Improved Interference Alignment Performance for MIMO OFDM Systems by Multimode MIMO Antennas Mohamed El-Hadidy∗ , Mohammed El-Absi∗ , Leen Sit∗∗ , Markus Kock∗∗∗ Thomas Zwick∗∗ , Holger Blume∗∗∗ and Thomas Kaiser∗ ∗ Duisburg-Essen
University, Institute of Digital Signal Processing, Bismarckstr. 81, 47057 Duisburg, Germany ∗∗ Karlsruhe Institute of Technology, Institut f¨ ur Hochfrequenztechnik und Elektronik, Kaiserstr. 12, 76131 Karlsruhe, Germany ∗∗∗ Leibniz Universit¨ at Hannover, Institute of Microelectronic Systems Appelstr. 4, 30167 Hannover, Germany Email:
[email protected]
Abstract— This contribution presents an improved Interference Alignment (IA) method for arbitrary MIMOOFDM communication systems by exploiting spatial degrees of freedom of sophisticated multimode MIMO antennas. It is widely known that IA needs sufficient orthogonality between all the multi-user channels which is in typical indoor environments often not given due to insufficient spatial diversity. A significant improvement of the IA system performance has been achieved by using multimode MIMO antennas instead of classical and idealized omni-directional antennas. Such multimode MIMO antennas are capable to switch between different modes of the radiation patterns which significantly reduces the relevant channel coherence. Simulations of an indoor multi-user environment are carried out by a deterministic MIMO-OFDM channel model based on hybrid Electro Magnetic (EM) ray-tracing for being as close as possible to reality. Moreover, hardware implementation aspects are discussed as well demonstrating the feasibility of the overall IA based MIMO OFDM system. Index Terms— OFDM, Interference Alignment, MIMO, Multimode Antennas, Ray-tracing, Deterministic Channels
I. I NTRODUCTION MIMO is merged with OFDM to improve spectral efficiency and minimize fading effects [1] in wireless communication systems. Unfortunately, multi-user Interference dramatically affects the channel capacity and the robustness of the OFDM system. IA is a promising technique which theoretically overcomes multi-user interference and hence achieves the maximum degrees of freedom (DoF) for the K users in interference channels [2]. The basic idea of IA is to force interfering signals at each receiver in one subspace and place the desired signal in another orthogonal to the first one [3]. Most of the IA literature are based on statistical channel models [4],[5] assuming rich scattering environments and
non-coherent channels. A real MIMO interference channel testbed was presented in [6] where it is illustrated by measurements and real scenarios that the results of the theoretical channels are significantly overestimated. In real-world indoor environments, the correlation between the MIMO channels at each node might be high because of typical small distances between the neighboring antennas. Furthermore, the scattering caused by the environment is mostly not sufficient to provide the required independency for a robust IA communication system. In this paper, we create diversity using a multi-mode based MIMO antenna system, which provides orthogonal radiation patterns. This decreases the coherence between the channels and significantly enhances the overall system performance. Simulation results and analysis are based on a wideband deterministic channel model, where the antennas and the real-world environment are well integrated [7], [8]. The OFDM IA System Model is described in section II. In section III, the detailed description of the multimode MIMO antenna and the corresponding concepts are presented. Simulation results are illustrated in section IV followed by hardware implementation aspects in Section V. Finally, the conclusions are presented in the last section of the paper.
II. OFDM IA S YSTEM M ODEL Consider a K-user OFDM interference channel with Mj transmit omnidirectional antennas at transmitter j and Ni receive omnidirectional antennas at receiver i. All users transmit N ds streams using N sub-carriers, where ds is the data stream transmitted by each subcarrier. Every transmitter communicates with its desired receiver leading to interference to other pairs of transmitters-receivers. The discrete-time complex received signal over nth subcarrier
at ith receiver over flat channel is represented as [4], [9]: yin =
K
Hnij Vjn xnj + zni
j=1
=
Hnii Vin xni
+
(1)
K
Hnij Vjn xnj
+
zni
j=1,j=i
where yin is the Ni × 1 received vector at receiver i, Hnij is the Ni × Mj flat frequency domain channel matrix over nth subcarrier between jth transmitter and ith receiver, Vjn is the Mj × ds orthonormal precoding matrix which is applied to the transmitted Mj × 1 vector xnj from jth transmitter, and zni is the Ni × 1 zero-mean unitvariance circularly symmetric additive white Gaussian noise vector added at receiver i. We assume the channel state information (CSI) Hnij is perfectly known at each node. To reconstruct the transmitted ds signals at ith receiver, the received signal is Ni × ds decoded using an orthonormal linear suppression interference matrix Uni . The reconstructed data xi at receiver i is defined as: ⎞ ⎛ K ni = Uni H Hnii Vin xni + ⎝ x Uni H Hnij Vjn xnj ⎠ j=1,j=i
+Uni H zni
(2)
(a)
(b)
Fig. 1: Block diagram of the multimode antenna system comprising 4 monopoles and a mode decomposition network.
With perfect interference alignment, we require [1]: rank (Uni H Hnii Vin ) = ds and
Uni H Hnij Vjn = 0
∀i
∀j = i
(3) (4)
According to (3) and (4), the received signal in (2) after linear suppression interference matrix becomes: ni = Uni H Hnii Vin xni + Uni H zni x
(5)
The simulation results of such multi-user scenarios presents low robustness about the feasibility of the IA algorithms as shown [6]. The main reason is that the spatial diversity of the system is not sufficient to provide statistically independent channels and the correlation among the users channels is typically non-neglectable. Replacing the omni-directional antennas with multimode MIMO antennas having orthogonal radiation patterns can significantly improve the Bit Error Rate (BER) system performance. The orthogonality of the antennas radiation patterns decreases the coupling among the neighboring antennas and indirectly increases the spatial diversity. Details of the multimode MIMO antennas are discussed in the following section. III. M ULTIMODE MIMO A NTENNA For testing the IA algorithm with a real world antenna, a multimode MIMO antenna developed at the Institut f¨ur Hochfrequenztechnik und Elektronik (IHE) was chosen. This antenna has been designed and measured for use at the frequency range from 5.9 GHz to 6.15 GHz, where the measured S11 is lower than -8 dB. The multimode
antenna consists of 4 monopole antennas built on a finite ground plane of 7 cm × 3.8 cm (as illustrated in Fig. 1) to include real world non-idealities. The spacing between two adjacent monopoles is 0.32 λ (based on 5.9 GHz) while the spacing between two opposite monopoles is 0.45 λ. Depending on the antenna excitation, different radiation patterns known as modes results are yielded. To produce the different modes, each monopole is excited with the same amplitude but with different phase, either in-phase 0◦ or out-of-phase 180◦ . This multimode antenna system can radiate 4 different modes, which are orthogonal to each other, and two of them shown in Fig. 2 were chosen for simplicity. The detailed design parameters can be found in [10], where the word ”orthogonal” means that the main beam directions of the antenna radiation patterns are perpendicular” to each other. A passive Mode Decomposition Network (MDN) based on the design in [11] is used to decouple the input signals to the monopoles to produce the different modes. It excites each monopole for the specific mode with the corresponding phase offset. Therefore the whole antenna system consisting of the monopoles and the MDN can be viewed as a system with 4 inputs, in which each excitation scheme produces 1 mode, and two excitation schemes are used for producing two different radiation patterns at the output as follows: Excitation scheme 1: Signals at the four ports 1, 2, 3 and 4 (frequency=6.025 GHz) [[1, 0o ] + [1, 180o ] + [1, 180o ] + [1, 0o ]]
Excitation scheme 2: Signals at the four ports 1, 2, 3 and 4 (frequency=6.025 GHz) [[1, 0o ] + [1, 0o ] + [1, 180o ] + [1, 180o ]]
Fig. 3: Deterministic EM ray-tracing channel modeling for the three users scenario in an indoor office environment. User 1 100 Multimode Antenna HWD
10−1
BER
(a)
10−2
10−3
0
2
4
6
8
10
12
14
16
SNR / dB →
Fig. 4: Comparison of BER vs. Eb/No at user 1 by applying multimode antenna and using HWD antennas.
are also considered. The effective channel between each transmitting and receiving nodes can be described in eq. (6) as (b)
Fig. 2: Simulated radiation patterns of the 4 possible modes in CST. (a) Excitation scheme 1 (b) Excitation Scheme 2 The transfer functions of this antenna and its corresponding radiation patterns have been computed using an EM simulation tool of CST microwave studio [12] and merged into the ray-tracer tool of Wireless Insite [13] to emulate a real-world indoor office environment. IV. S IMULATION R ESULTS The deterministic hybrid EM ray-tracing channel model is considered for the MIMO OFDM channel [14]. The spatial channel and the environmental effects such as pathloss, frequency dependence, reflections, transmissions and diffractions are taken into account in this model. The characteristics of the antennas as part of the effective channel such as directional gain, matching and polarization
π 2ππ 2π h T (t, φT , θT )
heff (t) = 0
0
0
0
∗h C (t, φT , θT , φR , θR ) (6) ∗h R (t, φR , θR ) dφT dθT dφR dθR
where h T and h R are the transmitting and receiving antenna impulse responses respectively and h C is the spatial channel between the transmitting and receiving nodes. Fig. 3 illustrates the real-world indoor office environment, where the transmitting and the receiving nodes of the three users are randomly distributed. Simulations have been performed for OFDM QPSK modulation scheme of 128 subcarriers within the frequency range from 5.9 to 6.15 GHz. Results shows considerable improvements of the BER system performance for
the three users in the case of using the multimode antenna of orthogonal radiation patterns compared with the Half Wave Dipoles (HWD) of omnidirectional characteristics as shown in figures 4, 5, 6.
In the previous simulation results, only two fixed orthogonal radiation modes of the four available modes are chosen for simplicity. The results illustrate significant improvement of using orthogonal modes than using omnidirectional ones. This improvement could be considerably enhanced, if we dynamically switch between the four available orthogonal radiation patterns and chose the best two out of four for achieving the best BER system performance. An experimental testbed for fixed antenna patterns is presented in [15]. In this section, we consider the resource requirements of an optimized efficient integer implementation of the proposed novel antenna-selection IA algorithm, based on first FPGA implementation results for the 3-user 2x2 MIMO channel IA. Target systems include SDR platforms, FPGAs and ASICs. A. System model The algorithm constitutes the two-step process of 1) channel rate processing (CRP) and 2) symbol rate processing (SRP). Based on a full set of given channel estimations, the CRP select the best radiation mode and the corresponding precoding- and decoding matrices V and U for all devices. On the transmitter side, the SRP distributes each transmit symbol to both antennas by multiplication with V . The two received antenna symbols are linearly combined into a single symbol by multiplication with U H on the receiver side. Multimode Antenna HWD
BER
10−1
10−2
0
2
4
6
8
10
12
14
16
18
HWD
10−1
10−2
10−3
0
2
4
6
8
10
12
14
16
SNR / dB →
Fig. 6: Comparison of BER vs. Eb/No at user 3 by applying multimode antenna and using HWD antennas. computation and normalization. All intermediate matrices can be independently scaled by arbitrary scalars without affecting the antenna decision or V and U . Exploiting this makes the cost of all involved matrix inversions negligible and allows intermediate matrix results to be block-normalized by shifting resulting in reduced integer word lengths. Table I summarizes the number of required real-valued mathematical base operations for radiation mode selection and the computation of V and U per antenna combination and the OFDM subcarriers. Complex multiplications are composed of three real multiplications, three additions and two subtractions, INVSQRT denotes the reciprocal square root. Operation Matrix mult. Eigenvectors Metric score Total
ADD/SUB 468 15 23 506
MUL 234 4 11 249
SQR 0 4 30 34
SQRT 0 3 3 6
INVSQRT 0 0 1 1
TABLE I: Basic operation counts per antenna combination and subcarrier
User 2 100
10−3
Multimode antenna
BER
V. H ARDWARE IMPLEMENTATION ASPECTS
User 3 100
20
SNR / dB →
Fig. 5: Comparison of BER vs. Eb/No at user 2 by applying multimode antenna and using HWD antennas.
To keep the total transmit power constant, the chosen antenna combination’s precoding matrices V need to be normalized, resulting in 3 ADD, 4 MUL, 4 SQR and 1 INVSQRT additional operations per transmitter and subcarrier. The above analysis implies that in general, the implementation cost is dominated by the multiplications in terms of silicon area and power consumption. As an example, a typical 128 subcarrier OFDM system with 2 radiation patterns chosen from 4 patterns per transmitter, 2 antennas per receiver and 1 ms IA processing latency requires approx. 7.8 GMUL/s for realtime operation. VI. C ONCLUSION
B. Computational complexity As the SRP is straight forward, this section focuses on the costs of the 3-user 2x2 MIMO CRP consisting of matrix inversions, matrix multiplications, eigenvector
In this paper, IA is applied to a classical multiuser MIMO OFDM communication system by using a multimode MIMO antenna instead of typical omnidirectional antennas. It has been demonstrated that such advanced antennas could significantly improve the system
performance due to its inherent orthogonality, which substantially increases the statistical independency between the multi-user channels. Realistic simulations have been carried out based on such EM simulated antennas and a multi-user indoor office environment being simulated by a professional ray tracer software. A fair comparison between using half-wave dipole antennas as omnidirectional antennas and dual-mode MIMO antennas show a considerable improvement of the BER performance at each user for the dual-mode antennas. Finally, hardware and implementation complexity aspects are investigated as well and, beside the practicability of the antennas, confirm the general feasibility of the proposed extended IA approach. ACKNOWLEDGMENT This work has been carried out in the framework of the project Real-World Design of a cognitive MIMOUWB Communication System (DeciMUS) which is funded by the German Research Foundation (DFG) program within Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications (UKoLoS). The authors thank German Academic Exchange Service (DAAD) for their financial support. R EFERENCES [1] A. Batra, J. Balakrishnan, and A. Dabak, ”Multi-band OFDM: a new approach for UWB,” in Proc. IEEE Int. Conf. on Ultra Wideband Systems and Technol., Reston, VA, USA, Nov. 2003. [2] V. R. Cadambe, S. A. Jafar, ”Interference alignment and degrees of freedom of the K-user interference channel,” IEEE Trans. on Inf. Theory, vol. 54, no. 8, pp. 3425-3441, Aug. 2008. [3] V. R. Cadambe, S. A. Jafar, ”Reflections on interference alignment and the degrees of freedom of the K-user MIMO interference channel”, IEEE Information Theory Society Newsletter, Vol. 54, No. 4, pp. 5 - 8, Dec. 2009. [4] S. Peters, R. Heath, Jr., ”Interference alignment via alternating minimization,” Int. Conf. on Acoust. Speech and Signal Processing,(ICASSP), Taiwan, Taipei, 2009. [5] K. Gomadam, V. Cadambe, and S. Jafar, ”Approaching the Capacity of Wireless Networks through Distributed Iinterference Alignment”, Proc. of IEEE Global Telecommunications Conference, pp. 16, December 2008. [6] O. El Ayach, S.W. Peters and R.W. Heath, ”The Feasibility of Interference Alignment Over Measured MIMO OFDM Channels,” IEEE Trans. Vehicle Technology, vol. 59, no.9, pp. 4309-4321, Nov. 2010. [7] M. El-Hadidy, T.O. Mohamed, F. Zheng, and T. Kaiser, ”3D hybrid EM ray-tracing deterministic UWB channel model, simulations and measurements”, Proc. IEEE Int. Conf. on Ultra Wideband Systems, Vol. 2, pp. 14, 2008. [8] M. El-Hadidy and T. Kaiser, An UWB channel model considering angular antenna impulse response and polarization, The Second European Conference on Antennas and Propagation, EuCAP 2007, pp. 15, 2007. [9] M. Shen, C. Zhao, X. Liang, Z. Ding, ”Best-Effort Interference Alignment in OFDM Systems with Finite SNR”, 2011 IEEE International Conference on Communications (ICC), page(s): 1 - 6, Volume: 2 Issue: 5-9 June 2011 [10] G. Jereczek. Design of Capacity Maximizing MIMO Antenna Systems for Car-2-Car Communication. Diploma Thesis, Karlsruher Institut fuer Technologie (KIT), 2010. [11] L. K. Yeung and Y. E. Wang. Mode-Based Beamforming Arrays for Miniaturized Platforms. IEEE Transactions on Microwave Theory and Techniques, 57:45-52, 2009. [12] CST Microwave Studio User Manual, http://www.cst.com/Content/Products/MWS/Overview.aspx, version 2012.
[13] Wireless InSite User Manual,http://www.remcom.com/WirelessInSite/, version 1.5.1, 2003 [14] Mohamed El-Hadidy, ”Realistic UWB MIMO Channel Model Considering Analogue Aspects and Antennas Effects”, ISBN 9783-925658-10-5, Druck und Verlag: DruckTeam Druckgesellschaft GmbH, Germany, 2009. [15] Gonzlez, O., Ramrez, D., Santamara, I., Garca-Naya, J. and Castedo, L. ”Experimental validation of interference alignment techniques using a multiuser MIMO testbed”, Smart Antennas (WSA), 2011 International ITG Workshop on, pp. 1 8.
