ZF Detector Research Articles

Is RIS-Aided Massive MIMO Promising With ZF Detectors and Imperfect CSI?

This paper provides a theoretical framework for understanding the performance of reconfigurable intelligent surface (RIS)-aided massive multiple-input multiple-output (MIMO) with zero-forcing (ZF) detectors under imperfect channel state information (CSI). We first introduce a low-overhead minimum mean square error (MMSE) channel estimator, and then derive and analyze closed-form expressions for the uplink achievable rate. Our analytical results demonstrate that: 1) regardless of the RIS phase shift design, the rate of all users scales at least on the order of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {O}\left ({\log _{2}\left ({MN}\right)}\right)$ </tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> are the numbers of antennas and reflecting elements, respectively; 2) by aligning the RIS phase shifts to one user, the rate of this user can at most scale on the order of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {O}\left ({\log _{2}\left ({MN^{2}}\right)}\right)$ </tex-math></inline-formula> ; 3) either <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> or the transmit power can be reduced inversely proportional to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> , while maintaining a given rate. Furthermore, we propose two low-complexity majorization-minimization (MM)-based algorithms to optimize the sum user rate and the minimum user rate, respectively, where closed-form solutions are obtained in each iteration. Finally, simulation results validate the accuracy of all derived analytical results. Our simulation results also show that the maximum sum rate can be closely approached by simply aligning the RIS phase shifts to an arbitrary user.

Diversity analysis of ML and ZF detectors in physical layer network coding relay system over frequency selective channels

Diversity analysis of ML and ZF detectors in physical layer network coding relay system over frequency selective channels

Ergodic Rate Analysis of Reconfigurable Intelligent Surface-Aided Massive MIMO Systems With ZF Detectors

This letter investigates the reconfigurable intelligent surface (RIS)-aided massive multiple-input multiple-output (MIMO) systems with a two-timescale design. First, the zero-forcing (ZF) detector is applied at the base station (BS) based on instantaneous aggregated channel state information (CSI), which is the superposition of the direct channel and the cascaded user-RIS-BS channel. Then, by leveraging the channel statistical property, we derive the closed-form ergodic achievable rate expression. Using a gradient ascent method, we design the RIS passive beamforming relying only on the long-term statistical CSI. We prove that the ergodic rate scales on the order of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {O}\left ({\log _{2}\left ({MN}\right)}\right)$ </tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> denote the number of BS antennas and RIS elements, respectively. We also prove the striking superiority of the considered RIS-aided system with ZF detectors over the RIS-free systems and RIS-aided systems with maximum-ratio combining (MRC).

ZF and MMSE Detectors Performances of a Massive MIMO System Combined with OFDM and M-QAM Modulation

This paper presents a least squares channel estimation (LSCE) in the UpLink transmission for a Massive MIMO systems in 5G wireless communications, combined with Orthogonal Frequency Division Multiplexing and higher-order M-QAM modulation. The Mean Square Error (MSE) of the LSCE is computed, and the performance of ZF, MMSE and V-BLAST detectors is also evaluated. Using 128-QAM modulation (i.e., increasing the noise system sensibility) with 1024 subcarriers and increasing the Base Station antennas array decreases more the Bit Error Rate (BER) for the ZF, MMSE and V-BLAST detectors with respect to the MSE. The performance degradation both ZF and MMSE compared to V-BLAST is negligible in a high receive antennas; hence, faster data rates and higher spectral efficiency levels for the communication systems. Consequently, the ZF, MMSE and V-BLAST detectors achieve a better BER with respect to channel estimation.

ZF detectors for uplink distributed massive MIMO systems over Rayleigh‐inverse Gaussian composite fading channels

Massive multiple-input multiple-output (MIMO), together with distributed antenna systems has emerged as a promising technology in modern wireless networks because of their remarkable capacity potential and link reliability. The combined architecture, that is distributed massive MIMO (DM-MIMO) comprises of arbitrarily located multiple radio ports (RPs) each having more than one antennas and a base station containing asymptotically large number of antennas. At the outset, the instantaneous output signal to noise ratio (SNR) corresponding to individual subchannel is obtained for ZF detector. Subsequently, closed form expression of exact and high SNR approximated ergodic capacity are obtained in the context of DM-MIMO. The lower bound of ergodic capacity are then derived using a generalized approach, which may be applicable to all composite fading channels. Moreover, lower bound over all users are formulated in closed form considering large number of RPs located in a circular topology. In subsequent analysis, SER and OP characterization of the ZF detector over DM-MIMO channel is presented with tractable mathematical expressions. In addition to the per subchannel based SER, the global average SER is also evaluated for the considered configurations. Finally, the implications of model parameters on ZF detectors are analysed through a set of Monte-Carlo simulations.

A comparative analysis of the performance of linear detectors for wireless multicasting through interference limited cognitive radio channels

We consider the problem of wireless multicasting through multiple-input multiple-output MIMO cognitive radio channel in which primary and secondary users simultaneously communicate with their corresponding group of receivers instead of waiting for an idle channel as we see in the traditional cognitive radio. Using a code-division multiple-access CDMA technique, we evaluate the performance of minimum mean square error MMSE detector in multicasting application through interference limited cognitive radio channels. We also compare the performance of MMSE detector with conventional zero-forcing ZF and maximal-ratio-combining MRC detectors. Our results show that MMSE detector performs better than ZF and MRC detectors.

QR Decomposition-Based Antenna Selection for Spatial Multiplexing UWB Systems with Zero-Forcing Detectors Followed by Rake Combiners

This letter presents a criterion for selecting a transmit antenna subset when ZF detectors followed by Rake combiners are employed for spatial multiplexing (SM) ultra-wideband (UWB) multiple input multiple output (MIMO) systems. The presented criterion is based on the largest minimum post-processing signal to interference plus noise ratio of the multiplexed streams, which is obtained on the basis of QR decomposition. Simulation results show that the proposed antenna selection algorithm considerably improves the BER performance of the SM UWB MIMO systems when the number of multipath diversity branches is not so large and thus offers diversity advantages on a log-normal multipath fading channel.

An Ordered Successive Interference Cancellation Scheme in UWB MIMO Systems

In this letter, an ordered successive interference cancellation (OSIC) scheme is applied for multiple-input multiple-output (MIMO) detection in ultra- wideband (UWB) communication systems. The error rate expression of an OSIC receiver on a log-normal multipath fading channel is theoretically derived in a closed form solution. Its bit error rate performance is analytically compared with that of a zero forcing receiver in the UWB MIMO detection scheme followed by RAKE combining. Performance of the ZF detector is known to be similar to that of the MMSE receiver at high signal-to-noise ratios (SNRs). This work focuses on the analysis of a ZF related scheme. In this letter, we present the error performance of a ZF scheme with an ordered successive interference cancellation (OSIC) for UWB SM MIMO detection in a log-normal fading channel. We analytically investigate the theoretic bit error rate (BER) performance of the ZF-OSIC architecture followed by RAKE combining, called a ZF-OSIC-RAKE, in an UWB SM MIMO receiver. The diversity order that the ZF-OSIC-RAKE offers for detecting the n-th transmitted data stream is obtained for UWB MIMO systems. It is also seen that the ZF-OSIC-RAKE scheme outperforms the ZF-RAKE.

Full vectoring optimal power allocation in xDSL channels under per-modem power constraints and spectral mask constraints

In xDSL systems, crosstalk can be separated into two categories, namely in-domain crosstalk and out-of-domain crosstalk. In-domain crosstalk is also referred to as self crosstalk. Out-of-domain crosstalk is crosstalk originating from outside the multi-pair system and is also denoted as external noise (alien crosstalk, radio frequency interference,...). While self crosstalk in itself can easily be canceled by a linear detector like the ZF detector, the presence of external noise requires a more advanced processing. Coordination between transmitters and receivers enables the self crosstalk and the external noise to be mitigated using MIMO signal processing, usually by means of a whitening filter and SVD. In this paper, we investigate the problem of finding the optimal power allocation in MIMO xDSL systems in the presence of self crosstalk and external noise. Optimal Tx/Rx structures and power allocation algorithms will be devised under practical limitations from xDSL systems, namely per-modem total power constraints and/or spectral mask constraints, leading to a generalized SVD-based transmission. Simulation results are given for bonded VDSL2 systems with external noise coming from ADSL2+ or VDSL2 disturbing lines, along with a comparison between algorithms with one-sided signal coordination either only at the transmit side or the receive side.