Performance Assessment of MIMO Precoding on Realistic Mmwave Channels
Total Page：16
File Type：pdf, Size：1020Kb
Performance Assessment of MIMO Precoding on Realistic mmWave Channels ∗Mattia Rebato, yLuca Rose, ∗Michele Zorzi ∗Department of Information Engineering, University of Padova, 35131 Padova, Italy yNokia Bell Labs, Paris – Saclay, France frebatoma, [email protected] – [email protected] Abstract—In this paper, the performance of multi-user gNB in order to perform beamforming of information toward Multiple-Input Multiple-Output (MIMO) systems is evaluated in the served UEs. terms of SINR and capacity. We focus on the case of a downlink Many works in the literature focused on the evaluation of single-cell scenario where different precoders have been studied. Among the considered precoders, we range from different Grid precoding techniques for MU mmWave systems with massive of Beams (GoB) optimization approaches to linear precoders MIMO. The closest works to ours are [4]–[7]. In [4], massive (e.g., matched filtering and zero forcing). This performance MIMO was proposed and studied under the ideal condition evaluation includes imperfect channel estimation, and is carried of almost infinite antennas. In [5], precoding techniques such out over two realistic mmWave 5G propagation channels, which as Minimum Mean Square Error (MMSE), Matched Filtering are simulated following either the measurement campaign done by New York University (NYU) or the 3GPP channel model. (MF) and Zero Forcing (ZF) were studied under the assump- Our evaluation allows grasping knowledge on the precoding tion of a Rayleigh channel model and under the condition of performance in mmWave realistic scenarios. The results highlight perfect Channel State Information (CSI) acquisition. In [6], the good performance of GoB optimization approaches when a channel estimation errors were introduced to estimate the realistic channel model with directionality is adopted. implementation loss in terms of precoding gain, whereas in Index Terms—Millimeter-wave, multi-user MIMO, 5G, inter- [7] the authors link the precoding performance with channel ference optimization, linear precoder, grid of beams. correlation. Finally, a recent piece of work [8] uses a realistic I. INTRODUCTION channel model to perform an evaluation of a MU system in terms of bit error rate as a function of the number of The volume of mobile data is continuously increasing, antenna elements used at the transmitter side, while however especially with high capacity applications that are emerging overlooking the effect of different precoding strategies and together with the next generation (i.e., 5G) of cellular commu- channel estimation errors. nications [1]. As an enabler for these capacity-intensive appli- From the literature, it emerges that linear precoding schemes cations, the millimeter wave (mmWave) band (approximately can be used to reach high performance under ideal assump- between 10 and 300 GHz) has been identified as a promising tions. Less known is however their performance when re- candidate for future mobile communications [2]. In addition alistic channel models are considered. To be precise, under to the use of mmWave frequencies, another major aspect of a Rayleigh fading model, it is known that MMSE performs the new mobile generation is the densification of the network appreciably better in terms of balancing the resources among applying small cells in large numbers. Furthermore, Multi- the UEs acting as a trade-off between MF and ZF approaches. User (MU) massive Multiple-Input Multiple-Output (MIMO) However, the Rayleigh fading model oversimplifies the chan- systems became of high interest as they contribute to reaching nel characterization, resulting in a channel model that does not the 5G high demands (e.g., in terms of rates and densities), due reflect the real mmWave propagation specifics. arXiv:1903.11330v1 [cs.IT] 27 Mar 2019 to their ability to greatly increase network capacity [3]. For In 3GPP NR systems, the exploitation of mmWave fre- this reason, it is important to study and evaluate MU massive quency bands (both at 28 GHz and at 60 GHz) for the next MIMO systems over 5G mmWave propagation channels. By generation of mobile communications is currently defined [9]. exploiting such technologies, data transmission rates are ex- Within the standard, different types of CSI feedback mecha- pected to increase in the Radio Access Network (RAN), and nisms have been included to support MIMO transmissions. In a more efficient use of the radio spectrum can be achieved. particular, release 15 includes Type-I and Type-II codebook The purpose of MU MIMO systems is to account for CSI feedback, enabling different trade-offs between CSI res- channel scattering and reflections, thus exploiting the spatial olutions and feedback overhead [10]. More precisely, when a dimension and creating multiple beams of the signal in the Type-I CSI feedback scheme is adopted, the UE feeds back the direction of the User Equipments (UEs), so that each user index of a vector taken from a suitable oversampled DFT code- can benefit from the whole allowed bandwidth at any time book that best approximates the dominant eigenvector of the instant. This can be achieved by precoding the information at channel matrix; conversely, when Type-II CSI is adopted, the the Next Generation Node Base (gNB) side. Using a precoder, feedback is composed of a linear combination of two or more data is distributed on the different antenna elements of the (up to 4 per polarization) vectors taken from the oversampled N×1 N×M angles of departure by C, with C and C being the generalizations to Ω(" vectors and matrices, respectively. The M ×M identity matrix Ω gNB "" - clusters ,-th is written as IM and the zero matrix of size NT ×M is denoted … +( subpaths array NLoS cluster as 0NT×M . Finally, we generally indicate with Xb the Frobenius LoS ray normalized matrix of X. )* antenna elements II. SYSTEM MODEL UE1 We consider a narrowband single-cell downlink multi-user MIMO mmWave system where a single gNB sector with 2 NT transmit antennas is serving M single-antenna UEs. # UE1 ℎ" The channel to the m-th user is assumed narrowband and is N ×1 ℎ# described by the vector of coefficients hm 2 C T , and its $ UE gNB 2 j-th element describes the channel response between the j- # ℎ% th transmitting antenna element and the receive antenna. This UE3 # input-output relationship can be described as ℎ& H UE4 ym = hmx + nm; m 2 f1; 2;:::;Mg (1) where x is the NT ×1 transmitted vector signal, ym 2 C is the Figure 1: Illustration of the mmWave system model considered (bottom) and received signal, and nm is the noise term. Assuming to use representation of the channel model used for each link in the framework (top). PM a precoder, the transmitted vector signal is x = i=1 wisi, where s is the data symbol and w is the N × 1 linear DFT codebook. In this latter case, both the indices of the i i T precoding vector. chosen vectors and the linear combination coefficients are fed Aggregating together the precoding vectors of all the back to gNB. Finally, it is worth observing that the accuracy of M UEs we can define the precoding matrix W = a Type-II CSI feedback scheme is larger, and so is the resulting [w ;:::; w ] 2 NT×M . We note that, in order to respect the overhead [11]. The reason behind such mechanisms is to be 1 M C power constraint kWsk2 = 1, we normalize the precoding found in the attempt to reduce the amount of CSI acquisition E matrix with the Frobenius norm as follows Wc = W . Using overhead while exploiting MIMO advantages, such as spatial kWkF multiplexing and beamforming. Although at the moment full this notation, it is possible to write the system input-output 1 equation as CSI is not included in the standard, ongoing discussions are H attempting to assess the trade-off between precoding gain and y = H Wsc + n (2) overhead cost. where y; s and n are vectors with dimension M × 1, while Differently from the prior art, the objective of this study channel matrix H is defined in CNT ×M . is twofold. First, we aim at evaluating the performance of Finally, we define H¯ (p) as the M × M equivalent matrix diverse precoders when a realistic channel is considered, obtained with the product where “realistic” denotes both the adoption of a channel ¯ (p) H (p) model supported by experimental evidence and the inclusion H = H Wc (3) of CSI imperfections. Second, we compare the aforementioned where superscript p is used to identify the different precoding linear precoders against Grid of Beams (GoB) optimization approaches evaluated as described in the following. approaches, with the goal of assessing the gain of linear precoders overs simpler (and less demanding in term of CSI) A. Channel Models GoB approaches. In our evaluation, MIMO channel vectors h are generated As reported in Figure 1, we consider a scenario with both a according to three distinct statistical channel models. The first realistic sectorization and an antenna array radiation pattern, as model under analysis is a standard Rayleigh fading channel suggested by the 3GPP specifications in [12]. Moreover, two model; the second is derived from a set of extensive measure- measurement-based realistic channel models are considered, ment campaigns in New York City by NYU–Wireless [13]; the one from New York University (NYU) [13] and one from last model considered is the one provided by the 3GPP [14], 3GPP as suggested in [14], both used to evaluate and compare which was obtained from multiple measurement campaigns the performance of different precoders. from different research groups all around the world. For this Notation: In this paper, column vectors and matrices study, we adopt the channel model with the settings of the are respectively denoted by boldface lowercase and uppercase Urban Macro (UMa) scenario.