Predicting radio channel capacity

Use patterns in a conventional two-way system affect channel capacity, which can be predicted using a voice message analogy similar to a data packet. User effects can then be modeled with an adaptive user-protocol concept.

Individuals involved in the design and support of conventional two-way radio systems may have asked themselves at one time or another, “What is the real capacity of this single radio channel anyway?” Over the years, figuring out the actual capacity of a single channel has seemed a bit elusive. Although single channel capacity is not constant, it is predictable. It’s no surprise that as more users try to access a system, it becomes congested. What is a surprise is another dimension to the problem that isn’t so obvious.

This article presents an approach to understanding why and how land mobile channels can get congested so quickly during periods of heavy use. This approach models the radio user as an “adaptive protocol machine.” Specifically, the user’s radio etiquette is treated as an analogy to protocol schemes that control communications channels. In the context of this article, “protocol” applies to the relaying of voice communications between two users on a single shared conventional channel (non-trunked).

Multiple-access channel The conventional land mobile radio is a shared, multiple-access medium with several users competing to use it. These users randomly capture the channel, one at a time, and fill it with voice messages of varying lengths, each separated by a random idle time. (See Figure 1 below.) Given this constant competition, a user’s radio etiquette, or protocol, can determine how effectively a single channel can be shared by many. The concept of a multiple-access communications medium is more popularly identified with packet radio or LANs. However, it can also apply to the conventional channel if the following analogies are made between parameters that define a packet data channel and a conventional voice channel: * Channel capacity: typically measured in data bits per second. The conventional channel analogy is voice messages per minute. * Packet: defined for data in bits per frame per transmitted packet. For the voice analogy it can be defined as seconds per message per PTT. * Collision vulnerability window: generally defined in data channels as propagation time vs. packet time. A voice channel analogy can be PTT activation time vs. idle time between messages. * Protocol: a tightly followed procedure programmed in data modems. The voice radio analogy can be thought of as a loosely followed radio behavior (etiquette) in humans. * Throughput delay: total time to successfully receive a complete message (consider these equal for both the data and the voice analogy). The mathematics for calculating the throughput capacity of a data channel can be scaled with these analogous channel parameters to calculate the expected throughput capacity of voice messages in the conventional channel. (Based on statistics of random events.)

Protocol A protocol is a set of rules governing the use of a communications medium. Protocols are programmed into several layers of a communications system to promote efficient use of the communications medium and to ensure optimum throughput. Generally, protocols are designed to ensure that most of the offered load (a transmitted message) becomes a successful throughput (a message successfully received and understood). Several types of multiple-access schemes exist, but only two are considered for this adaptive user definition-pure ALOHA (non-slotted), a transmit when ready scheme, and carrier-sense, multiple-access (CSMA), a transmit after listening scheme.

Adaptive user protocol concept To illustrate the adaptive user protocol concept, consider the typical user’s call behavior when using a conventional channel, and how it mimics the ALOHA or CSMA protocols previously described. The user will either: 1. Transmit immediately without regard to whether the channel is being used. 2. Listen until the channel is idle before transmitting. When the channel is idle, the user may (a) transmit immediately, (b) wait a random time before transmitting or (c) choose not to transmit at all and try later.

Each of these user choices represents a different type of multiple-access protocol scheme. The behavior in Case 1 illustrates pure ALOHA, with the user transmitting without regard as to whether the channel is busy. The Case 2 behavior is similar to a CSMA scheme with a listening action (carrier sensing) prior to transmission (access). Each subsequent transmit decision in Case 2 is defined by a range of probabilities that the user will transmit in the idle timeframe. This is referred to as the persistence probability and is represented by p, with values from 0 to 1.

For instance, the immediate transmit decision in Case 2a pertains to a 1-persistant CSMA, meaning there is a 100% chance that an immediate transmission will take place when the channel becomes idle. The Case 2b decision, waiting a random time before transmitting, represents p-persistent CSMA, reflecting the distributed probability of transmission among all users, some of whom may choose immediate transmission (p = 1), and some of whom may choose to wait a while (p < 1).

The choice to not transmit at all but to try again later, Case 2c, represents n-persistent CSMA (p ~ 0). Many conventional LMR systems have users falling in either the p-persistent CSMA or 1-persistent CSMA protocol category. The study on which this article is based assumed 1-persistent CSMA behavior by all users, choosing to transmit as soon as the channel is idle.

For normal (light to moderate) radio traffic, most users will exercise proper radio etiquette, resulting in channel stability, high potential channel throughput and minimum throughput delay times (no waiting, no message repeats). When a crisis occurs, more users attempt to communicate on the channel, resulting in more messages with fewer, shorter times between messages to gain access. This behavior increases the chance for message collisions, especially as users grow impatient from waiting a long time for the chance to transmit. In turn, this result increases the throughput delay because of wait times and repeated messages caused by collisions.

On a collision path Concerning collisions, it is important to note that in the conventional LMR channel, no immediate collision awareness exists because the receiver is muted during a transmission. Therefore, a user won’t know if another user is transmitting at the same moment. Consequently, these messages collide and both users continue talking, each assuming exclusively channel access. Both messages are unintelligible (because of distortion from radio heterodyne, in most cases).

During this collision, the channel is unusable to others and is actually blocked until both users finally release their PTTs. This situation further increases throughput delay and reduces channel availability for everyone. In extreme crisis situations, some users may forget their proper radio etiquette and become a bit selfish. More users may transmit without waiting for the channel to become idle and try to “punch through” the radio clutter. Such action causes many more message collisions and the channel starts sounding like a continuous stream of noise with no discernible communications.

Eventually, the effective throughput of the channel is reduced to nearly zero. Such anxious user behavior mirrors the pure ALOHA multiple-access protocol scheme. No listening is being done, and users are transmitting whenever they feel like it, just hoping to get through.

Protocol simulation To test the utility of this concept, an adaptable multiple-access algorithm was modeled with MATLAB to predict the channel capacity and to simulate how capacity is affected as users change behavior. To model behavior change, I used a variable, the collision vulnerability window, that made it possible to assess how the adaptive user protocol affects overall channel capacity. This variable measures the period of possible collision and can be universally applied in any random-access protocol.

The vulnerability window is the key to understanding how a change in user protocol can severely affect a radio’s channel capacity. The vulnerability window, a, was defined in the model as the ratio of human PTT activation time (Tptt ~ 0.2sec.) vs. the average idle time between messages (W ~ many sec.), with the equation:

A = Tptt/W

This illustrates to what degree a changing user protocol affects the channel capacity. Outputs from the adaptive user protocol model are graphed in Figure 2 on page 25.

Although an average five-second message length was used in this model, real message lengths vary randomly around that figure, some even lasting 15 seconds or more. In periods of low message load, W is quite large compared to Tptt, and the vulnerability window is nearly zero (a = 0), meaning almost no vulnerability period exists (no collisions). The tallest curve in Figure 2 shows the throughput characteristics of the 1-persistent CSMA protocol throughput with a = 0. The peak channel throughput is at Smax = 0.54, meaning that, at best, 54% of the offered load can be passed successfully through the channel. As the message traffic increases, W reduces significantly, and the vulnerability window value grows larger. The second curve, “1-p CSMA,” models a channel in an early phase of a high use with a = 0.4. The throughput drops to Smax = 0.38. Under heavy loads, a nearly continuous vulnerability period is present (many collisions). Consequently, as the load increases, the throughput eventually converges to the pure ALOHA value (dashed line), where the best throughput is only Smax = 0.18, with a maximum probability of collisions, and low throughput. This variable, as it turns out, is not so obvious. When radio users forget their good protocol behavior, it degrades the channel’s throughput potential. The channel not only suffers from a rise in users trying to get “on the air,” but the channel’s capacity to handle this increasing load is reduced by the many users who forget their etiquette out of frustration. This is why congestion occurs rapidly during periods of heavy use. It’s like standing on a hose when you’re trying to get more water through it.

A word about trunking In a trunked radio system, especially one with a central control channel, users have no direct impact on the channel capacity. The control channel manages the vulnerability window by providing a protocol buffer between the human operator and the channel. This buffer allows for full capacity use of the channel, minimum throughput delay and no message collisions, especially during heavy use. These are just some of the reasons why trunking provides a more efficient use of the spectrum by providing maximum throughput capacity of channels and preventing users from compromising capacity.

A useful concept The concept of creating an analogy between the conventional radio channel and a packet data channel, with the radio users as “adaptive protocol machines,” is helpful in calculating the maximum throughput capacity that can be expected from a conventional channel. It aids understanding of how maximum throughput of a single channel, during various channel loads, is affected by the adaptability of the users. The concept also illustrates why system users need to learn how to maintain their call etiquette during crisis situations.

The model is helpful in several other ways. It illustrates the underlying mechanisms of how users directly affect systems, and it is especially valuable in creating a model for predicting the actual changing load and capacity of a conventional multiple-access channel. It also illustrates how, by comparison, trunking can benefit channel efficiency. Finally, it shows that maximum theoretical throughput for a single channel to be about 54% of the offered load. This factor yields a maximum of about five to seven five-second user messages per minute that can be transmitted under a heavy offered user load of nine to 11 five-second messages per minute, which is an example of a busy channel. Beyond that, if users begin changing their protocol, channel throughput drops rapidly to zero.

So, how many users can a typical channel support? To find out, determine the parameters of maximum throughput and the probability of user access. With a maximum throughput of about six messages per minute, and a probability of user access of 0.08 (the chance of any user with one five-second message per minute, per user), a single channel could support as many as 75 users. That is:

# users = throughput/probability of user access * message length

or:

N = 30sec./0.08 * 5sec.

It is interesting to note that in the FCC guidelines (47 CFR Part 90.633a), the per-channel loading for non-SMR conventional channels is authorized for a minimum of 70 users. I guess I could have just looked it up.