EuCAP 2006 - European Conference on Antennas & Propagation

 
Session: Session 2A03P - MIMO Channel Characterization (04c)
Type: Oral Propagation
Date: Tuesday, November 07, 2006
Time: 08:30 - 12:20
Room: Risso 6
Chair:
Co-chair:
Remarks:


Seq   Time   Title   Abs No
 
1   08:30   Measurements of MIMO Capacity at 1800 MHz with in- and Outdoor Transmitter Locations
Garcia-Garcia, L.1; Jalden, N.2; Lindmark, B.2; Zetterberg, P.2; de Haro, L.1
1Universidad Politecnica de Madrid, SPAIN;
2Royal Institute of Technology, SWEDEN

In recent years, the increasing interest in multiple-input multiple-output systems has lead to a significant research effort in this topic. In order to properly evaluate MIMO schemes and algorithms, measurements in real environments are of great importance. Most work on characterization of MIMO channels in mobile communications examines either indoor or outdoor environments; however, measurements and system evaluation including mixed cases (outdoor to indoor scenario) are scarce. Likewise, most of the previous work considers a single base station in the MIMO system. In this paper we present the results obtained from MIMO measurements, where we have considered several base station locations. Different combinations at system level are proposed and the achievable capacity for each case is calculated.

In order to obtain results from real environments, an extensive measurement campaign was carried out. A 4x4 MIMO testbed was used to collect the data. The receiver module (mobile station, MS) was mounted on a trolley and carried along different indoor routes in an office building, including several floors. Four different locations were used for the transmitter module, which was split into 2 groups or base stations (BS) with 2 antennas each. For the first two cases (setup A and D), the 2 BSs are co-located (indoor and outdoor locations, respectively), while for the other two cases (setup B and C) the 2 BSs are situated in indoor locations and spatially separated (at the same end of the office floor for setup B and in opposite ends for setup C). To compare different setups for the two BSs, 3 options regarding signal processing at system level were studied: 1) no information is shared between BSs and a fixed BS is considered (capacity of 2x4 system); 2) no information is shared between BSs but the MS selects the BS based on the strongest received power; 3) the base stations shares channel information and full CSI at the 4 transmitters is assumed (4x4 system).

The MIMO channel has been analysed for the different considered BS configurations and studied environments. The path loss, the spatial correlation between antennas and the eigenvalue analysis of the covariance matrix of the channel have been computed. The co-located indoor case shows a high correlation, while the spaced locations offer a lower correlation, as expected. The outdoor case shows an interesting reduction in correlation when using different polarizations, but the indoor case outperforms the outdoor one when taking into account path loss, which is higher for the latter BS location.

When considering different options for signal processing at system level, we see that the full 4x4 waterfilling scheme is a large improvement compared to the 2x4 waterfilling with fixed BS, since a higher spatial diversity order may be obtained when using a larger number of antennas. However, the differences between the full 4x4 scheme and the 2x4 with BS selection is not so clear when spatially separated BSs are considered. As a conclusion, the 2x4 waterfilling scheme with BS selection is an interesting solution, since it simplifies the implementation in a realistic scenario compared to a full 4x4 system where CSI must be shared.

 
 
2   08:50   Outdoor to Indoor MIMO Radio Channel Measurements at 5.25 GHz - Characterization of Propagation Parameters
Alatossava, M.; Holappa, V-M.; Ylitalo, J.
Centre for Wireless Communications (CWC), University of Oulu, FINLAND

In this paper, the results of outdoor to indoor multiple-input multiple-output (MIMO) measurement campaign at 5.25 GHz are presented. Outdoor to indoor concept has not been studied extensively for high carrier frequencies even though it is defined as one of the propagation scenarios in [1]. Moreover, it is foreseen that the future wireless communication systems employ multiple antennas at both ends of the transmission link. In order to create realistic spatio-temporal models for performance simulations, accurate real time channel measurements are needed with a specific environment and multiple antennas.

Propsound CSTM, a state-of-the-art radio channel sounder, was used to measure the MIMO channel [2]. Attention is given to temporal and spatial parameters including delays, small scale fading and the angle of arrivals/departures (AoA/AoD). Transmitter (Tx) was located outside the building at the height of 12 m and consisted of 16 dual polarized antenna (DPA) elements in a rectangular array whereas the omni-directional Rx antenna included 9 DPA elements. Applied bandwidth was 100 MHz and used code length was 1023 chips. The measurement scenario and the floorplan of the building with 30 cm thick concrete walls are shown in Figure 1. The measured Rx route is marked with red line and Tx/Rx zero-angle directions are illustrated with a dashed line and a black arrow, respectively.

The azimuth directions in Tx and Rx are obtained with ISISTM (Initialization and Search Improved SAGE) [3] and shown in Figure 2 with coloured dots. Red denotes strong signal and blue represents weak signal. From this figure, it is clear that clustering phenomena [4] is valid also in the outdoor to indoor propagation environment. The deviations in AoD are due to the building on the left side of the Tx as shown in Figure 1. The fading of the signal envelope is close to Rayleigh with a Ricean factor of 3 for the strongest tap and 1-2 for the weaker paths. In Figure 3, channel capacity is shown. Capacity is higher when the Rx moves along the window with the venetian blinds open (normalized channel samples 0.1-0.3), whereas the capacity decreases as the window with venetian blinds shut is next to the Rx. RMS delay spread is small (approximately 100 ns for 50 percent of the channel samples) due to short distance between Tx and Rx and reasonably small office room.



[1] IST-2003-507581 WINNER D5.4. v.1.0, "Final Report on Link Level and System Level Channel Models", September 2005.
[2] L.Hentilä, P.Kyösti, J. Ylitalo, X. Zhao, J. Meinilä, and J-P. Nuutinen, "Experimental Characterization of Multi-Dimensional Parameters at 2.45 GHz and 5.25 GHz Indoor Channels", in WPMC2005, Aalborg, Denmark, September 2005.
[3] A. Stucki and P. Jourdan, "MIMO Radio Channel Parameter Estimation Using the Initialization and Search Improved SAGE Algorithm", in MPRG Symposium, Blacksburg, VA, June 2003.
[4] L.Correia, Ed., "Wireless Flexible Personalized Communications", COST 259 Final Report, John Wiley & Sons Ltd., June, 2001.

 
 
3   09:10   MIMO Channel Characterization Through Ray Tracing Simulation
Vitucci, E. M.; Degli-Esposti, V.; Fuschini, F.
University of Bologna, ITALY

Multiple Input - Multiple Output (MIMO) techniques, i.e. radio transmission techniques based on the adoption of multiple antennas (arrays) at both terminals of the radio link, have been proposed and widely studied in recent years [1]. The channel capacity gain MIMO can provide increases with the number of antennas (inputs and outputs), but also with the so called "multipath richness" which is in short the property of multipath propagation of being composed of many contributions with similar amplitude and large spreading in both angle of arrival/departure and time delay.

A complete, multidimensional propagation characterization, can be achieved through experimental channel sounding techniques [2]. However, such techniques are very expensive and time consuming, especially if a characterization in different environment classes with a sufficient statistical base is needed.

Multipath propagation prediction, and thus MIMO channel simulation through computer programs, if reliable, would be therefore very welcome. In theory, Ray Tracing (RT) or in general, ray models represents the most appropriate MIMO channel prediction models since they strictly simulate multipath and its multi-dimensional (space/time/frequency) de-correlation effects on the radio channel. Recent studies [3] have shown that RT performance can be sensibly improved by extending RT capabilities to diffuse scattering prediction through the simple "Effective Roughness" (ER) model. In the present work, the advanced 3D RT program described in [3] is applied to MIMO channel characterization in meaningful environments. The capability of RT to properly reproduce MIMO-related propagation parameters such as angle spread, delay spread, and spatial correlation in the different environments (with different propagation mechanisms) is analyzed in the present work. Then, RT output is post-processed to get different realizations of the channel matrix H, and the theoretical MIMO capacity is evaluated through simple capacity estimation formulas in the various cases.

The considered simulation scenario is an ideal, "Manhattan-like" scenario, with 100x30 m city blocks and building heights variable between 20 m and 140 m. Street width is of 20 m.

As an example the comparison between RT simulated and measured [4] MIMO capacity CDF's is shown in Figure 1. The system is a dual polarized MIMO system with different number of inputs/outputs and a signal to noise ratio of 10 dBs, with power control. The simulated case is the 4x4 case, and no tuning of any kind has been applied to simulated results. It is evident that the agreement between the simulated and the measured capacity CDFs is very good, although the simulated one is slightly less steep than the measured one.

Fig. 1 Measured and RT simulated MIMO capacity CDFs

This first result suggests that advanced RT is capable of predicting MIMO performance with a good accuracy. Other similar results will be presented and analyzed in the full paper.

[1]D. Gesbert, M. Shafi, "From Theory to Practice: An Overview of MIMO Space-Time Coded Wireless Systems", IEEE JSAC, 2003.
[2]K. Kalliola, "3-D double-directional radio channel characterization for urban macrocellular applications," IEEE Trans. AP, 2003.
[3]V. Degli Esposti, "An advanced field prediction model including diffuse scattering," IEEE Trans. AP, 2004.
[4]D. Chizhik, "Multiple-input-multiple-output measurements and modelling in Manhattan", IEEE JSAC, 2003

 
 
4   09:30   Propagation Measurement in Indoor Environment for MIMO Systems Using Polarization Property
Hirayama, H.; Kurose, A.; Kikuma, N.; Sakakibara, K.
Nagoya Institute of Technology, JAPAN

1 Introduction MIMO systems are getting large interest in communication systems. We have investigated a method to enlarge channel capacity by using two orthogonal polarizations. Since the effectiveness to use polarization property depends on the Cross Polarization Discrimination (XPD) in propagation channel, it is necessary to make clear the XPD of propagation in a practical environment. In this paper, we have measured the MIMO propagation from a viewpoint of polarizations.

2 Received power measurement
At first, cumulative distribution function (CDF) of the received power is investigated to make clear the propagation channel. The measurement of received power was done in a ferroconcrete building shown in Fig. 1. Since the wall is made of a plasterboard, electro-magnetic wave can pass through the wall. As shown in this figure, the transmitting antenna with a signal generator (TX) was set in the room. The receiving antenna with a spectrum analyzer (RX) was moved along the passage and the received power was recorded. Measurement frequency was 2.45 GHz. TX power was 0 dBm. A preamp of 20 dB gain was used in RX. TX and RX antennas were half-wavelength dipoles. To obtain the XPD of propagation, measurement was done in horizontal (H) and vertical (V) polarizations of both TX and RX antennas. In the case of horizontal polarization, TX and RX antennas were set so as to direct main beam to the east-west direction. In the room with TX, there was a blind on a window, which was made of aluminum strips. Measurement was done with and without the blind. Figure 2 shows the result.

By calculating median value of received powers, it is estimated that the XPD of propagation without the blind is 3.2 dB for V-pol and 1.9 dB for H-pol. The XPD of propagation caused by the blind is estimated to be 16 dB for V-pol and -0.3 dB for H-pol. It is considered that the blind acts as a polarization-selective reflector array for horizontal polarization. From this result, it is clear that the blind affects significantly the XPD of propagation.

3 Round Trip Time measurement
Next, we measured the MIMO propagation. A commercially available 802.11g LAN units with MIMO were used. Two antennas were equipped both with TX and RX units. Spacing of two antennas was 1 wavelength. ICMP packets were sent by a PC connected to the TX unit. The Round Trip Time (RTT) of the ICMP packet was measured. Variation of bit error rate is observed as variation of the RTT because time is spent due to error correction in lower layer. Figure 3(a) and (b) show the results with and without the blind, respectively.

In comparison of Fig. 3(a) with 3(b), it is clear that RTT with the blind is better than that without the blind. It is suggested that this is because the blind makes the channel multipath rich. Furthermore, in Fig. 3(b), RTT for the three combinations of polarizations show different tendencies while they show similar one in Fig. 3(a). It is considered that this is caused by variation of the XPD of propagation between H-pol and V-pol as discussed in Sec. 2.

4 Conclusion
The received power measurement and RTT measurement in indoor environment were done to make clear the XPD of propagation. We have found that the blind makes large effect on XPD of propagation and MIMO channel.


 
 
5   09:50   Testing MIMO Systems with Coupled Reverberations Chambers: A Wideband Channel Model
Delangre, O.1; De Doncker, Ph.1; Lienard, M.2; Degauque, P.2
1Université Libre de Bruxelles, BELGIUM;
2Université des sciences et technologies de Lille, FRANCE

Introduction

MIMO systems have gained a lot of attention since they promise an increase of the capacity with a very high spectral efficiency. Many channel models have been proposed in order to enhance the understanding of the propagation characteristics. Those models need to be validated by measurements. Unfortunately, those measurements are a not so easy task due to many difficulties like the ability to reproduce a given environment. A new testbed was proposed in [1]. It is composed of two reverberation chambers coupled through a waveguide whose transverse dimensions can be changed. By means of the movement of the mechanical stirrers in the chambers, one can create a wide sense stationnary stochastic environment. Each chamber reproduces the environment around respectively the transmitting and receiving antenna and the waveguide models the channel.

Wideband channel model

In this paper, a new wideband wave-based model is proposed. This model includes the effect of the waveguide. The spectrum of incoming plane wave coupling to a mode is computed showing that each mode in the waveguide is excited by specific directions. The radiation pattern of each mode at the output of the waveguide is also presented. It has been shown that the power in each mode is not identically distributed [1], and this fact is therefore also included in the model. Each propagating mode is a path between the emitter and the receiver and the number of paths gives the degrees of freedom of the channel. Finally the coupling between modes in a rough waveguide is also included. By changing the waveguide or the working frequency, one can create an environment where the effective degree of freedom is varying. This fact has been experimentally checked. The wideband effects are included by means of a tap delay model. The amplitudes of the taps are obtained through some measurements of the power delay profile in the chambers. The power delay profile shows very long delays with typical values of rms delay spread of a few hundreds of ns. Without modification, this testbed is more suitable for outdoor environments where the delays are much higher than in indoor environments. The effect of placing absorbing materials is also investigated. The main conclusion is that the power delay profile decays faster when placing absorbing materials in the transmitting chamber rather than in the receiving chamber. This is due to the lowering of the incoming plane wave spectrum on the waveguide leading to less amount of power going through the paths in the waveguide. The values for rms delay spread are lowered from about 700 ns to 350ns with absorbing material in the transmitter chamber. Placing absorber in the receiver chamber gives typical values of rms delay spread of 550 ns.

Conclusion

By means of the testbed, one can create a stochastic environment and test different propagation characteristics of wireless systems. The notion of paths have been emphasized allowing to test transient conditions between different degrees of freedom.

[1] O. Delangre, Ph. De Doncker, M. Liénard, P. Degauque, "Adaptable measurement testbed for wireless systems applied to MIMO channel modeling", IEEE WCNC 2006, Las Vegas, Apr. 2006

 
 
6   10:40   Empirical Characteristics of Urban Macrocell MIMO Channel at 2.53 GHz
Taparugssanagorn, A.; Ylitalo, J.
Centre For Wireless Communications (CWC), University of Oulu, FINLAND

Due to the multipath richness, multiple-input multiple-output (MIMO) systems are used to increase capacity gain. Most researches have mentioned on this property by normalizing the Signal to Noise Ratio (SNR) out of the channel matrix. However, Non Line Of Sight (NLOS) scenarios with rich multipath often experience low SNR. On the other hand, scenarios with Line Of Sight (LOS) usually have high SNR but low multipath richness. The relationship between SNR and multipath richness will be investigated in this paper using urban environment measurements conducted at 2.53 GHz in downtown Oulu, Finland within a bandwidth of 100 MHz. As results, a variety of MIMO channel parameters including the small-scale fading characteristics, delay dispersion, and correlation property as well as wideband channel capacity are illustrated as the transition from the LOS to the NLOS cases. Also, the polarization dependency on the LOS/NLOS condition is investigated.

The measurements were conducted using PropsoundTM multi-dimensional radio channel sounder, which is based on the spread spectrum sounding method and time-division multiplexed (TDM) switching of transmit and receive antennas. Thus sequential radio channel measurement between all possible transmit (TX) and receive (RX) antenna pairs is achieved. The center frequency was 2.53 GHz with the measurement bandwidth of 100 MHz. A PN-sequence (Pseudo Noise) with 511 chips is transmitted continuously. The antenna height of the base station (BS) was 32 m and it was about 2 m above the roof top of the BS building and a few metres above the average rooftop level. The mobile station was moved with vehicular speed of 20 km/h at street level and the mobile TX antenna height was 2 m.

The empirical cumulative distribution functions (CDFs) of the Nakagami-m factor for both LOS and NLOS cases are depicted in Figure 1. The antenna polarization dependency is also included in the plots. The dual polarized cases evidently trend to be more Rayleigh distributed. The temporal progression of the RMS delay spread over the selected measurement run is depicted in Figure 2. We can clearly see that the RMS delay spread is significantly large in the NLOS case. The RMS delay spread increases sharply when TX is moving behind the corner. Furthermore, there is no significant effect of polarization in the RMS delay spread. In addition, we investigate the eigenvalue , which interprets the power gain of the eigenmode on sub-channel. As revealed in Figure 3, the LOS case can always provide higher gain comparing with the NLOS case due to the higher SNR at the receiver branch. Therefore, the 50 % outage channel capacity illustrated in Figure 4 in the LOS case is higher than the one in the NLOS case, even though the channels in the NLOS case are less spatial correlated. In addition, when the dual polarization is used, we can gain higher capacity due to the antenna polarization diversity.

As a conclusion, it can be stated that LOS scenarios having high SNR can provide higher channel capacity compared to NLOS scenarios, even if NLOS scenarios have more multipath richness.

 
 
7   11:00   MIMO Cube in Realistic Indoor Environment
Nagy, L.
Budapest University Of Technology, HUNGARY

Abstract The multi-input multi-output (MIMO) antenna can give recently a promise in increasing the capacity of wireless radio systems. The theoretical capacity is mainly calculated in rich scattering environment and results low-correlation diversity channels. In our present paper the MIMO system is analysed in real indoor scenario and the system capacity is compared with the ideal 3D double bouncing stochastic scattering model.

Introduction

The ideal stochastic scattering model gives very promising capacity increase for the MIMO systems, but our investigations show that in simulated real environment this capacity increase can not be reach because of the real physical propagation conditions.

The channel between two MIMO antennas (Fig. 1.) was investigated in simulated indoor environment. The scatterers (50-50 at each side) were placed near to the walls in different forms of cubes and cylinders. The 4x5x3 meter room was discretised with a 1 cm resolution for the FDTD analysis method. Sinusoidal 2 GHz excitation was used and the transmission matrix between the antenna terminals was calculated. Fig. 1. The two MIMO transmitter and receiver antenna pairs investigated Fig. 2. Indoor scenario Fig. 3. Mean capacity vs. SNR Table 1. Transmission matrix elements for MINO cube (magnitude in dB) H1,1 H1,2 H1,3 H1,4 H1,5 H1,6 H1,7 H1,8 H1,9 H1,10 H1,11 H1,12 -37.6 -43.4 -45.2 -49.1 -58.8 -62.4 -80.1 -60.5 -66.2 -66.5 -72.9 -59.0 Results

After calculating the transmission matrix elements the singular value decomposition and mean capacity of the two antenna pairs were calculated (Fig. 3.) Our simulations results in almost half of the capacity for the same SNR and antenna distances in comparison of [1]. The effect is based on the non ideal scattering environment which doesnt give perfect conditions for low-correlated channels. On the Table. 1. the polarisation coupled dipoles have approximately 10 dB higher coupling than the non polarisation coupled ones. This outcomes of the highly reflecting walls and of the scatterers positions which is more realistic than the randomly uniformly distributed scatterers in spheres.

In the paper measured results will be presented for indoor scenarios and compared with our simulations.

Reference

[1] B. N. Getu, J.B. Andersen: The MIMO Cube A compact MIMO Antenna, IEEE Trans. On Wireless Comm., Vol. 4, pp. 1136-1141, 2005.

 
 
8   11:20   Experimental Comparison of the IST-WINNER Indoor MIMO Channel Model
Laselva, D.1; Kyosti, P.2; Hentila, L.2
1Elektrobit Ltd., FINLAND;
2Elektrobit Testing Ltd., FINLAND

This paper draws a comparison, for the non line-of-sight indoor scenario, between the WINNER MIMO radio channel model developed within the IST-Wireless World Initiative New Radio (WINNER) project and a few sets of radio channel measurements. The WINNER model, double directional geometry-based stochastic and measurement-based, defines the channel in time, space, frequency and polarization domains at 5 GHz frequency band and 100 MHz bandwidth. The channel measurements were performed at 5.25 GHz with 100 MHz bandwidth using PropsoundTM CS, a wideband multidimensional channel sounder employing MIMO arrays: a 4x4 dual-polarized planar array at base station and an omni-directional 25 element dual-polarized 3D-array at the mobile. Spatio-temporal parameters extracted from the measurements via the space-alternating generalized expectation-maximization (SAGE) high resolution parameter estimator are used to feed the synthetic model WINNER and to regenerate the propagation channels. The radio channel realizations are generated embedding few MIMO antenna configurations to the synthetic and estimated propagation paths.

Model designers are required to validate thoroughly synthetic channel models against channel measurements in terms of which predictions of the reality the models offer in many MIMO aspects. A close or better prediction of the reality establishes the goodness and the suitability of a model in a particular respect. Other than the spatio-temporal propagation parameters, many metrics have been introduced for the validation of a channel model, each of them reflecting a particular MIMO feature, such as:

  • Mutual information in flat and frequency-selective fading (multiplexing gain).
  • Single-number metrics: diversity measure (diversity order); Demmel condition number (diversity/multiplexing trade-off); relative condition numbers (transmission symbol rate); correlation matrix distance (stationarity); effective degrees of freedom (multipath richness).
  • Joint angular power spectrum (APS) (beamforming gain).
  • Distributions of the eigenvalues and their variation with the angle spread (AS) (channel eigenmodes).

    The WINNER predictions for some of the above metrics (e.g., outage capacity, diversity measure) have been previously investigated showing an acceptable fit on some extent to the estimations from the measurement data. In this paper we focus on the comparison in respect to the following metrics: multipath richness, joint APS, distributions of the eigenvalues and their variation with the AS, calculated from the synthetic and regenerated realizations.

    As far as the authors know, currently, WINNER is the only measurement-based channel model which supports wideband MIMO systems at 5GHz. Lacking other models to assess which performs better and lacking agreement on the degree of accuracy required (i.e., how much a certain discrepancy in the metrics impacts on the upper layer performance is an open question), therefore, this study is limited to quantify, compare and explain the discrepancy of the considered metrics. Indeed this paper leaves open the judgement about how appropriate this model is: it should be assessed by the model users according to the studied MIMO performance accounting for system level and cross-layer design issues.

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    9   11:40   Near-Field Correction for Incoherent Source Location: Simulations and Measurements

    The problem of finding unknown sources through narrowband measurements via a bidimensional virtual array in near-field conditions is addressed. Subspace based methods for Direction-of-Arrival (DoA) estimation generally works on the assumption that the source is located at the far-field region so signal wave front impinging on a array is plane. When this condition is broken, performance of these algorithms becomes degraded and the algorithms are unable to focus the source located at the near-field region, where signals exhibit spherical wave front.

    Measuring the path travelled by the signal from the source to each array element, the signal phase at each array element can be correctly computed so we can construct the true steering vector associated to the signal emitted from a near-field source having assumed the distortion of the spherical wave front. With this near-field approximation, the DoA as well as the range of the source can jointly be estimated by subspace based methods.

    In order to control the environment conditions, some measurements were accomplished in a range compact anechoic chamber. A 2.4GHz pulse was emitted from the probe antenna in order to have only one point source in the environment. Multipath due to the reflections is not considered since levels are less than -40dB. Scanner positions were set up to have γ/2 spacing between each measurement point along the x-axis as well as along the y-axis, where γ represent the wavelength. A total of 128 samples were taken at each measurement point to form the snapshots at the array output. The total number of points measured over a length of 3.75[m] were 61 on each axis. Near-field conditions were accomplished for three cases. Case 1. The probe was located to 8γ from the x-y plane so the source was located at (22.67γ,45°,69.3°), in spherical coordinates. Case 2. The probe was located to 12γ from the x-y plane leading to a source located at (24.37γ,45°,60.5°). Case 3. The source was located at (29.7γ,45°,45.5°) where the probe was separated 20.8γ from the x-y plane. Antenna employed as array element was a corrugated circular horn which was characterized through its radiation pattern to take into account the effect of using a nonomnidirectional antenna. The same antenna was used as probe.

    In this paper we show that eliminating the distortion introduced by the far-field steering assumption for estimating a near-field source, the subspace based algorithms, like MUSIC, provide a spatial spectrum showing perfectly the source location. Fig. 1a) depicts that the spatial spectrum can not resolve any near-field source based on the far-field assumption while fig. 1b) y 1c) shows the improvement introduced by the near-field correction. Finally, simulation results are presented and compared with the experimental results to validate the near-field approach.