Cellular ALOHA Networks
Many cellular data networks
have an uplink channel with bursty (say, Poissonian) message traffic.
For instance,
- Slotted ALOHA is used by most
cellular telephone nets
for call set-up requests from mobiles
- Satellites often use a kind of ALOHA for random access messages
from ground stations.
- ISMA is used by CDPD.
A similarity between ISMA/CSMA and ALOHA is that message collisions can occur.
This page addresses the throughput and capture probability is a wireless ALOHA
net, considering the distribution of terminal over the cell and frequency reuse.
(
See also more basic pages on throughput and capture)
Uniformly Distributed Traffic in Mobile ALOHA Cell
Uniform Offered Traffic
Often it is assumed that the attempted traffic is uniformly distributed over the cell.
In such case the throughput decreases with distance.
Figure: Probability that an access attempt is successful
versus the distance between terminal and base station.
- Average message arrival and retransmission rate: 1 packet per unit of time.
- Terminals
quasi-uniformly distributed over cell, with cell boundary approximately at unity distance.
- Receiver threshold 6 dB.
- Plane earth loss (40 log d)
and narrowband Rayleigh fading.
- Various packet durations T, normalized to the Doppler spread.
- Median signal-to-noise ratio (for user at distance 0.734)
is 20 dB.
- New arrivals and retransmissions for a stationary Poisson process. The network is stable. Theoretically, this condition can only
be satisfied if the retransmission backoff delay is infinitely large.
Terminals in remote areas faces a larger probability to
be unsuccessful during a transmission attempt.
If new packet arrivals are uniformly distributed over the cell,
the number of attempts (successful plus unsuccessful)
increases with range.
Offered traffic (number of attempts per slot per unit of area) to transmit a packet in an ALOHA
random access network.
- Throughput: 0.4 packet per cell per slot uniformly spread over area.
- Receiver threshold z = 4 (6 dB)
- Effect of interference from co-channel cells is included:
- orange line: reuse pattern C = 4 (same frequency used in all cells)
- blue line: C= 9
- green line: very large reuse pattern
- Signal-to-noise ratio 10 dB and infinity at unity distance (just beyond cell boundary)
- Circular cell of radius 0.91 to approximate hexagon of size 1.
- Total traffic: traffic per unit of area times surface area of cell (0.91^{2} pi)
- Number off attempts: offered traffic divided by throughput, where throughput is 0.4
divided by 0.91^{2} pi (= 0.15).
This also has an effect on backlog drifts and stability. The delay becomes highly dependent on terminal location. In a
network with relatively fixed terminal locations, as in a wireless LAN,
some terminals may by accident be positioned in a bad propagation spot,
for instance a multipath null. These terminal
may have to do many transmission attempts before being successful. Their delay
may be unacceptably large, unless special measures are taken (e.g. diversity or frequency hopping).
Total Throughput for Uniform Offered Traffic
The total throughput critically depends on whether we assume that terminals can be arbitrarily
close to the receiving base station or not.
We assume that terminal transmission attempts are uniformly distributed
in the range ( r_{1}, r_{2}). with r_2 = 1 being the cell boundary.
Figure: Total throughput (in message attempts per time slot per unit area)
versus offered traffic in the cell for uniform offered traffic.
- Blue: slotted ALOHA in ideal channel without capture
- Orange: Mobile Rayleigh fading channel. Uniform attempted traffic between r_{1} and 1.
For positive r_{1}, the throughput reduces to zero for large offered traffic.
For r_{1} =0, some packet have extremely strong signals, so they are likely to capture
the receiver despite interference from very many packets.
The throughput goes to
2
lim S = ----------
G->INF p SQRT(z)
with z the receiver capture threshold.
Interference from Other Cells
In the extreme case with the same channel used in an infinitely large area,
we an model the offered traffic as a Poisson process with infinite extension.
The throughput for such network appears only slightly affected by interference from outside the cell.
In cellular ALOHA networks, the optimum ALOHA reuse pattern appears to be C = 1.
A network with C = 1 can exploit site diversity: packets
received at various base stations can be combined.
This is exploited in the Virtual Cellular Network and can also be used in applications such as collection of floating car data
The optimum frequency reuse pattern for such a random access network differs from typical solutions for
cellular telephone.
Cellular reuse pattern with seven different frequencies
In the example of a 7-cell reuse pattern, interference between cells is very small, and even at the fringe of each cell the outage probability is not more than a few percent. However,
the use of 7 different channels means that within each cell only 1/7 of the total bandwidth is available.
Hence, the transmission rate is 7 times smaller, as compared to a 1 frequency reuse plan.
Each time slot needs to be seven times larger. For a given arrival rate of packets per second, the
message arrival rate per slot is thus 7 times larger. If an ALOHA, CSMA, ISMA or similar access scheme is used, this leads to a substantially larger number of collisions
and interference from other packets within each cell. So it appears useful to use a very small cluster size for cellular
ALOHA networks
Performance and Efficiency
In a cellular ALOHA network, the optimum frequency reuse factor is C
= 1, i.e., all base stations listen to
the same channel.
Note that this result does not rely on any spread spectrum
spreading gain. It applies also to unspread transmission.
For the efficiency of an ALOHA-type random access network, it is often
not favorable to apply spreading. (see: Performance of stack collision resolution algorithm with DS-CDMA)
The figure below compares various cluster sizes. Uniform offered traffic is assumed
in all cells. A modulation technique with 1 bit/s/Hz is assumed that can provide successful
packet reception for C/I ratios above 6 or 20 dB.
Figure: Throughput of Cellular Slotted ALOHA network (in packets per time slot per base station)
for various cluster sizes C. In practice, only the integer values C = 1, 3, 4, 7 , 9 ..
exist. Receiver Threshold: orange: z = 4 (6 dB); violet: z = 100 (20 dB)
Example
See a demo and discussion on how a multi-base station ALOHA network
performs the collection of telemetric data from probe vehicles.