of $l^{\prime}_{3}$, as shown in Fig. 3, instead of far away at the location of $l_{3}$ as in the conventional carrier-sensing mechanism.

Compared with the conventional carrier-sensing mechanism, the advantages of IPCS are

1. 1.

   IPCS is a pairwise carrier-sensing mechanism. In the IPCS mechanism, the power from each and every concurrent link is checked individually. This is equivalent to checking the separation between every pair of concurrent transmission links. With IPCS, all the analyses based on the concept of a carrier-sensing range remain valid.

2. 2.

   IPCS improves spatial reuse and network throughput. In the conventional carrier-sensing mechanism, the link separation requirement increases as the number of concurrent links increases. In IPCS, however, the link separation requirement remains the same. Furthermore, because IPCS is a pairwise mechanism, the order of the transmissions of links will not affect the spatial reuse.