CQI algorithm design in MIMO systems with maximum likelihood detectors

Abstract

In this paper, we investigate throughput optimization in $2\times 2$ multi-input multi-output (MIMO) systems using channel quality indicator (CQI) based scheduling. Existing MIMO CQI algorithms are mostly designed for sub-optimal linear symbol detectors such as minimum mean square error (MMSE). We consider in this paper how to select CQIs for both streams in order to maximize the total throughput when the non-linear optimal symbol detection technique, maximum likelihood (ML) detector, is employed. Specifically, we formulate a simple yet accurate mathematical model for throughput maximization in a $2\times 2$ MIMO channel using an ML detector. We make use of constellation constrained capacity to characterize the feasible rate region of such MIMO systems. Based on the information-theoretic analysis, a novel CQI algorithm for $2\times 2$ MIMO transmission is proposed. Numerical results indicate that the proposed CQI algorithm yields up to 4% throughput improvement over the CQI algorithm optimized for MMSE detectors in High Speed Downlink Packet Access (HSDPA).

Introduction

The success of 3rd generation wireless cellular networks is mainly based on efficient provisioning of the expected wide variety of services requiring different Quality of Service (QoS) with respect to data rate, delay and error rate. As a promising way of providing higher throughput, multiple antenna transmission techniques with advanced signal processing algorithms have been extensively investigated for over a decade in both academia and industry. Multiple input multiple output (MIMO) technologies, such as spatial multiplexing, transmit diversity, and beamforming, are key components for providing higher peak rate at a better system efficiency, which are essential for supporting future broadband data service over wireless links. As a result, this has led to MIMO technology being standardized in Rel-7 and beyond of the 3rd Generation Partnership Project (3GPP) specifications, including High Speed Downlink Packet Access (HSDPA) and Long Term Evolution (LTE) standards [1], [2].

In modern communication systems, to satisfy the QoS under varying radio channel conditions, radio link adaptation is necessary, which involves channel quality measurement and control. Measurement of the wireless channel quality is usually done at the receiver side. It includes the estimation of certain channel quality measures such as the signal-to-interference-plus-noise ratio (SINR) and the bit-error-rate (BER). The control part of radio link adaptation involves adapting the modulation, coding, or power of the transmitted signal within system constraints based on the results of channel quality measurements. Radio link adaptation at the transmitter is done in response to link adaptation requests to maintain the QoS close to the intended target value. In 3GPP standards [1], [2], the channel quality indicator (CQI) feedback mechanism provides various signaling options to enable the radio link adaptation between a user equipment (UE) and a base-station. For example, in HSDPA, the UE monitors the quality of the downlink wireless channel and periodically reports this information to the base station (referred to here as NodeB) on the uplink. This feedback CQI is an indication of the highest data rate that the UE can reliably receive in the existing conditions on the downlink wireless channel. The frequency of reporting CQI is typically set to once every few milliseconds. It is recommended in [1] that, in static channel conditions, the UE report CQI such that it achieves a block error rate (BLER) 10% when scheduled data corresponding to the median reported CQI. Using the channel quality reports, the NodeB accordingly schedules data on the High Speed Physical Downlink Shared Channel (HS-PDSCH). Specifically, based on its interpretation of the reported CQI, the NodeB selects the transport block size (TBS), i.e. the number of information bits per sub-frame, number of channelization codes, modulation schemes, etc.

For the purpose of efficient signal transmission, a well-designed CQI reporting mechanism should be able to accurately predict link error-rate performance [3], [4]. Adaptive modulation and coding has been considered for link adaptation, in which the symbol modulation order, error-control coding rate, and spatial multiplexing order are optimized to maximize the data rate under error-rate constraints [5], [6]. Link adaptation schemes that take into account channel estimation errors at transmitter side have also been proposed [7], [8], [9]. Machine learning algorithms have recently been applied in effective link adaptation due to their flexibility and ability to capture environmental effects [10], [11], [12]. Various channel quality metrics including exponential effective SNR mapping [13], average effective SNR [14], [15], [16], ordered post-processing SNR [11], mean and variance of post-processing SNR [17], [18], and minimum post-processing SNR [19], have been proposed to measure wireless link qualities.

The CQI algorithm design for MIMO systems is much more challenging than the single-input single-output (SISO) case, because the throughput performance in MIMO is governed by multiple factors, including the employed detection technique, e.g. MMSE or maximum likelihood (ML) detector, and the decoding technique, e.g. one-shot decoding, successive interference cancellation (SIC), or iterative decoding. It is critical to have a simple link error probability predictor that takes into account these factors to model MIMO system performance. For linear detection algorithms, such as MMSE detector, we can usually derive the closed-form expressions of the post-detection SINR, which greatly simplifies the CQI algorithm design [20], [21]. CQI algorithm design for non-linear detection techniques is not so straightforward. Non-linear detection techniques, such as ML detection, are desirable to achieve near-optimal performance in MIMO channels. In practical MIMO coded systems, there have been some efforts for the development of MIMO ML soft demodulators to calculate the likelihood of each bit. Brute-force exhaustive search method and soft versions of the sphere decoder have been developed to compute bit log-likelihood ratios (LLR)[22], [23], [24], [25], [26]. However, no simple rule was known to determine the optimal size of the candidate list used by sphere decoder. A novel Layered Orthogonal Lattice Detector (LORD) detection algorithm that adopts a new lattice formulation and relies on a channel orthogonalization process was proposed in [27]. For two transmit antennas LORD can be generate max-log bit soft-output information and for greater than two antennas LORD can achieve approximate max-log detection. These ML detectors generally involve an exhaustive search over all the possible sequences of transmitted symbols. The nonlinear operations make it hard to predict the post-detection SINR for individual input streams. Moreover, applying CQI algorithms that are designed for linear receivers to non-linear detectors is sub-optimal. As a result, the CQI algorithm design for non-linear MIMO detectors is very challenging and few theoretical results about SNR estimation for ML decoded spatial multiplexing exist in the literature[28], [29].

This paper investigates the problem of choosing a CQI for individual streams in a 2×2 MIMO system using an optimal ML detector, where the goal is to maximize the total throughput when data is scheduled based on the CQI chosen. The main contributions of this paper are two-fold. First, we derive a simple step function model for the feasible rate region of the ML detector based on the observation that the BLER on one MIMO stream for the ML detector is sensitive only to the interfering stream’s modulation scheme, and is insensitive to the interfering stream’s TBS. Second, we connect the information–theoretic notion of constellation constrained capacity for discrete constellations with the manner in which the non-linear ML detector exploits the discrete nature of the interference, and use this connection to derive a semi-analytical approach to calculating the vertices of the rate region. This approach eliminates the need to perform computationally expensive two-dimensional Monte Carlo integrations. Having determined the rate region, it is easy to find the vertex of the rate region that maximizes throughput. This CQI algorithm requires relatively few additional computations over a CQI algorithm designed for linear detectors. It is also readily applicable to scenarios in which SIC is employed.

For ease of presentation, this paper discusses the CQI algorithm design in MIMO HSDPA as a concrete example. As a matter of fact, the same methodology is by no means restricted to HSDPA and it applies to LTE and other MIMO systems as well. The rest of this paper is organized as follows. Section 2 describes the system model of MIMO HSDPA and introduces the CQI-based throughput maximization problem. Based on three important observations obtained in numerical simulations, Section 3 presents a simple yet accurate mathematical model to simplify the CQI-based throughput maximization. In the same section, we also propose a constellation constrained capacity based approach to estimate the key parameters of the simplified model and solve the overall throughput maximization. Section 4 addresses how to extend the proposed algorithm when the SIC decoding technique is deployed or when higher order MIMO channels are used or when information about modulation switching points in the TBS domain is not available. Simulation results are provided in Section 5 and conclusions are drawn in Section 6.