Strong LOS MIMO for Short Range MmWave Communication

Transcription

1 Strong LOS MIMO for Short Range MmWave Communication Towards 1 Tbps Wireless Data Bus Xiaohang Song, Lukas Landau, Johannes Israel, and Gerhard Fettweis Vodafone Chair Mobile Communications Systems, Technische Universität Dresden, Dresden, Germany Institute of Numerical Mathematics, Technische Universität Dresden, Dresden, Germany {xiaohang.song, lukas.landau, johannes.israel, fettweis}@tu-dresden.de Abstract In this paper, we propose a wireless data bus system design which relies on a strong Line-of-Sight MIMO approach. An analog MIMO equalizer, which equalizes the deterministic MIMO channel is involved. Instead of interference suppression, the analog MIMO equalizer aligns the phases of the received signals and enhances the desired signal while it suppresses the undesired ones simultaneously. Although the magnitudes of different signal components of the received signals are preferred to be unique, further studies are applied in our work to investigate the validation of our system design with non-unique magnitudes by using practical on-board antennas. It is shown that the proposed system works well with non-unique magnitudes where undesired remaining interference occurs with limited power in comparison with the desired ones. Furthermore, the proposed design shows a great potential for putting a 1 Tbps wireless data bus into practical systems with moderate transmit power and fairly simple modulation schemes which provide high energy efficiency. I. INTRODUCTION The previous works [1] and [] showed that beamforming as well as beam switching can be utilized for setting up communication links between computing nodes that are facing each other. However, in order to provide high enough spatial resolution such that independent wireless channels can be set up for every pair of the boards, very large arrays have to be utilized for generating pencil beams. In our approach, independent parallel SISO channels can be generated via a switching network and an analog network. Due to the fact that the channel in board-to-board communication is deterministic and can be modeled as a strong Line-of-Sight (LoS) channel especially for short range communications. Our new approach considers the optimal antenna arrangement that maximizes the spatial multiplexing gain as shown by works in [3], [4], [5], [6]. For higher frequencies at millimeter waves, the size of the proposed arrays is more compact as compared to designs based on lower frequencies and can be easier embedded on board. Instead of strict parallel boards, the full spatial multiplexing can also be achieved with arrangements on any arbitrary This work has been supported by the German Research Foundation in the framework of the Collaborative Research Center 91 Highly Adaptive Energy-Efficient Computing and in the framework of priority program SPP 1655 Wireless Ultra High Data Rate Communication for Mobile Internet Access. Fig. 1: Illustration of the wireless board to board communication with strong LOS MIMO channel. Shown are two computing board with 16 computing nodes each (black). The beams from all transmit antennas (orange) cover the complete receive array. It is aimed to have aligned interference such that a full spatial multiplexing on the links can be achieved. rotated non-parallel planes as indicated by [6], [7], [8], and [9]. In MIMO channels, the transmitted signals are superposed at the receiver side. However, post processing can be applied for parallelization or equalization of the transmitted signals. Works in [1], [11] have shown that analog components like delay lines or phase shifters are capable to create an analog equalizing network that mixes received copies from different antennas and reconstructs the transmitted signals correspondingly. Due to the fact that the sub-channels are deterministic channels, the equalizing networks aiming at creating independent parallel channels have not to be adaptive. By transmitting the signal over the corresponding channel with assistance from a switch network, the computing nodes on the transmitter side can communicate with their targeting receiver as desired. In /15/$ IEEE

2 case all computing nodes on one board are transmitting to computing nodes on the neighboring board without overlapping of the intended pairs, a full MIMO utilization of strong LoS MIMO channel can be expected. Furthermore, instead of minimizing the undesired interference with pencil beams, received signals with similar magnitudes of their components can be aligned and the undesired interference can cancel each other. Then, the superposed signal can have better SNR and suppresses the interference. Hence, the requirements on the antenna element design, the beamforming capabilities as well as the Butler matrix network can be reduced. II. OPTIMAL LOS MIMOARRAY DESIGN Our previous work [1] has validated the channel model as strong LoS as the power of the second largest channel impulse response is 15 db less than the direct path. Considering a transmit array (T A ) and a receive array (R A ) with N antenna elements on both sides, the received signal in a frequency flat strong LoS MIMO channel is modeled as y = ρ(d) H s + n, (1) where s C N 1 is the transmitted signal with unique transmit power P T at every transmit antenna, i.e., E( s k ) P T for k {1,...,N}. Here, we did not follow the approach from E. Telatar [1] that transmit power is shared by the complete array as in practical systems. Instead of that, the transmit power at every transmit antenna is similar even if the antenna number increases. The vector n denotes the white complex Gaussian noise in base-band with n CN(,σ ni N ).The magnitude attenuation factor that varies with respect to the transmit distance D lk between k-th transmit antenna and l- th received antenna is denoted as ρ(d lk ). As discussed in detail in [13], the attenuation differences on sub-channels can be neglected if the antenna size is much smaller than the transmit distance. For simplicity, we also neglect the differences between the attenuation factors on sub-channels with approximation ρ(d lk ) ρ(d), whered is the common distance between the transmit and receive arrays. By H C N N we denote the phase coupling matrix in the strong LoS MIMO channel with entities h lk e j π λ (D lk D). () As indicated by [4], [7], [8], and [14], the optimal antenna arrangements are mainly influenced by the carrier wavelength λ, the number of antenna elements N, and the transmit distance D. With high carrier frequency and short distance, the optimal design has the potential for developing ultra-high speed board-to-board communication systems with reasonable antenna sizes. For the parallel uniform linear array (ULA) with N antennas, the optimal antenna spacings d t and d r between antennas at transmitter and receiver side given in [7], [8] satisfy d t d r = λd N. (3) Meanwhile, d t,v, d r,v, d t,h,andd r,h for horizontal and vertical directions of the parallel uniform rectangular array (URA) given in [14] satisfy d t,v d r,v = λd N v, d t,h d r,h = λd N h, (4) where the transceivers consist of N = N v N h antennas. According to Equation (4), for a 4 4 MIMO system (N = N v N h = =4) with symmetric transceivers at high carrier frequencies of 18 GHz and a transmit distance of 1 centimeters, the optimal antenna spacing is given by 9 mm. For simplicity, the system design that is presented in the later sections is based on parallel URA design. However, the system can be adjusted easily via changing the analog equalizing network when non-parallel transceiver boards are considered. In the latter sections, we investigate fully orthogonal subchannels H between each antenna pair. With ideal optimal antenna arrangement, the vectors of the phase coupling matrix H are orthogonal to each other with HH = N I N, (5) where ( ) denotes the Hermitian transpose operator. However, the validation of this orthogonality is based on an assumption that the pathloss values ρ(d lk ) on different sub-channels including antenna gains are unique, i.e., ρ(d lk )=ρ(d) for all l, k {1,...,N} and the transmitted signals are expected to arrive with equal magnitudes. This requires that antenna gains in the direction of corresponding elements should be unique or approximately equal. Therefore, a practical system should be very compact to assure that the geometric and magnitude assumptions hold. For a given number of antennas N, the number of antennas in the horizontal and vertical directions N h, N v of the most compact design follows arg min (N v N h ) s.t. N = N v N h. (6) N v N h This array design considers that the uniform rectangular arrays provide less angle spread on the antenna pattern of the elements on the other side compared to ULAs with the same number of antennas, thus being more compact with respect to the antenna aperture. III. OPTIMAL LOS MIMOSYSTEM DESIGN A. Analog Signal Equalization The proposed system is sketched in Fig.. The switch network can schedule the transmitted signal from m-th computing node from transmitter side (Tx m) tok-th transmit antenna (T A k) in case a communication channel is demanded from Tx m to l-th receiver (Rx l). The switcher can be modeled as a permutation matrix. In this paper, the work is focusing on the maximum transmission rate that can be provided between two boards. Hence, we focus on the analog signal equalization and capacity of the MIMO channel after the switch network. As a LoS MIMO channel is involved in the system, the received signal y l at the l-th antenna of the received antenna

3 Tx-1 Tx- Tx-M Switcher TA-1 TA- TA-N RA-1 RA- RA-N j e e j e j N Rx-1 Rx- Rx-N Fig. : System model. array is a superposition of all transmitted signals that is modeled as y l = ρ(d) h T l s + n l, (7) where h T l =[h l1 h l... h ln ] is the l-th row of H and n l is the white complex Gaussian noise with n l CN(,σn). However, due to the fact that the LoS MIMO channel can be independent sub-channels with a fixed decoupling matrix, the communication system can be employed as parallel SISO channels. Instead of the traditional approach of having the signal processed in digital band which requires high quantization resolution, we propose to utilize an analog equalizing network W that can decouple the LoS MIMO matrix in pass-band. The analog equalizing network can be realized via introducing different delays or fixed phase shifts to the different received signals at different Rx antennas and reconstruct new signals y W at the end of the RF chain. We consider that the equalizing network W is modeled with a fixed realization W = H.The l-th row and k-th column entry W lk of W is suggested to be modeled as a delay line or a phase shifter with W lk = h kl. As described above the equalized signal y W is formulated as y W = W y = N ρ(d) s + H } {{ n }, (8) where ñ CN(,Nσ n I N ) is the equivalent Gaussian noise. Note that the analog equalizing network design is based on the Hermitian matrix of the phase coupling matrix. B. Link Budget When assuming equal power transmission and constant radiated power from each antenna element, the channel capacity of the MIMO transmission given by [15], [1] can be formulated as [ C = W log det HH ] ñ I N + ρ(d) P T σ n ( = N W log 1+ ρ(d) P T σn N ), (9) where W is the allocated bandwidth. The noise variance σ n consists of noise figure P nf and thermal noise P th.thethermal noise P th in terms of dbm satisfies P th [dbm] 1 log 1 (1 k B T W ), (1) where k B is the Boltzman constant (k B = J/K) andt is the absolute temperature in Kelvin. The power attenuation factor P L (D) =ρ(d) in a strong LoS wireless channel can be formulated in [db] as P L (D)[dB] G TA [dbi] P TA FE [db] P fs(d)[db] + G RA [dbi] P RA FE [db], (11) where the P fs (D), G TA, G RA, P Tx Rx FE,andPFE are the free space path loss, antenna gain of the T x and R x, and the front end loss of T x and R x, respectively. The free space path loss P fs is modeled as ( ) np 4πD P fs (D), (1) λ where n p is the pathloss exponent. IV. NUMERICAL RESULTS In this section, the capacity of a practical wireless communication MIMO channel between two boards is evaluated numerically. As an example, we consider an LoS MIMO system consisting of 16 antennas on each side with N v = N h =4 at a transmit distance of.1 meter. As suggested by [16], the pathloss exponent n p should be and this result is confirmed for short range board-to-board communication by our earlier work [1] in detail. We design the system with a bandwidth of W =3GHzand assume that the carrier frequency for boardto-board wireless communication is 18 GHz. The absolute temperature and the noise figure are considered as T = 93K and P nf =1dB, respectively. In our system design, we assume that the transmit signal arrives at different receiver antenna elements with equal magnitude. However, for practical systems the antenna patterns are anisotropic. The spreading angle is less than 16 on the azimuth angle. Therefore, the main lobe of the radiated pattern is recommended to have a beam width larger than 16. An integrated stacked Vivaldi-Shaped on-chip antenna was designed at 18 GHz in [17]. The taped-out antenna has an antenna pattern with gain of 9. dbi in the main direction

4 z.5 k -th antenna y x 9 β x-z -plane (β = ) 9 β y -z -plane (β = 9 ) Channel Capacity [Tbps] GTA [dbi] N = 4, Unconstrained N = 16, QPSK N = 4, QPSK N = 9, Unconstrained N = 1, Unconstrained N = 9, QPSK N = 1, QPSK Fig. 3: Radiation Pattern of an integrated stacked Vivaldi-Shaped N = 16, Unconstrained 5 On-Chip antenna at 18 GHz [17]; and β are the elevation and azimuth angles of the antenna radiation pattern PT [dbm] 5 Fig. 4: Link Budget for strong LOS board-to-board MIMO communication with unique antenna gain. and 7.8dB feeding loss. The half power beam width is 75 in the x-z-plane and 61 in the y-z-plane, as displayed in Fig. 3. Channel Capacity [Tbps] Due to the fact that the received copies at different subchannels are preferred to have unique magnitudes as explained before, we first neglect the difference of the antenna gain on different directions. Fig. 4 illustrates the channel capacity of the proposed system with unique antenna gains on different subchannels as 9 dbi. It can be seen that for a given amount of transmit power at every transmit antenna, the capacity increases faster than linear with respect to the number of antennas. This is because more energy is received at the receiver side. Meanwhile, the numerical evaluation shows a great potential that the antenna array with N = 9 or higher number of elements provides the possibility to achieve more than 1 Tbps for wireless board-to-board communication as shown by the capacities with unconstrained input and power less than dbm. However, especially when considering Multigigabit per second communication for short distance, the power amplifier is no longer the dominant building block w.r.t. total power consumption of the link. In order to design energy-efficient interconnects one approach is to consider only moderate resolution at the analog-to-digital and digital-toanalog converters. As a consequence the transmit symbol alphabet is constrained according to the capabilities of the converters. To this end, also an example to constrained input is provided in Fig. 4, namely the capacities with QPSK input. In this regard, it has been shown that the capacity with N = 16 antennas and QPSK input is capable to achieve.96 Tbps between two boards (6 Gbps between each transceiver pair) with about 5 dbm transmit power. Indeed, the achievable rate might be further increased with low-resolution quantizers by considering advanced sequence designs which are matched to energy-efficient 1-bit quantization at oversampling rate such as [18] and [19]. This is an interesting topic to be further investigated as the analog MIMO equalizers can significantly reduce the required complexity on the quantizer. Fig. 5 illustrates the channel capacity of the proposed.5 N = 16, Unconstrained N = 4, Unconstrained N = 16, QPSK N = 4, QPSK N = 9, Unconstrained N = 1, Unconstrained N = 9, QPSK N = 1, QPSK PT [dbm] 5 Fig. 5: Link Budget for strong LOS board-to-board MIMO communication with integrated stacked Vivaldi-Shaped On-Chip antennas at 18 GHz [17]. The light colored lines are the results from Fig. 4 with unique antenna gain. system in a more realistic system with element gains as shown in Fig. 3. It can be seen that the channel capacities for anisotropic antenna elements are slightly smaller than channel capacities with unique antenna gains. However, the proposed channel model is a good approximation to the realistic channel with anisotropic antenna patterns. V. C ONCLUSIONS The proposed new computer design relies on wireless interconnects based on the so called Line-of-Sight MIMO approach. Instead of interference suppression which comes with the burden of large antenna arrays and lossy feeding networks, the proposed approach exploits the interference in terms of analog equalization. By considering real antenna measurement data of a 18GHz Vivaldi antenna and optimal

5 antenna positioning it has been shown that the corresponding channel is nearly unitary which allows for delay based equalization in analog domain. This enables full spatial multiplexing gains which can be utilized in a flexible fashion like parallel energy-efficient independent SISO channels. The numerical evaluation shows that 1 Tbps and above can be achieved at moderate transmit power which obviates the need for power amplifiers. ACKNOWLEDGMENT The authors would like to thank Ronny Hahnel and Michael Jenning for the valuable input regarding the antenna design. Furthermore, the authors would like to thank Eduard Jorswieck who initialized the study during a discussion. REFERENCES [1] G. P. Fettweis, N. ul Hassan, L. Landau, and E. Fischer, Wireless Interconnect for Board and Chip Level, in Proceedings of the Conference on Design, Automation & Test in Europe, 13, (invited). [] J. Israel, A. Fischer, J. Martinovic, M. Jenning, and L. Landau, Optimal Antenna Positioning for Wireless Board-to-Board Communication Using a Butler Matrix Beamforming Network, in Proceedings of the International ITG Workshop on Smart Antennas, 13. [3] F. Bohagen, P. Orten, and G. Oien, Design of Optimal High-Rank Lineof-Sight MIMO Channels, IEEE Transactions on Wireless Communications, vol. 6, no. 4, pp , 7. [4] P. Larsson, Lattice Array Receiver and Sender for Spatially Orthonormal MIMO Communication, in IEEE 61st Vehicular Technology Conference, vol. 1, May 5, pp [5] F. Bohagen, P. Orten, and G. Oien, Construction and Capacity Analysis of High-rank Line-of-sight MIMO Channels, in IEEE Wireless Communications and Networking Conference, vol. 1, March 5, pp [6], Optimal Design of Uniform Planar Antenna Arrays for Strong Line-of-Sight MIMO Channels, in IEEE 7th Workshop on Signal Advances in Wireless Communications, July 6, pp [7] D. Gesbert, H. Bolcskei, D. GORE, and A. Paulraj, Outdoor MIMO Wireless Channels: Models and Performance Prediction, IEEE Transactions on Communications, vol. 5, no. 1, pp , Dec. [8] T. Haustein and U. Kruger, Smart Geometrical Antenna Design Exploiting the LOS Component to Enhance a MIMO System Based on Rayleigh-fading in Indoor Scenarios, in 14th IEEE Proceedings on Personal, Indoor and Mobile Radio Communications, vol., Sept 3, pp [9] X. Song and G. Fettweis, On Spatial Multiplexing of Strong Line-of- Sight MIMO with 3D Antenna Arrangements, IEEE Wireless Communications Letters, 15, accepted and preliminary version can be found at IEEE Xplore Digital Library. [1] C. Sheldon, E. Torkildson, M. Seo, C. Yue, U. Madhow, and M. Rodwell, A 6GHz Line-of-sight x MIMO Link Operating at 1.Gbps, in IEEE Antennas and Propagation Society International Symposium, July 8, pp [11] C. Sheldon, M. Seo, E. Torkildson, M. Rodwell, and U. Madhow, Fourchannel Spatial Multiplexing Over a Millimeter-wave Line-of-sight Link, in IEEE MTT-S International Microwave Symposium Digest,, June 9, pp [1] E. Telatar, Capacity of Multi-antenna Gaussian Channels, European Transactions on Telecommunications, vol. 1, no. 6, pp , [13] X. Song, C. Jans, L. Landau, D. Cvetkovski, and G. Fettweis, 6GHz LOS MIMO Backhaul Design Combining Spatial Multiplexing and Beamforming for a 1Gbps Throughput, in IEEE Global Communications Conference (GLOBECOM), Dec 15, to appear. [14] X. C. Chunhui Zhou, M. Z. Xiujun Zhang, Shidong Zhou, and J. Wang, Antenna Array Design for LOS-MIMO and Gigabit Ethernet Switch- Based Gbps Radio System, International Journal of Antennas and Propagation, 1. [15] G. J. Foschini, Layered Space-time Architecture for Wireless Communication in a Fading Environment when Using Multi-element Antennas, Bell Labs Technical Journal, vol. 1, no., pp , [16] H. Friis, A Note on a Simple Transmission Formula, Proc. IRE, vol. 34, p. 54, [17] R. Hahnel, B. Klein, and D. Plettemeier, Integrated Stacked Vivaldishaped On-Chip Antenna for 18 GHz, in 15 IEEE Antennas and Propagation Society International Symposium (APS/URSI), 15. [18] L. Landau and G. P. Fettweis, On Reconstructable ASK-sequences for Receivers Employing 1-bit Quantization and Oversampling, in Proceedings of the IEEE International Conference on Ultra-Wideband, 14. [19], Communications Employing 1-Bit Quantization and Oversampling at the Receiver: Faster-than-Nyquist Signaling and Sequence Design, in a submission to IEEE International Conference on Ubiquitous Wireless Broadband, Workshop on Broadband Wireless Communication between Computer Boards (Atto-Nets), 15.