Advanced Wireless Networks - 4G Technologies

bushes. Typical Danish residential area. The terrain around the village is rolling with some minor hills. No line-of-sight between MS and BS. MS–BS distance varies from 0.3 to 2.0 km

along a certain route. The local average power azimuth-delay spectrum is given as

From Equation (3.2), local power azimuth spectrum (PAS) and the local power delay spectrum (PDS) are given as

The radio channels’ local azimuth spread (AS) σA and the local delay spread (DS)σD are defined as the root second central moments of the corresponding variables. The values of the local AS and DS are likely to vary as the MS moves within a certain environment. Hence, we can characterize σA and σD as being random variables, with the joint pdf f (σA, σD).

Delay spread (μs)

Figure 3.2 Examples of empirical CDFs of the DS in different environments. The CDF of a log–normal distribution is fitted to the empirical results for comparison. (Reproduced by permission of IEEE [4].)

Table 3.2 Summary of the first and second central moments of the AS, DS, and shadow fading in the different environments (reproduced by permission of IEEE [4])

sults for these parameters is given in Table 3.2. For characterization of shedowing fading see References [1–30].

3.2 URBAN SPATIAL RADIO CHANNELS IN MACRO/MICROCELL

ENVIRONMENT (2.154 GHz)

The discussion in this section is based on the experimental results collected with a wideband channel sounder using a planar antenna array [31]. The signal center frequency was 2154 MHz and the measurement bandwidth was 100 MHz. A periodic PN-sequence, 255 chips

Transmitter

Hotel Torni

Figure 3.3 The measurement area with all three RX sites; TX-positions of the sample plots are marked. (Reproduced by permission of IEEE [31].)

long, was used. The chip rate was 30 MHz, the sampling rate 120 MHz, giving a oversampling factor 4. The correlation technique was used for the determination of the impulse response. Hence, the delay range was 255/30 MHz = 8.5 μs, with a resolution of 1/30 MHz = 33 ns. The transmit antenna at the MS was a vertically polarized omnidirectional discone antenna. The vertical 3 dB beamwidth was 87◦ and the transmit power 40 dBm. Approximately 80 different transmitter positions were investigated.

The receiving BS was located at one of three different sites below, at and above the rooftop level (RX1–RX3, see Figure 3.3). A 16-element physical array with dual polarized λ/2-spaced patch antennas was combined with a synthetic aperture technique to build a virtual two-dimensional (2-D) antenna structure. The patches were linearly polarized at 0◦ (horizontal direction) and 90◦ (vertical direction). With these 16 × 62 elements the direction of arrival (DOA) of incoming waves both in azimuth (horizontal angle) and elevation (vertical angle) could be resolved using the super-resolution Unitary ESPRIT algorithm [32–34]. Note that the number of antenna elements limits the number of identifiable waves, but not the angular resolution of the method. Together with a delay resolution of 33 ns, the radio channel can be characterized in all three dimensions separately for the two polarizations. Array signal processing, including estimation of the DOAs and a comparison of ESPRIT with other algorithms, can be found in Glisic [1].

One prerequisite for the applicability of the synthetic aperture technique is that the radio channel is static during the whole data collection period. To avoid problems, the whole procedure was done at night with minimum traffic conditions.

3.2.1 Description of environment

A typical urban environment is shown in Figure 3.3 [31] with three receiver locations (RX1–RX3) marked by triangles pointing in the broadside direction of the array. Figure 3.3 also shows all the corresponding TX positions. The location RX 1 (height hRX = 10 m)

52 CHANNEL MODELING FOR 4G

was a typical microcell site below the rooftop height of the surrounding buildings, and measurements were performed with 20 different TX positions. RX 2 (height hRX−27 m) was at the rooftop level, and 32 TX positions were investigated. RX 3 (height hRX = 21 m) was a typical macrocell BS position above rooftop heights, and 27 TX positions were measured.

3.2.2 Results

The measurement results show that it is possible to identify many single (particular, different) multipath components, impinging at the receiver from different directions. However, these components are not randomly distributed in the spatial and temporal domain; they naturally group into clusters. These clusters can be associated with objects in the environment due to the high angular and temporal resolution of evaluation. (Sometimes even individual waves, within a cluster, can be associated with scattering objects.) The identification of such clusters is facilitated by inspection of the maps of the environment. A cluster is defined as a group of waves whose delay, azimuth and elevation at the receiver are very similar, while being notably different from other waves in at least one dimension. Additionally all waves inside a cluster must stem from the same propagation mechanism. The definition of clusters always involves a certain amount of arbitrariness. Even for mathematically ‘exact’ definitions, arbitrary parameters (e.g. thresholds or number of components) must be defined. Clustering by human inspection, supported by maps of the environment, seems to give the best results. The received power is calculated within each cluster (cluster power) by means of unitary ESPRIT and a following beam-forming algorithm. The results are plotted in the azimuth-elevation-, azimuth-delay- and elevation-delay-planes

According to the obvious propagation mechanism, each cluster is assigned to one of three different classes:

Class 1, street-guided propagation – waves arrive at the receiver from the street level after traveling through street canyons.

Class 2, direct propagation over the rooftop – the waves arrive at the BS from the rooftop level by diffraction at the edges of roofs, either directly or after reflection from buildings surrounding the MS. The azimuth mostly points to the direction of the transmitter with some spread in azimuth and delay.

Class 3, reflection from high-rise objects over the rooftop – the elevation angles are near the horizon, pointing at or above the rooftop. The waves undergo a reflection at an object rising above the average building height before reaching the BS. The azimuth shows the direction of the reflecting building; the delay is typically larger than for class 1 or class 2. The sum of the powers of all clusters belonging to the same class is called class power. In some cases the propagation history is a mixture of different classes, e.g. street guidance followed by diffraction at rooftops. Such clusters are allocated to the class of the final path to the BS.

For the evaluation of delays we define the vector P containing the powers of the clusters and vector τ of corresponding mean delays. A particular cluster i has mean delay τi , and power Pi . The relation between the delays τ and the powers P is modeled as exponential:

Table 3.3 The model parameters a and b for both received polarizations (VP and HP) averaged over all available clusters. The transmitter was VP

Experimental data are fit into the model (3.11) using the least square (LS) estimation. The logarithmic estimation error v is defined as

In equation (14.21) σv was defined as the standard deviation of the logarithmic estimation error in dB. This estimation error was found to be log–normally distributed and, up to a delay of about 1 μs, σv is independent of the delay τ . The value of σv is 9.0 and 10.0 dB (co-and cross-polarization), respectively, averaged over the first microsecond. The average powers for different classes of clusters are shown in Table 3.5. Additional data on the topic can be found in References [31–41].

3.3 MIMO CHANNELS IN MICROAND PICOCELL ENVIRONMENT

(1.71/2.05 GHz)

The model presented in this section is based upon data collected in both picocell and microcell environments [43]. The stochastic model has also been used to investigate the capacity of MIMO radio channels, considering two different power allocation strategies, water filling and uniform and two different antenna topologies, 4 × 4 and 2 × 4. It will be demonstrated that the space diversity used at both ends of the MIMO radio link is an efficient technique in picocell environments, achieving capacities within 14 and 16 b/s/Hz in 80 % of the cases for a 4 × 4 antenna configuration implementing water filling at a signal-to-noise ratio (SNR) of 20 dB.

56 CHANNEL MODELING FOR 4G

3.3.1 Measurement set-ups

The TX is at the MS and the stationary RX is located at the BS. The two set-ups from Figure 3.4 provide measurement results with different correlation properties of the MIMO channel for small antenna spacings of the order of 0.5λ or 1.5λ . The BS consists of four parallel RX channels. The sounding signal is a MSK-modulated linear shift register sequence of a length of 127 chips, clocked at a chip rate of 4.096 Mcs. At the RX, the channel sounding is performed within a window of 14.6 μs, with a sampling resolution of 122 ns (half-chip period) to obtain an estimate of the complex IR. The narowband (NB) information is subsequently extracted by averaging the complex delayed signal components. A more thorough description of the stand-alone testbed (i.e. RX and TX) is documented in References [23, 45]. The description of the measurement environments is summarized in Table 3.6.

A total of 107 paths were investigated within these seven environments. The first measurement set-up was used to investigate 15 paths in a microcell environment, i.e. environment A in Table 3.6. The MS was positioned in different locations inside a building while the BS was mounted on a crane and elevated above roof-top level (i.e. 9 m) to provide direct line-of-sight to the building. The antenna was located 300 m away from the building. The second set-up was used to investigate 92 paths for both microcell and picocell environments,

Table 3.6 Summary and description of the different measured environments (reproduced by permission of IEEE [43])

i.e. environment B and C–G, respectively, as shown in Table 3.6. The distance between the BS and the MS was 31–36 m for microcell B, with the BS located outside.

3.3.2 The eigenanalysis method

The eigenvalue decomposition (EVD) of the instantaneous correlation matrix R = HHH(not to be confused with RMIMO), where [·]H represents Hermitian transposition, can serve as a benchmark of the validation process. The channel matrix H may offer K parallel subchannels with different mean gains, with K = Rank (R) ≤ min (M, N ) where the functions Rank (·) and min (·) return the rank of the matrix and the minimum value of the arguments, respectively [27]. The kth eigenvalue can be interpreted as the power gain of the kth subchannel [27]. In the following, λk represents the eigenvalues.

3.3.3 Definition of the power allocation schemes

In the situation where the channel is known at both TX and RX and is used to compute the optimum weight, the power gain in the kth subchannel is given by the kth eigenvalue, i.e. the SNR for the kth subchannel equals

where Pk is the power assigned to the kth subchannel, λk is the kth eigenvalue and σN2 is the noise power. For simplicity, it is assumed that σN2 = 1. According to Shannon, the maximum capacity normalized with respect to the bandwidth (given in terms of b/s/Hzspectral efficiency) of parallel subchannels equals [46]

Given the set of eigenvalues {λk }, the power Pk allocated to each subchannel k was determined to maximize the capacity using Gallager’s water filling theorem [27] such that each subchannel was filled up to a common level D, i.e.

with a constraint on the total TX power such that

K

k=1