Delay-Doppler Domain Tomlinson-Harashima Precoding for OTFS-based Downlink MU-MIMO Transmissions: Linear Complexity Implementation and Scaling Law Analysis
Shuangyang Li, Jinhong Yuan, Paul Fitzpatrick, Taka Sakurai, Giuseppe Caire
Orthogonal time frequency space (OTFS) modulation is a recently proposed delay-Doppler (DD) domain communication scheme, which has shown promising performance in general wireless communications, especially over high-mobility channels. In this paper, we investigate DD domain Tomlinson-Harashima precoding (THP) for downlink multiuser multiple-input and multiple-output OTFS (MU-MIMO-OTFS) transmissions. Instead of directly applying THP based on the huge equivalent channel matrix, we propose a simple implementation of THP that does not require any matrix decomposition or inversion. Such a simple implementation is enabled by the DD domain channel property, i.e., different resolvable paths do not share the same delay and Doppler shifts, which makes it possible to pre-cancel all the DD domain interference in a symbol-by-symbol manner. We also study the achievable rate performance for the proposed scheme by leveraging the information-theoretical equivalent models. In particular, we show that the proposed scheme can achieve a near optimal performance in the high signal-to-noise ratio (SNR) regime. More importantly, scaling laws for achievable rates with respect to number of antennas and users are derived, which indicate that the achievable rate increases logarithmically with the number of antennas and linearly with the number of users. Our numerical results align well with our findings and also demonstrate a significant improvement compared to existing MU-MIMO schemes on OTFS and orthogonal frequency-division multiplexing (OFDM).
In this work, we investigate the performance of Rate-Splitting (RS) based on Tomlinson-Harashima Precoding (THP) in a multiple-antenna broadcast channel with perfect and imperfect Channel State Information at the Transmitter (CSIT). In particular, we consider RS using centralized and decentralized THP structures, where only one user splits its message into a common and private part, and develop expressions to describe the signal-to-interference-plus-noise (SINR) ratio and the sum rates associated with these schemes. Furthermore, we also assess the performance achieved by RS combined with Dirty…
In this paper, we propose successive optimization non-linear precoding strategies for physical-layer security in wireless networks. We also investigate different precoding techniques for multi-user MIMO systems under various conditions of channel state information (CSI) between the access point and the users and the eavesdroppers. A non-linear precoding technique based on Successive Optimization Tomlinson-Harashima Precoding (SO-THP) and Simplified Generalized Matrix Inversion (S-GMI) technique is proposed along with a strategy for injecting artificial noise prior to transmission. Simulation r…
Rate splitting (RS) has emerged as a valuable technology for wireless communications systems due to its capability to deal with uncertainties in the channel state information at the transmitter (CSIT). RS with linear and non-linear precoders, such as the Tomlinson-Harashima (THP) precoder, have been explored in the downlink (DL) of multiuser multi antenna systems. In this work, we propose a multi-branch (MB) scheme for a RS-based multiple-antenna system, which creates patterns to order the transmitted symbols and enhances the overall sum rate performance compared to existing approaches. Closed…
Tomlinson-Harashima precoding (THP) is considered as a prominent precoding scheme due to its capability to efficiently cancel out the known interference at the transmitter side. Therefore, the information rates achieved by THP are superior to those achieved by conventional linear precoding schemes. In this paper, a new lower bound on the achievable information rate for the regularized THP scheme under additive white Gaussian noise (AWGN) channel with multiuser interference is derived. Analytical results show that the lower bound derived in this paper is tighter than the original lower bound pa…
This paper studies the sum rate performance of a low complexity quantized CSI-based Tomlinson-Harashima (TH) precoding scheme for downlink multiuser MIMO tansmission, employing greedy user selection. The asymptotic distribution of the output signal to interference plus noise ratio of each selected user and the asymptotic sum rate as the number of users K grows large are derived by using extreme value theory. For fixed finite signal to noise ratios and a finite number of transmit antennas $n_T$, we prove that as K grows large, the proposed approach can achieve the optimal sum rate scaling of th…
This paper introduces multiuser multiple-input multiple-output (MU-MIMO) architectures based on non-linear precoding and stream combining techniques using rate-splitting (RS), where the transmitter often has only partial knowledge of the channel state information (CSI). In contrast to existing works, we consider deployments where the receivers may be equipped with multiple antennas. This allows us to employ linear combining techniques based on the Min-Max, the maximum ratio and the minimum mean-square error criteria along with Tomlinson-Harashima precoders (THP) for RS-based MU-MIMO systems to…
Tomlinson-Harashima precoding (THP) is a nonlinear processing technique employed at the transmit side to implement the concept of dirty paper coding (DPC). The perform of THP, however, is restricted by the dimensionality constraint that the number of transmit antennas has to be greater or equal to the total number of receive antennas. In this paper, we propose an iterative coordinate THP algorithm for the scenarios in which the total number of receive antennas is larger than the number of transmit antennas. The proposed algorithm is implemented on two types of THP structures, the decentralized…
In this paper, robust transceiver design with Tomlinson-Harashima precoding (THP) for multi-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) relaying systems is investigated. At source node, THP is adopted to mitigate the spatial intersymbol interference. However, due to its nonlinear nature, THP is very sensitive to channel estimation errors. In order to reduce the effects of channel estimation errors, a joint Bayesian robust design of THP at source, linear forwarding matrices at relays and linear equalizer at destination is proposed. With novel applications of elegant chara…
We consider joint transceiver design for general Multiple-Input Multiple-Output communication systems that implement interference (pre-)subtraction, such as those based on Decision Feedback Equalization (DFE) or Tomlinson-Harashima precoding (THP). We develop a unified framework for joint transceiver design by considering design criteria that are expressed as functions of the Mean Square Error (MSE) of the individual data streams. By deriving two inequalities that involve the logarithms of the individual MSEs, we obtain optimal designs for two classes of communication objectives, namely those …
In this paper, we propose novel non-linear precoders for the downlink of a multi-user MIMO system with the existence of multiple eavesdroppers. The proposed non-linear precoders are designed to improve the physical-layer secrecy rate. Specifically, we combine the non-linear successive optimization Tomlinson-Harashima precoding (SO-THP) with generalized matrix inversion (GMI) technique to maximize the physical-layer secrecy rate. For the purpose of comparison, we examine different traditional precoders with the proposed algorithm in terms of secrecy rate as well as BER performance. We also inve…
In this paper, Tomlinson-Harashima Precoding (THP) is considered for multi-user multiple-input single-output (MU-MISO) non-orthogonal multiple access (NOMA) donwlink. Under the hierarchical structure in which multiple clusters each with two users are formed and served in the spatial domain and users in each cluster are served in the power domain, THP is applied to eliminate the inter-cluster interference (ICI) to the strong users and enlarge the dimension of the beam design space for mitigation of ICI to weak users as compared to conventional zero-forcing (ZF) inter-cluster beamforming. With t…
This paper considers the implementation of Tomlinson-Harashima (TH) precoding for multiuser MIMO systems based on quantized channel state information (CSI) at the transmitter side. Compared with the results in [1], our scheme applies to more general system setting where the number of users in the system can be less than or equal to the number of transmit antennas. We also study the achievable average sum rate of the proposed quantized CSI-based TH precoding scheme. The expressions of the upper bounds on both the average sum rate of the systems with quantized CSI and the mean loss in average su…
Tomlinson-Harashima precoding (THP) is a nonlinear processing technique employed at the transmit side and is a dual to the successive interference cancelation (SIC) detection at the receive side. Like SIC detection, the performance of THP strongly depends on the ordering of the precoded symbols. The optimal ordering algorithm, however, is impractical for multiuser MIMO (MU-MIMO) systems with multiple receive antennas due to the fact that the users are geographically distributed. In this paper, we propose a multi-branch THP (MB-THP) scheme and algorithms that employ multiple transmit processing…
In this paper, we propose a novel low-complexity hybrid linear/Tomlinson-Harashima precoder (H-L-THP) for downlink large-scale multiuser multiple-input multiple-output (MU-MIMO) systems. The proposed precoder comprises an inner linear precoder which utilizes only the second order statistics of the channel state information (CSI) and outer THPs which use the instantaneous overall CSI of the cascade of the actual channel and the inner precoder. The user terminals are divided into groups, where for each group a THP successively mitigates the intra-group interference, whereas the inter-group inter…
This paper proposes the design of robust transceivers with Tomlinson-Harashima precoding (THP) for multiple-input multiple-output (MIMO) relay systems with amplify-and-forward (AF) protocols based on a multi-branch (MB) strategy. The MB strategy employs successive interference cancellation (SIC) on several parallel branches which are equipped with different ordering patterns so that each branch produces transmit signals by exploiting a certain ordering pattern. For each parallel branch, the proposed robust nonlinear transceiver design consists of THP at the source along with a linear precoder …
G.fast is an upcoming next generation DSL standard envisioned to use bandwidth up to 212 MHz. Far-end crosstalk (FEXT) at these frequencies greatly overcomes direct links. Its cancellation based on non-linear Tomlinson-Harashima Precoding (THP) proved to show significant advantage over standard linear precoding. This paper proposes a novel THP structure in which ordering of successive interference pre-cancellation can be optimized for downstream with non-cooperating receivers. The optimized scheme is compared to existing THP structure denoted as equal-rate THP which is widely adopted in wirele…
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Filter bank based multicarrier with Offset-QAM systems (FBMC/OQAM) are strong candidates for the waveform of future 5-th generation (5G) wireless standards. These systems can achieve maximum spectral efficiency compared to other multicarrier schemes, particularly in highly frequency selective propagation conditions. In this case a multi-tap, fractionally spaced equalizer or precoder needs to be inserted in each subcarrier at the receiver or transmitter side to compensate inter-symbol interference (ISI) and inter-carrier interference (ICI). In this paper we propose a new Tomlinson-Harashima pre…
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The dirty paper channel (DPC) under a peak amplitude constraint arises in an optical wireless broadcast channel (BC), where the state at one receiver is the transmitted signal intended for the other receiver(s). This paper studies a class of peak-constrained DPC that is applicable to the optical wireless BC, where the channel state (i.e, `dirt') takes values from some evenly-spaced grid. For the discrete-state DPC studied this paper, a capacity upper bound is obtained from its state-free counterpart. To lower bound its capacity, classical dirty paper coding schemes are revisited, including Cos…
Block diagonalization (BD) is an attractive technique that transforms the multi-user multiple-input multiple-output (MU-MIMO) channel into parallel single-user MIMO (SU-MIMO) channels with zero inter-user interference (IUI). In this paper, we combine the BD technique with two deterministic vector perturbation (VP) algorithms that reduce the transmit power in MU-MIMO systems with linear precoding. These techniques are the fixed-complexity sphere encoder (FSE) and the QR-decomposition with M-algorithm encoder (QRDM-E). In contrast to the conventional BD VP technique, which is based on the sphere…
Cooperation in a cellular network is seen as a key technique in managing other cell interference to observe a gain in achievable rate. In this paper, we present the achievable rate regions for a cloud radio network using a sub-optimal zero forcing equalizer with dirty paper precoding. We show that when complete channel state information is available at the cloud, rates close to those achievable with total interference cancellation can be achieved. With mean capacity gains, of up to 2 fold over the conventional cellular network in both uplink and downlink, this precoding scheme shows great prom…
In this paper, we present robust joint non-linear transceiver designs for multiuser multiple-input multiple-output (MIMO) downlink in the presence of imperfections in the channel state information at the transmitter (CSIT). The base station (BS) is equipped with multiple transmit antennas, and each user terminal is equipped with one or more receive antennas. The BS employs Tomlinson-Harashima precoding (THP) for inter-user interference pre-cancellation at the transmitter. We consider robust transceiver designs that jointly optimize the transmit THP filters and receive filter for two models of …
The so-called "replica method" of statistical physics is employed for the large system analysis of vector precoding for the Gaussian multiple-input multiple-output (MIMO) broadcast channel. The transmitter is assumed to comprise a linear front-end combined with nonlinear precoding, that minimizes the front-end imposed transmit energy penalty. Focusing on discrete complex input alphabets, the energy penalty is minimized by relaxing the input alphabet to a larger alphabet set prior to precoding. For the common discrete lattice-based relaxation, the problem is found to violate the assumption of r…
In this paper we investigate the practical design for the multiple-antenna cognitive radio (CR) networks sharing the geographically used or unused spectrum. We consider a single cell network formed by the primary users (PU), which are half-duplex two-hop relay channels and the secondary users (SU) are single user additive white Gaussian noise channels. In addition, the coexistence constraint which requires PUs' coding schemes and rates unchanged with the emergence of SU, should be satisfied. The contribution of this paper are twofold. First, we explicitly design the scheme to pair the SUs to t…
