Performance evaluation of a MIMO channel model for simplified OTA test systems
© Pasisingi et al.; licensee Springer. 2013
Received: 17 August 2013
Accepted: 25 November 2013
Published: 17 December 2013
This paper shows performance evaluation results of the proposed multiple-input multiple-output (MIMO) channel model with simplified configuration for OTA measurement systems. The key feature of our proposal is the adoption of a simple antenna branch-controlled configuration for generating various Rayleigh fading environments composed of a number of multipath delayed waves. The scheme matches well with FPGA implementation with IF band signal processing. The channel model and its theoretical background, and the basic configuration of the measurement system are presented. From an eigenvalue analysis of the generated channel matrix, it is verified that an 8-probe antenna system can realize a very accurate multipath environment for the performance measurement of a 2 × 2 MIMO system, while a 12- or 16-probe antenna system can do the same for a 4 × 4 MIMO system.
Over-the-air (OTA) test methods are of growing interest for the evaluation of multiple-input multiple-output (MIMO) terminals in LAN, WiMAX, LTE, and other wireless communication systems that adopt MIMO technologies. In OTA testing, a realistic propagation environment is generated around the receiving terminals for measurement of transmission performance characteristics. For OTA system development, the multipath propagation channel models that have been proposed thus far, such as [1–4], have been used in clarifying fundamental concepts. Standardization of OTA measurement methods is currently under consideration by the Third Generation Partnership Project (3GPP) .
In OTA test methods, the environment for MIMO terminal evaluation is generated by either a reverberation chamber or a fading emulator [5, 6]. In the reverberation chamber system, a chamber with metallic walls that effectively reflect waves is used to generate a rich multipath propagation environment [5, 7]. In fading emulator systems, hereinafter denoted as FE systems, a number of virtual scattering probe antennas are positioned circularly around the terminals being tested (devices under test, DUTs) in order to generate a fading environment [8–13]. Although both methods have advantages and limitations, we investigated FE OTA systems with a focus on channel control flexibility.
Among FE MIMO-OTA systems, time-varying multipath signal generation using an available fading simulator scheme is a promising candidate in 3GPP  because the fading simulator is able to flexibly control propagation parameters such as delay spread, Doppler spread, and angular spread. Although this type of system can easily realize all necessary functions, the construction cost is generally extremely high. Therefore, in our previous papers [14, 15], we proposed an FE MIMO-OTA system with a simplified configuration named as the antenna branch-controlled system and carried out narrowband experiments without any delayed paths. In addition, field-programmable gate array (FPGA) implementation of the proposed scheme has been conducted . Although performance identification of the proposed channel model is essential for system development, quantitative evaluations have not yet been achieved in previous papers.
Accordingly, in this paper, after introducing the channel model and its theoretical background, we will make clear the generated channel performance as a function of the number of probe antennas. From an eigenvalue analysis of the generated channel matrix, we verify that an 8-probe antenna system can realize a very accurate multipath environment for the performance measurement of a 2 × 2 MIMO system, while a 12- or 16-probe antenna system can do the same for a 4 × 4 MIMO system.
2. Antenna branch-controlled FE-type MIMO-OTA system and its channel model
2.1 FE-type MIMO-OTA system
2.2 Channel model for the FE-2 system
The weight wTX_lm is the element of the TX connection matrix with row l and column m composed of WH codes to realize independent Rayleigh fading for each input port m. The coefficient c(k) is the amplitude of the k th delayed wave, and the weight w l (k) is the coefficient for probe antenna l with delayed path k to realize independent fluctuations of each delayed path. In the above equation, reception array is adopted as a linear equally spaced array (d r ) in the direction of θ0 although the channel characteristics, ARX, connecting the probe antenna array to the receiver antenna array as a DUT are more variable than we assumed here. The Doppler shift fDl and direction of θ l for probe antenna l are discussed below.
We must avoid a symmetrical arrangement in the x-axis direction because the same Doppler shift frequency appears for the pair of directions. This reduces the variety of Doppler frequencies generated and works as if the number of probe antennas is smaller than the actual number L.
We must avoid a symmetrical arrangement in the y-axis direction because the arrangement cancels the imaginary part of the received signal for the pair of directions. This causes a deviation from Rayleigh distribution, as shown in Figure 6.
We must avoid a symmetrical arrangement about the center point for the same reason stated above.
The proposed arrangement is shown in Figure 5. The above Doppler shift setting rule appears to satisfy requirements 1 through 3 above. The validity of the assumption is examined in the next section.
3. Investigation of the generated channel performance
3.1 Single-input channel characteristics
In this section, we consider the model having channel characteristics of a11(1)(t) with L = 8. We proposed the Doppler shift assignment shown in Figure 5. Figure 6 shows the cumulative distribution functions (CDFs) of the amplitude variations for three different Doppler shift arrangements, i.e., regular positions without any angular offsets, fixed offsets, and double offsets (proposed arrangement), with the theoretical Rayleigh distribution. The maximum Doppler shift fD in this simulation is set to be fDTs = 0.01, where Ts is the sampling period. Although the regular and fixed offset arrangements have a large discrepancy from the Rayleigh distribution, the proposed arrangement shows very good agreement.
3.2 Eigenvalue characteristics of generated MIMO channels
Input ports (M)
1 ~ 4
Probe antennas (L)
8, 12, 16
Receive antennas (N)
1 ~ 4
Delay paths (K)
Normalized maximum Doppler shift (fDTs)
Total sampling points
SNR for channel capacity calculation
Performance comparison of generated environments as viewed from the eigenvalue characteristics
FE-1 (N × M)
FE-2 (N × M)
2 × 2
3 × 3
4 × 4
2 × 2
3 × 3
4 × 4
3.3 Wideband characteristics
Correlation characteristics among generated delayed waves
We evaluated a simplified configuration for OTA test systems. The key element of the proposed model is the adoption of an antenna branch-controlled configuration (FE-2) for generating multipath delayed waves. We introduced an orthogonal code weighting for generated delayed waves to realize independent amplitude fluctuations among all of the generated delayed paths with multiple input ports, and the performance of the generated channel was evaluated.
By assigning the appropriate Doppler shift to each probe antenna branch, very accurate Rayleigh fluctuations for both amplitude distribution and temporal variation statistics can be generated using eight-probe antennas.
From the viewpoint of eigenvalue analysis in generating the MIMO propagation channel, at least 8-probe antennas are necessary for evaluating the 2 × 2 MIMO system, whereas 12- or 16-probe antennas are necessary for the 3 × 3 and 4 × 4 MIMO systems.
From the viewpoint of channel capacity analysis, eight-probe antennas are sufficient, even in the case of 4 × 4 MIMO system measurement.
By introducing orthogonal code set weighting, almost-independent Rayleigh fluctuations of delayed paths for different input ports are realized with a very simple configuration based on the antenna branch-controlled scheme.
One of the primary practical advantages of the proposed scheme is the realization of a flexible MIMO-OTA testing system in a very simplified configuration without the loss of necessary functions or a reduction in performance for the purpose of measurement. Due to the way the fading functions are configured in a cascade, an implementation of the scheme into an FPGA circuit is promising from a practical viewpoint. One disadvantage of the proposed scheme is the difficulty involved in the flexible control of a Tx connection matrix excepting a case of M = 2, as compared to a path-controlled configuration (FE-1).
The necessary number of probe antennas in an FE OTA system increases with increasing complexity of the radiation pattern of the DUT or the angular power profile of the multipath environment, such as a multicluster environment. Moreover, a dual polarization system requires twice the number of probe antennas. For practical applications, typical standard channel models described in Section 6.2 in  should be evaluated using the proposed model. Since the proposed channel model has the capability to realize such standard channel models by setting the parameter values appropriately, we can show calculation examples. However, it seems very difficult to present the evaluation results with a systematic comparison. Since very careful evaluations are necessary, these evaluations are left for future studies.
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