Background

The Wireless Propagation Channel

A wireless propagation channel is characterized by its impulse response, i.e the signal one would receive if the transmitted signal was a single impulse with infinitesimal temporal extension and unlimited energy. That would be the so called delta-pulse. Given multipath propagation the receiver detects a whole sequence of these pulses. Their amplitude depends on two parameters:

The length of the propagation path: Because of wave attenuation in free space, the signals will become weaker with propagation length and correspondingly time.

The way the multipath components interfere at the receiver: Depending on the path length and the frequency of the signal, the waves interfere either constuctively or destructively because of different phase values. Such a channel is called frequency selective.

Consequently the impulse response characterizes the propagation channel of a given scenario at a particular moment in time.

Channel Impulse Response

As the idea of an impulse with infinitesimal temporal extension and unlimited energy is only theoretical, it can't however be applied to practice. Furthermore, the simplifying assumption of a quasi-static channel often is made. This means that the channel is assumed to stay constant over a certain, though very short period of time.

Channel Measuring

In a real scenario, there are several methods to perform channel measuring. The so-called Wobbel method does not directly measure the channel impulse response, but instead identifies the transfer function of the channel. In order to achieve this, a harmonic oscillation is transmitted. The current frequency is moved in small steps periodically over the measurement interval while the receiver measures the complex output of the channel. The narrowband signal is barely distorted by the channel. However, a certain settling time has to be temporized at every frequency step until the transfer function of the system is identified. Wide band channel measurement may take up to a couple of seconds. Because the the channel must not change over that time, the Wobbel method is applicable only for measuring static channels.

The correlation method refers to the case where the transmitter sends a carrier, which is modulated by a pseudo-noise sequence with a certain bandwidth. At the receiver, the channel is identified via sliding correlation in realtime. The smaller the ratio of the chip duration to the sequence length, the more the correlation function resembles a delta function. If such an idealisation is assumed, the time inverse channel impulse response appears at the correlator output. However, the correlation method can only approximate the channel impulse response, because the transmit signal is distorted by non-linearities of the measuring system.

Strongly related to the correlation method is the multi sinus method. A periodic signal is used, too, but instead of a code-sequence, a so-called multi sinus signal is tranmsitted. Similar to the Wobble method, all frequency values in a certain band are stimulated with the same power, but in a short time T which is comparable to the correlation method. At the receiver, an inverse filter is used instead of a correlator. In contrast to the correlation method, the linear distortion caused by the measurement system can be compensated. This is because the transfer function of the tansmitter as well as the transfer function of the receiver can be included.

Multihop Channels

A multihop scenario is a scenario, where the transmitted data is forwarded by active relays. If the relays perform an amplify and forward scheme, they act as active scatterers. More complex relays could be able to decode the received signal, thus regaining the transmitted signal before retransmitting it.

To cope with the problem of characterizing highly complex multihop channels, we have to find answers to a couple of questions:

Is it possible to split the complex problem of a multi-hop scenario up into smaller problems? If yes, how can it be done effectively?

Which assumptions can be made as to simplify the models?

Which assumptions can't be made? Why is this so?

And finally: How do real Systems behave? Can our theoretical models be verified or do we have to refine them further?

Example of a Multihop Scenario

The illustration below shows a possible setup for the channel measurement of cooperative relaying in multihop channels. In this example the transmitter as well as the receiver have 3 antennas. The 3 amplify-and-forward nodes are arranged in arbitrary order.

Introduction >> Background