MIMO Geometry and Antenna Design for High Capacity and Improved Coverage in mm-Wave Systems

Hindawi Publishing Corporation International Journal of Antennas and Propagation Volume 2013, Article ID 572830, 9 pages http://dx.doi.org/10.1155/2013/572830 Research Article MIMO Geometry and Antenna Design for High Capacity and Improved Coverage in mm-Wave Systems Tommaso Cella,1 Pål Orten,2 and Jens Hjelmstad3 1 NTNU and UniK, 7491 Trondheim, Norway ABB and UniK, 1396 Billingstad, Norway 3 NTNU, 7491 Trondheim, Norway 2 Correspondence should be addressed to Tommaso Cella; Received 28 February 2013; Accepted 11 September 2013 Academic Editor: Yuan Yao Copyright © 2013 Tommaso Cella et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We show a way to optimize the capacity and at the same time achieve high coverage in LOS for a mm-wave system indoor. We optimize MIMO with regard to maximum Shannon capacity for a pure LOS channel. We describe the general procedure in order to maximize the capacity for our considered geometry, which consists of a circular arc array at the transmitter and a uniform linear array (ULA) at the receiver. The method is based on the optimization of the interelement distances at the transmitter and the receiver. High coverage is obtained with the use of the circular geometry and beamforming. We propose an example mm-wave system in the 70 GHz portion of the E-band (71–76) GHz. The results show that the proposed system is able to achieve full coverage in LOS as well as high capacity, with practical dimensions. 1. Introduction During the last years, there has been an increased interest in mm-wave communications. The demand for fast data rate had a crucial role, and communication systems in the mm-wave bands have been intensively investigated [1, 2]. Although mm-wave extends from 30 GHz to 300 GHz, with a resultant wavelength from 10 mm to 1 mm, we commonly refer to fewer bandwidths, which include the V-band (57– 66 GHz), the E-band (71–76 GHz and 81–86 GHz), and the W-band (92–95 GHz). Millimeter-wave wireless technologies provide higher data rates which are comparable to that of fiber optics but are less costly and easy to set up. The propagation characteristics at those frequencies are different compared to the lower ones, both in indoor and outdoor environments. While outdoor, the main sources of attenuation are due to atmospheric oxygen, humidity, fog, and rain [3]; indoor the signal experiences very high wall attenuation. In previous studies, in fact, it was shown that communications at mmwave bands are mainly LOS [4, 5]. This is due not only to high attenuation, but also typically narrow antenna beams. A well-known method to improve the system capacity is the use of MIMO [2]. With the use of MIMO, communication links take advantage of multiplexing gain, because different information streams are sent from different transmitters towards different receivers at the same frequency. In order to get spatial multiplexing at lower frequencies, rich multipath is needed. The main advantage of using MIMO at mmwave bands is that by having a proper interelement spacing between transmitting and receiving antennas, multiple streams, and thus high capacity, can be obtained, even in LOS [6]. The capacity of LOS MIMO channels has been studied by several authors [7, 8]. Different prototypes using mm-wave LOS MIMO were already developed [9, 10]. Indoor MIMO channels at 5 GHz and 60 GHz were modeled and compared [11, 12]. A further advantage of mm-wave MIMO systems at those bandwidths is that highly directive transmission and reception with electronically steerable beams can be achieved, using compact antenna arrays. Beamforming is then another practical way to improve the performance. Our work is focused on guaranteeing two important requirements for mm-wave wireless communications: provide high capacity and full LOS coverage, and we consider an indoor scenario. As mentioned before, a way to maximize 2 International Journal of Antennas and Propagation the capacity in MIMO systems is to adjust the interelement distances at the transmitter and the receiver. A closed-form expression for the geometry maximizing capacity was found for the case of two uniform linear arrays (ULAs) in [6]. We consider a slightly different geometry, where the transmitter is a circular arc array, while the receiver is a ULA [13]. The rationale for this geometry will be explained later. An expression describing the geometry which maximizes the capacity in this case is derived in Section 3 of this paper. Applying this configuration, together with the use of beamforming, makes it possible for the receiver to be reached everywhere in LOS indoor. This would not be possible for the case of two ULAs, as will be described later in the paper. In our proposal, each MIMO element at the transmitter is itself a subarray, which can electronically scan the beam towards the receiver. The transmitter can then be considered an array of subarrays, in which each subarray represents an element of the MIMO system. The concept of array of subarrays was already investigated considering outdoor mm-wave links [14]. The rest of the paper is organized as follows: in Section 2 the capacity of MIMO systems is described; Section 3 is dedicated to the MIMO channel model and will focus on the geometry we introduce. In Section 4, an example mm-wave system is presented, while simulation results are shown in Section 5. Finally, the paper is concluded. 2. Capacity of MIMO Systems A MIMO transmission system employs a number of transmit and receive antennas to transmit data over a channel. We denote the number of transmit antennas by 𝑁 and the number of receive antennas by 𝑀. Assuming slowly varying and frequency flat fading channels, we can model the MIMO transmission in complex baseband as [15] r = Hs + n, (1) where r is the 𝑀 × 1 received complex-valuated signal vector, s is the 𝑁 × 1 transmitted complex-valued signal vector, H is the 𝑀 × 𝑁 complex-valued channel matrix, and n is the 𝑀 × 1 complex-valued additive white Gaussian noise (AWGN) vector. The additive noise vector contains i.i.d. circularly symmetric complex Gaussian elements with zero mean and variance 𝜎𝑛2 , denoted CN(0, 𝜎𝑛2 ). We denote the covariance matrix of the transmitted signal by Q = 𝐸[ss𝐻]. In practical systems, we usually need to fulfill an average transmit power constraint over the array. If the total average transmit power is limited to 𝑃𝑇 , then trace (Q) ⩽ 𝑃𝑇 must be fulfilled. In the remainder of this paper, we will look at uncorrelated branch sources with equal power; that is, Q = (𝑃𝑇 /𝑁)I𝑁. This is optimal with regard to capacity when H is unknown at the transmitter [2]. When such sources are used, the channel capacity of a MIMO system described by (1) becomes [6] 𝐶 = log2 [det (I𝑀 + 𝑃𝑇 HH𝐻)] bits/s/Hz, 𝑁𝜎𝑛2 where H𝐻 is the Hermitian transpose of the H matrix. ( (...truncated)