IEEE 802.11b multipath channel simulation

Multipath Models

In this paper, we consider the environmental impact on the reception of IEEE 802.11b signals in a room environment. The influence of three types of radio wave propagation channels is considered: the Gaussian channel, the Rice channel, and the Rayleigh channel.

The radio signal, on the propagation path from the source to the receiver, may encounter obstacles. In this case, the signal can be absorbed by them or reflected. The reflected signal will reach the receiver, but this will happen late. On the other hand, the rest of the signal energy can reach the receiver without re-reflection in a shorter time or pass more reflections, which in turn will lead to even greater delays. This effect occurs when several signal delivery paths arise between the source and the receiver. In this case, the signal energy will be distributed unevenly between the copies of the signal. This signal propagation is called multipath.

The study includes an analysis of the influence of various characteristics, such as Doppler shift, propagation delay, re-reflection, attenuation of the signal power to the multipath channel. The result of the study is the characteristics of the probability of signal errors at different transmission rates.

A Gaussian channel is a channel with additive white Gaussian noise. This channel is an ideal channel without fading and multipath. This channel will serve as a measure for assessing the quality of the implemented signal reception algorithm, and the evaluation will be carried out according to the error probability per bit (BER) characteristic.

The calculated BER characteristic can be calculated using the following formulas:
for DBPSK signals (1)
for DQPSK signals
where Q_1 (a, b) is a Markov Q-function and I_0 (ab) is a Bessel function of the first kind with parameters a and b:
(2)
BER for CCK encoded signals is defined as:,
(3)

In addition to Rayleigh and Rice channels the additive component of noise contains multiplicative noises caused by reflections and movements of objects in the medium. The passage of a signal through a channel can be represented as follows:
Gaussian additive channel: (Direct visibility, no reflected signals).
Rice Channel: (Line of sight, there are reflected signals).
Rayleigh Channel: (No line of sight, receiving only reflected signals).

The signal is formed according to the IEEE 802.11b standard, the filter “root from the raised cosine” is selected as the shaping and matched filters. Filters are used to eliminate intersymbol interference (Fig. 4 and Fig. 5). The signal is received according to its own algorithm. All algorithms are executed in MATLAB R.

Fig . 4 signal constellation after passing through the channel

Fig. 5 signal constellation after the matched filter

To create channel models in the Matlab environment, you must use the following functions: awgn - for the Gaussian additive channel, ricianchan and rayleighchan - for the Rice and Rayleigh channels, respectively.
The Rice channel is characterized by the following set of additional parameters: fading, Doppler shift frequency, Rice coefficient of the power ratio in the rays, as well as attenuation. The Rayleigh channel is characterized by the same effects as in the Rice channel, but the difference between these channels is the absence of a direct beam from the transmitter to the receiver.

The Doppler effect occurs when the relative movement of the receiver and transmitter or when moving objects in the path of signal propagation. Since this standard is intended for indoor signal transmission, in the Rice channel, the Doppler frequency can be set f_d = 11 Hz, which corresponds to a receiver speed of 5 km / h at a carrier frequency of 2.4 GHz. With a nonzero value of the frequency of the Doppler shift, signal constellations will be smeared (Fig. 5).

The values ​​of attenuation and delay in the propagation of signals in multipath channels were taken from [6] , studied specifically for signals of the IEEE 802.11 standard. In this paper, the values ​​of three different models are given:
Model A - a typical office space with no direct line of sight, mean square propagation delay of 50 ns.
Model B - open space or large office space, lack of line of sight, RMS delay of 100 ns.
Model C - large spaces (both indoor and outdoor), lack of line of sight, RMS delay of 150 ns.
In this work, model B is used, for which the following parameters are characteristic:
For the Rice channel:
f_d = 11 Hz; K = 20;
τ_i = [0 10 20 30 40] (ns); α_i = [0 -5.4 -10.8 -16.2 -21.7] (dB)
For the Rayleigh channel:
f_d = 11 Hz;
τ_i = [10 20 30 40] (ns); α_i = [- 5.4 -10.8 -16.2 -21.7] (dB)
In the Rayleigh channel, zero components are absent due to the absence of a direct beam.
After passing through the channel, the signal is fed to the input of the receiver.
The reception algorithm can be given if necessary.

Simulation results

When calculating the noise immunity characteristics, 50,000 bits of information encoded by DSSS (1 and 2 Mb / s) and CCK (5.5 and 11 Mb / s) were transmitted. To calculate the characteristics, the signal was reduced to a power of 1 Watt. The noise immunity characteristics were obtained for three channels: the Gaussian channel, the Rice channel and the Rayleigh channel (Fig. 6-8), the choice of parameters for each of the channels is indicated above.


Fig. 6 Immunity characteristic for a Gaussian channel.


Fig. 7 Immunity characteristic for the Rice channel.


Fig. 8 Immunity characteristic for the Rayleigh channel.

In fig. 6-8, the signal-to-noise ratio is given in decibels (abscissa). These results illustrate the noise immunity of an 802.11b signal in multipath channels for large rooms or open spaces. The frequency of the Doppler shift within 120Hz does not have much effect on the BER response.

The difference in the characteristics of the Rice and Rayleigh channels is due to the absence of a direct beam in the Rayleigh channel from the transmitter to the receiver.

The noise immunity characteristic depending on the K coefficient (Rice coefficient) for the Rice channel: (Fig. 9).

Fig. 9 Dependence of the BER characteristic on the K coefficient in the Rice channel.

From this characteristic it is seen that with an increase in the ratio of the power of the main to the power of the reflected rays, the characteristic improves. At K = 0, a direct beam does not exist, only reflected rays are received, which corresponds to the characteristic of the Rayleigh channel.

List of references

1. IEEE 802.11-2007 (Revision of IEEE Std 802.11-1999) NY 10016-5997, USA
2. “The Basics of Building Wireless LANs of the 802.11 Standard,” Pageman Roshan, Jonathan Lieri, Ed. Cisco Press 2004
3. "Modern Wireless Technologies" IV Shakhnovich, 2th ed. “Technosphere” 2006, 288 p.
4. "Broadband wireless networks for the transmission of information" V. M. Vishnevsky, A. I. Lyakhov, S. L. Portnoy, I. V. Shakhnovich, Izd. “Technosphere” 2005, 591 s.
5. “Basics of local networks” Novikov Yu.V., Kondratenko SV Internet University of Information Technologies - INTUIT.ru, 2005
6. “TGn Channel models”, Vinko Erceg, Laurent Schumacher, 2004, 45 p.
7. “Simulation of Communication Systems”, Jeruchim, MC, Balaban, P., and Shanmugan, KS, Second Edition, New York, Kluwer Academic / Plenum, 2000.

This is part of my thesis on “Development of a simulation model of formation, distribution paths. and receiving signals from IEEE 802.11b networks, "because the work is big, I did not publish everything, but, in fact, I published only the conclusions.

I will try to answer all your questions. I can help and put the source code on Matlab, if anyone needs it.