Our Location-Aware Channel Assignment: GRID

Next, we introduce our location-aware channel assignment scheme. The MANET envi-ronment is the same, except that each mobile host must be installed with a positioning device, such as GPS receiver. So our protocol is more appropriate for outdoor envi-ronment. As will be seen later, our approach will assign a channel to a host once the host knows its current location. As a result, in addition to the positioning cost, there is no communication cost for our channel assignment (no message will be sent for this purpose).

We will refer to our scheme as GRID. The MANET is assumed to operate in a pre-defined geographic area. The area is partitioned into 2D logical grids as illustrated in Fig. 1. Each grid is a square of size d × d. Grids are numbered (x, y) following the conventional xy-coordinate. To be location-aware, a mobile host must be able to determine its current grid coordinate. Thus, each mobile host must know how to map a physical location to the corresponding grid coordinate.

Our channel assignment works as follows. We assume that the system is given a fixed number, n, of channels. For each grid, we will assign a channel to it. When a mobile host is located at a grid, say (x, y), it will use the channel assigned to grid (x, y) for transmission. One can easily observe that if we assign the same channel to two neighboring grids, then there will be high chance that the transmission activities on these two neighboring grids will contend, or even interfere, with each other. Thus, we should assign the same channel to grids that are spatially separated by some distance, but will exploit the largest frequency reuse.

Figure 1: Assigning channels to grids in a band-by-band manner: (a) n = 9 and (b) n = 14. In each grid, the number on the top is the channel number, while those on the bottom are the grid coordinate. Here, we number channels from 1 to n.

The above formulation turns out to be similar to the channel arrangement in the GSM system. In the following, we propose a way to assign channels to grids. Let m = √

n . We first partition the grids vertically into a number of bands such that each band contains m columns of grids. Then, for each band, we sequentially assign the n channels to each row of grids, in a row-by-row manner. In Fig. 1, we illustrate this assignment when n = 9 and n = 14. It can readily be seen that when n is a square of some integer, each channel will be regularly separated in the area.

2.2.1 Grid Size vs. Transmission Range

Let r be the transmission range of an antenna. Suppose the value of r is fixed. In this section, we discuss an important design issue: the relationship between r and the side length of grids, d. Below, we discuss several possibilities. For simplicity, let’s assume that m =√

n is an integer.

• d  r: This means many hosts will stay in a grid and thus contend with each other on one channel. When d = ∞, this degenerates to the case of one single channel.

Figure 2: The effect of r/d ratio on channel co-interference when n = 25.

• d > 2r/(m − 1): This is the case that the transmission activities from two hosts choosing the same channel will never interfere with each other. As illustrated in Fig. 2(a), hosts A and B (both choosing the same channel) are located in the nearest possible locations, but their signals will not overlap in any location.

• d = 2r/m: This is the case that the transmission activities from two hosts which choose the same channel and which are each located in the center of a grid will not interfere with each other. This is illustrated in Fig. 2(b).

• d = r/m: This represents the minimal value of d such that two hosts (located at the grid centers) using the same channel will not hear each other. This is illustrated in Fig. 2(c). By simple calculus, we can find that each receiver of these two hosts will have a probability of 0.396 being interfered by the signals from the other sender. The value is the ratio of the intersection area that is covered by both hosts A and B to the area that is covered by either host A or host B.

• d ≈ 0: This means that the grid size is infinitely small. This degenerates to the case that a mobile host will randomly choose a channel to transmit its packets, and thus little channel reuse can be exploited.

The above analysis has indicated some tradeoffs. This concept will be captured by the ratio r/d. If the ratio is too large, then the chance of co-channel interference will be high. On the other hand, if the ratio is too small, although co-channel interference can be reduced, the channel reuse will be reduced too since a channel will be unavailable in

Figure 3: Tests of blocked sender-receiver pairs at different r/d ratios: (a) n = 36 and (b) n = 81.

many locations. Thus, we need to carefully adjust the r/d ratio for the best network performance. This will be further investigated through simulations in Section 4.2.

2.2.2 Some Experiments on the r/d Ratio

At this point, it deserves to predict, under ideal situations, how much benefit our location-aware channel assignment can offer over a non-location-aware one. We de-veloped a simple simulation without concerning the details of medium access, such as collision, timing, etc. (this will be explored in Section 4). We simulated an area of size 1000× 1000. On this area, we randomly generated a sender A and then randomly generated a receiver B in the circle of radius r = 100 centered at A. A transmitted using a channel selected by two methods: (i) a static one based on host ID (referred to as SCA, static channel assignment), and (ii) our GRID approach. We then repeated this process to generate more sender-receiver pairs. However, for each pair generated, we tested whether this transmission will interfere any earlier ongoing pairs. If so, the current pair will be deleted; otherwise, it will be granted.

Through this ideal experiment, we intend to observe how many more sender-receiver pairs can be generated in the physical area by GRID than SCA. This will verify whether

Figure 4: A snapshot of our experiment in Fig. 3 when n = 36 and r/d = 3.0: (a) GRID and (b) SCA. The snapshots are taken on a 1000× 1000 area, and each circle means a sender-receiver pair.

GRID has a better channel reuse. Another important issue we would like to explore here is: what is best ratio r/d to maximize channel reuse?

Fig. 3 shows our first experimental results. The x-axis is the number of sender-receiver pairs generated. The y-axis shows the number of pairs that fail and thus are deleted. For our GRID, we tested different r/d ratios. Fig. 3(a) uses a total number of n = 36 channels, and Fig. 3 (b) uses n = 81. Indeed, some r/d ratios are better than SCA, while some are worse. In Fig. 3(a), we see that the r/d ratios 2.5, 3.0, and 3.5 will outperform SCA, while in Fig. 3(b), the r/d ratios 4.0, 4.5, and 5.0 will outperform SCA.

We conclude from the above experiments that when r/d ≈ √

n/2, our GRID will perform well. The reason is as follows. Let’s consider any channel. At this ratio, it is more likely that we can place most circles (which represent transmission activities of this channel) in a physical area, while incurring the least overlapping among circles (which represents co-channel interference). This is how our GRID can offer better channel reuse. Fig. 4 shows a snapshot in our experiment when n = 36 and r/d = 3.0 on the use of channel 1. Clearly, the placement of circles by GRID is denser and more regular than that of SCA.

Figure 5: Tests of blocked sender-receiver pairs at various n’s.

In Fig. 5, we further vary the value of n to observe the trend. In this figure, we have picked the best r/d ratio for each n. The number of sender-receiver pairs generate is 2000. As can be seen, the best ratios are all very close to√

n/2, as we have predicted.

Also, with more channels, there are less pairs being blocked by both GRID and SCA.

But the gain of GRID over SCA will enlarge as a larger n is used.