Chapter 2 Overview of Channel Models for B3G Systems
2.3 Spatial channel models
2.3.2 MIMO Channel Models in Standards
A. IEEE 802.11n spatial channel model
To enable multiple-input multiple-output (MIMO) antenna technologies in wireless local area networks (WLAN), the task group n (TGn) of IEEE 802.11 standardization group proposed a set of channel models applicable to indoor MIMO WLAN systems [7].
Some of the channel models are an extension of the SISO WLAN channel models, and a newly developed multiple antenna models is based on the cluster model developed by Saleh and Valenzuela [6].
In [7], six clustering delay profile models are proposed for different indoor environments. The model parameters, such as number of clusters, number of taps in a particular cluster, and power, angular spread (AS), angle-of-arrival (AoA), and angle of departure (AoD) values of each tap are defined for each delay profile model. With the knowledge of each tap power, AS, and AoA (AoD), for a given antenna configuration, the channel matrix H can be determined.
The MIMO channel modeling approach, which is similar to the method presented in [30-31] that utilizes receive and transmit correlation matrices. For a 4×4 array, the MIMO channel matrix H for each tap can be separated into a fixed (constant, LOS) matrix and a Rayleigh (variable, NLOS) matrix
⎟⎟
where Xij (i-th receiving and j-th transmitting antenna) are correlated zero-mean, unit variance, complex Gaussian random variables as coefficients of the variable NLOS (Rayleigh) matrix HV, exp(j
φ
ij) are the elements of the fixed LOS matrix HF, K is the Rician K-factor, and P is the power of each tap. To correlate the Xij elements of the matrixX, the following method can be used
[ ] [ ] [
X = Rrx 12 Hiid][ ] (
Rtx 12)
T (2-19)where Rtx and Rrx are the receive and transmit correlation matrices, respectively, and Hiid is a matrix of independent zero mean, unit variance, complex Gaussian random variables, and
⎥⎥
⎥⎥
where
ρ
txij are the complex correlation coefficients between i-th and j-th transmitting antennas, andρ
rxij are the complex correlation coefficients between i-th and j-th receiving antennas.The complex correlation coefficient values calculation for each tap is based on the power angular spectrum (PAS) with angular spread (AS) being the second moment of PAS [32-33]. Using the PAS shape, AS, mean angle-of-arrival (AoA), and individual tap power, correlation matrices of each tap can be determined as described in [32]. For the uniform linear array (ULA) the complex correlation coefficient at the linear antenna array is expressed as parts (equal to the cross-correlation function between the imaginary parts) and between the real part and imaginary part, respectively, with
−
∫
= π
π D
φ
PASφ
dφ
D
RXX( ) cos( sin ) ( ) (2-23)
−
∫
= π
π D
φ
PASφ
dφ
D
RXY( ) sin( sin ) ( ) (2-24)
B. 3GPP SCM/SCME channel model
To enable multiple-input multiple-output (MIMO) antenna technologies in cellular systems, standardization groups 3GPP and 3GPP2 defined a spatial channel model (SCM) [8] for cellular systems with bandwidths up to 5 MHz. Recently, for 3GPP long-term evolution (LTE) standardization [2], an SCM extension (SCME) model including the wideband spatial channel characteristics was proposed to support bandwidths up to 20 MHz.
In [8], the spatial channel models for link level and system level simulations are defined. Link level simulations will not be used to compare performance of different algorithms. Rather, they will be used only for calibration, which is the comparison of performance results from different implementations of a given algorithm. Table 2-1 summarizes the physical parameters to be used for link level modeling. The MIMO channel matrix generation method of the link level model is similar to that described in Section 2.3.2-A.
As opposed to link simulations which simply consider a single BS transmitting to a single MS, the system simulations typically consist of multiple cells/sectors, BSs, and MSs.
Fig. 2-6 shows a roadmap for generating the channel coefficients. It defines three environments (suburban macro, urban macro, and urban micro) where urban micro is differentiated in line-of-sight (LOS) and non-LOS (NLOS) propagations. Detailed model parameters are listed in Table 2-2. In each environment, the number of paths is equal to 6.
Each path is further composed of 20 spatially separated sub-paths to produce a Rayleigh fading envelope. The main characteristics of the model include a narrow angle spread (AS) per-path, with specific base station angle of departure (AoD) and mobile station angle of arrival (AoA) models. The large-scale behaviors, described by the composite AS, DS and shadow fading (SF), are simultaneously correlated in the log-normal domain to produce the expected channel characteristics for each realization of the channel. Path powers, path delays, and angular properties for both sides of the link are modeled as random variables defined through probability density functions (PDFs) and cross-correlations.
For an S element linear BS array and a U element linear MS array, the channel coefficients for one of N multipath components are given by a U-by-S matrix of complex amplitudes. Denote the channel matrix for the nth multipath component (n = 1,…,N) as
) (
H
nt
. The (u,s)th component (s = 1, …, S; u = 1, …, U) ofH
n( t )
is given by( ) ( [ ( ) ] )
where the angular parameters are shown in Fig. 2-7.
The 3GPP SCME is an extension to the SCM for bandwidths up to 20 MHz. In 3GPP SCME, the 20 sub-paths of SCM are split into 3 subsets, denoted as mid-paths, which are moved to different delays relative to the original path as shown in Fig. 2-8. The delays and powers of these 3 mid-paths are predetermined by an exponential power decay function with 10-ns delay spread. To keep the fading distribution close to Rayleigh, a mid-path is lumped of 4 or more sub-paths. The mid-path ASs (ASi where i is the mid-path index) are optimized such that the deviation from the path AS (ASn where n is the path index), i.e. the AS of all mid-paths combined, is minimized. The delays and the corresponding sub-paths of each mid-path are listed in Table 2-3.
Table 2-1 The channel parameters of 3GPP SCM for link level simulations.
Table 2-2 The channel parameters of 3GPP SCM for system level simulations.
Table 2-3 Sub-paths to mid-paths assignment and resulting angle spread in 3GPP SCME
Fig. 2-6 The illustration of the procedure for generating MIMO channels.
Fig. 2-7 The illustration of multipath angle parameters at BS and MS sides.
Excess delay
Power
Path 4: composed of 20 zero-delay, spatially separated sub-paths
3 mid-paths with different relative delays
SCM: 6-path representation SCME: 6*3-path representation
Excess delay
Power
Path 4: composed of 20 zero-delay, spatially separated sub-paths
3 mid-paths with different relative delays
SCM: 6-path representation SCME: 6*3-path representation SCM: 6-path representation SCME: 6*3-path representation
Fig. 2-8 A diagram of the mid-path approach of SCME.