Spatial Channel Measurement and Modeling

	ABOUT THE AUTHORS Andreas F. Molisch received the doctoral degree in 1994 and the habilitation degree in mobile communications in 1999. His research interests lie in the field of spatial mobile radio channel measurement and modeling, as well as in diversity algorithms and MIMO systems. He has participated in the research initiative COST 259 and contributed to the development of the COST259 standard channel model. More...

The mobile radio channel ultimately determines the performance of smart antenna systems. As smart antennas exploit directional information, we need measurements and models of mobile radio channels that include the spatial component, such as the direction-of-arrival (DOA). Interest in smart antennas has been primarily during the last five years, resulting in a limited number of available measurement results. This paper discusses recent measurement programs, as well as methods for the efficient simulation of spatial channels.

Using a directional antenna in conjunction with a conventional channel sounder is the simplest available approach. We use a step motor to point the antenna in different directions and, for each direction, record the impulse response. Drawbacks of this method include long measurement time and limited resolution due to the beamwidth of the directional antenna.

Using antenna arrays is an alternative approach, where the impulse responses at each antenna element are recorded and subsequently processed. Theoretically, the measurement at all antenna elements should be simultaneous, or at least within the coherence time of the channel. We can obtain simultaneous measurements only when each antenna element has its own receiver train, which is expensive.

A more popular alternative is a multiplexed array, where the antenna elements are connected to a single receiver train via a fast switch. This arrangement allows measurements within 1ms (For a 16-element array), which is well within the coherence time even in the presence of fast-moving scatterers. The virtual array is a third approach, useful in static environments, where a single antenna is placed mechanically at different positions, thus stimulating the elements of an antenna array. This method is not only simple, but also avoids all mutual coupling between the elements. For our measurements we used virtual arrays and/or multiplexed arrays.

After collecting the impulse responses at the antenna elements, the next step is the extraction of the multipath parameters, namely delay and DOA. Though a Fourier analysis is possible, it suffers from poor resolution. The use of parametric estimation is preferable. Parametric estimation is simple when based on the model that a finite number of plane waves is incident on the array. The resolution of a parametric method is not limited by the number of antenna elements, but depends only on the signal-to-noise ratio and the deviation of the physical channel from the model assumption (for example, non-planar waves). However, the number of waves that we can distinguish is limited by the number of antenna elements.

For the evaluation of our measurements, we used Unitary ESPRIT, an improvement of the original ESPRIT algorithm. ESPRIT exploits the fact that in the narrowband case, a plane wave arriving at the array gives the same signal at each antenna element, apart from a phase shift that is proportional to the DOA. An important practical point is the determination of the number of arriving waves, in other words, the separation of signal subspace (from which we can determine the DOAs) and noise subspace. Several criteria are available in the literature, but suffer from practical problems. We use a method that minimizes the deviations of the modeled signal from the received signal.

• Scattering around the mobile station.
  The waves propagate essentially along the shortest path between base station (BS) and the vicinity of the mobile station (MS). In rare cases, there is a line-of-sight (LOS) connection, but it is more common in urban environments that houses block the LOS. With such blocking, the waves propagate over the rooftops, and are diffracted at the roof edge of the street where the mobile station stands and possibly reflected by the house walls of the street, or obstacles around the MS. These arriving waves thus have a more or less uniformly distributed azimuth, a short excess delay, and a large elevation spread.
  
  
• Waveguiding in street canyons.
  In this case, the waves propagate not necessarily along the shortest connection between BS and MS, but rather from the BS to a (somewhat distant) point in the street in which the MS is situated (henceforth called MS-street). This propagation may suffer from losses that are smaller than those along the shortest connection, because obstacles might be lower or nonexistent. The waves are then coupled into the MS-street at this remote point, and from there are guided along the MS-street canyon. These waves are characterized by azimuthal DOAs along the street direction, long delay, and low elevation.

Figure 1:  The figure depicts the azimuth delay power spectrum for a mobile station in a street canyon. The radial axis represents the delay, where the origin corresponds to the minimum excess delay. The axial coordinate is the azimuthal DOA. We see that, for small excess delays, waves are arriving from all directions, while longer-delayed waves are arriving along the direction of the street.

Figure 2:  (a) shows the angular power spectrum of all waves with a maximum excess delay up to 400 ns. These waves are more or less uniformly distributed. We can conclude that these waves propagate over the rooftops, and are then diffracted by a roof edge close to the mobile station. Additional reflections by the house walls or scatterers around the MS result in the uniform azimuthal distribution. (b) The angular power spectrum of the later waves are guided by the street. These waves propagate along wide boulevards and other favorable propagation paths, and are then coupled into the Rue de Rivoli (where the MS was located) far from the mobile station. The waves are then guided by the street canyon to the mobile station.

Measurements at Base Stations (BS)
Measurements at the BS were performed with different BS heights. We can anticipate that the propagation effects depend on this height. One common characteristic is that the waves arrive in clusters, in other words, groups with similar delay and DOA. A channel characterization thus should include the inter-cluster as well as intra-cluster parameters. A global characterization, such as by the rms angular spread defined as the second central moment of the angular power spectrum, is of rather limited usefulness.

Figure 3:  The first transmitter position is situated in a street canyon behind the theatre on the far side of the big square. The photograph of the square is taken from the position of the receiving base station, which was clearly below the rooftop level. The narrow street canyons on both sides of the theatre building fully define the propagation scenario. All waves arrive with low elevation angles from the azimuthal directions defined by the parallel streets ('street1 - street3'). The western street ('street 1') dominates, but some waves with short delays also arrive from 'street 3'. However, we also observe components with relatively long delays, which correspond to reflections from the park (behind the square transmitter) and multiple reflections in the street canyons.

Figure 4:  In the second transmitter position, the BS was at rooftop height at one end of a broad street canyon. The transmitter was located about 400 meters away on street level without line-of-sight to the receiver. There is a path from the transmitter to the receiver with a single reflection at the highest building in the surroundings, the Hotel Torni. The reflected component from Hotel Torni arrives about 1.5 µs after the first components and has the strongest power. For the first arriving waves two different propagation mechanisms exist. One component propagates over the rooftop with the azimuth angle of -45°. The relatively high-rising WTC building seems to block all components in the azimuthal range between -35° and -45° and the wave at -45° probably originates from a diffraction from the left corner of the WTC. Another significant short delay component is related to the coupling of the signal energy to the street canyon and the signal is observed at the receiver after reflections from the Makkaratalo building.

For base stations below rooftop height, the propagation effects are quite similar to those previously described in the section, "Measurements at Mobile Stations." The exact position of the mobile station does not matter as much as the propagation environment in the vicinity of the BS. Typically, waves can be reflected or diffracted several times before being coupled into the BS-street canyon. This leads to a large delay spread, but a rather small angular spread. Furthermore, the DOAs are independent of the delays of the waves. One important difference to "Measurements at Mobile Stations" is that the over-the-rooftop component is of much less importance. In a microcellular environment without LOS, the component is diffracted twice, leading to a very strong attenuation.

Another important propagation effect is reflection by dominant far reflectors. In urban environments, such a reflector is typically a high-rise building. It is especially dominant if it has line-of-sight both to the BS and the MS. Far reflectors lead to additional clusters, and thus a strong increase in the delay and angular dispersion. However, we also found that 75-80% of the power is carried in the three most powerful clusters.

Double-Directional Measurements
Up to now, we have considered transmission from an omni-directional antenna. To exclude the effect of the antenna pattern of the transmission antenna, we have to do a double-directional characterization of the channel. In other words, a multipath component is now characterized by the direction-of-departure (DOD) from the transmit antenna, as well as complex amplitude, delay, and DOA at the receive antenna. This is especially important for the estimation of the capacity of multiple input, multiple output (MIMO) channels. Furthermore, it is useful to determine whether single or multiple reflections are dominant; from the intersection between the line along the DOA and DOD, we can determine where the reflector for a single-scattering process would have to lie. If the run-time via this reflector does not agree with the measured excess delay, multiple reflections must have occurred.

We performed measurements in a courtyard in Ilmenau, Germany, and found multiple reflections to be of great importance. Furthermore, we found that the channel capacity was about 30% lower than that predicted for an ideal channel.

Figure 5:  This graph shows the measurement results for the courtyard in Germany. The red lines denote the directions of arrival and directions of departure. The length of the lines is proportional to the power of the multipath components in dB. The blue lines connect exemplary corresponding DOAs and DODs and are labeled by the number of encountered reflections. We can see different propagation mechanisms. Directly before the transmitter, there is an obstacle, so that no line-of-sight is possible. However, there is a quasi-line-of-sight component diffracted by that obstacle. Next, there are waves reflected a single time by the courtyard walls. Waves that are incident on the back of the receiver could not be observed, as the receive array consisted of patch antenna elements with an opening angle of about 120 degrees. Finally, we can also see multiply reflected components. Note that the propagation path of singly and doubly reflected components can be traced exactly when DOD, DOA, and delay are known. Higher-order reflections usually entail some guesswork.

The position of the scatterers corresponds to the true position of physical scatterers in a typical scenario, and can thus be easily derived from the measurements. However, if multiple scattering occurs in the physical propagation process, then we put equivalent scatterers in our model. These equivalent scatterers might be at positions where no physical scatterers are located, but waves going through a single-scattering process at this equivalent location will give the same signal at the receive antenna as a wave going through multiple reflection processes at the physical scatterer location. The scatterer pdf can be derived in an exact way by random variable transformations.

Following our measurement results, the scatterer pdf should show one or more distinctive clusters, where one cluster is always around the mobile station (corresponding to the over-the-rooftop component), while the other clusters are fixed in space. This model is also able to predict the long-term behavior of the channel, in other words, when the mobile station covers distances so large that the mean cluster DOAs and delays change. This phenomenon leads to one of the recommended implementation methods of the COST 259 directional channel model, a European-wide standard model for directional mobile radio channels.