ZF Beamforming Performance Analysis for Multiuser Spatial Multiplexing with Imperfect Channel Feedback

In this paper, we propose a novel unitary downlink precoding design scheme for multiuser (MU) spatial multiplexing (SM) multiple-input multiple-output (MIMO) systems. With the perfect channel state information (p-CSI) available at the transmitter and the linear decoder at the receiver, we construct the cost function based on the minimum average probability of vector symbol error (APVSE) and give the design method of the precoding matrices. Our proposed precoding matrices can completely eliminate co-channel interference (CCI) for each user at the transmitter, and each terminal user will eventually observe an interference-free single-user (SU) channel, thus simplify the decoding of each terminal user. Finally, we derive the upper bound APVSEs of several schemes for performance comparison and the latter simulation results have shown that our proposed downlink precoding for MU SM MIMO system obtains the almost same performance as the SU precoding system.

In this paper we present a local channel correlation based zero-forcing (ZF) beamforming framework for the cell edge users. Without the instantaneous CSI (ICSI) assisting, we derive the exact expression of the averaged pairwise error probability (PEP) upper bounds at both of the receivers. According to the derived PEP bounds, an multi-objective optimization problem is formulated to get the elaborate power allocation and ZF beamforming design with the knowledge of local statistical channel state information (SCSI) at the transmitter side. By factorizing each beamforming matrix as the multiplication of two matrices, we can avoid inter-user interference through column orthogonal matrix design. Moreover, the original complicated optimization problem can be further decoupled into four simple sub-optimization problems. Then utilizing the Lagrange multiplying method, we finally achieve the feasible distributed statistical ZF beamforming design, which only involves the distributed computations based on the local channel correlations. Both theoretical analysis and simulation results confirm that the multi-cell spatial diversity gain can be fully exploited with only local SCSI. For comparison, the traditional perfect ICSI based ZF beamforming is analyzed and discussed. It is shown that in the high regime of signal-to-noise ratio (SNR), the diversity gain of the proposed statistical ZF beamforming is even better than that achieved by the conventional ICSI-aided ZF beamforming.

In this paper, a comprehensive design and analysis of multiple-input multiple-output (MIMO) full-duplex (FD) relaying systems in a multi-cell environment is investigated, where a multi-antenna amplify-and-forward FD relay station serves multiple half-duplex (HD) multi-antenna users. The pivotal obstacles of loopback self-interference (LI) and multiple co-channel interferers (CCI) at the relay and destination when employing FD relaying in cellular networks are addressed. In contrast to the HD relaying mode, the CCI in the FD relaying mode is predicted to double since the uplink and downlink communications are simultaneously scheduled via the same channel. In this paper, the optimal layout of transmit (receive) precoding (decoding) weight vectors which maximizes the overall signal-to-interference-plus-noise ratio is constructed by a suitable optimization problem, and then a closed-form sub-optimal formula based on null space projection is presented. The proposed hop-by-hop rank-1 zero-forcing (ZF) beamforming vectors are based on added ZF constraints used to suppress the LI and CCI channels at the relay and destination, i.e., the source and relay perform transmit ZF beamforming, while the relay and destination employ receive ZF combining. To this end, unified accurate expressions for the outage probability and ergodic capacity are derived in closed form. In addition, simpler tight lower bound formulas for the outage probability and ergodic capacity are presented. Moreover, the asymptotic approximations for outage probability are considered to gain insights into system behavior in terms of the diversity order and array gain. Numerical and simulation results show the accuracy of the presented exact analytical expressions and the tightness of the lower bound expressions. The case of hop-by-hop maximum-ratio transmission/maximal-ratio combining beamforming is included for comparison purposes. Furthermore, our results show that while multi-antenna terminals improve the system performance, the detrimental effect of CCI on FD relaying is clearly seen. Therefore, our findings unveil that MIMO FD relaying could significantly improve the system performance compared to its conventional MIMO HD relaying counterpart.

Imperfect channel state information degrades the performance of multiple-input multiple-output (MIMO) communications; its effect on single-user (SU) and multi-user (MU) MIMO transmissions are quite different. In particular, MU-MIMO suffers from residual inter-user interference due to imperfect channel state information while SU-MIMO only suffers from a power loss. This paper compares the throughput loss of both SU and MU MIMO on the downlink due to delay and channel quantization. Accurate closed-form approximations are derived for the achievable rates for both SU and MU MIMO. It is shown that SU-MIMO is relatively robust to delayed and quantized channel information, while MU MIMO with zero-forcing precoding loses spatial multiplexing gain with a fixed delay or fixed codebook size. Based on derived achievable rates, a mode switching algorithm is proposed that switches between SU and MU MIMO modes to improve the spectral efficiency, based on the average signal-to-noise ratio (SNR), the normalized Doppler frequency, and the channel quantization codebook size. The operating regions for SU and MU modes with different delays and codebook sizes are determined, which can be used to select the preferred mode. It is shown that the MU mode is active only when the normalized Doppler frequency is very small and the codebook size is large.

Wireless network is one of the most important things in the development of telecommunication. However, the existing wireless technology has not been able to efficiently create a very high data rate because it was very sensitive to fading. Therefore, Orthogonal Frequency Division Multiplexing (OFDM) technology combined with MIMO (Multiple Input Multiple Output) transceiver system was used to gain more diversity and bandwidth efficiency. The propagation performed on the OFDM MIMO system was multipath propagation. To reduce Intersymbol Interference (ISI) was used Zero Forcing (ZF) equalizer which works by combining channel response and equalizer response itself to eliminate ISI. This study aims to determine the effect of Zero Forcing Equalizer on OFDM MIMO system using rayleigh fading channel and compared the result with OFDM MIMO STBC system. The research method used was simulation using MatLab R2015a. The simulation results showed that the performance of OFDM MIMO ZF system was worse than OFDM MIMO STBC system i.e BER vs EbNo simulation, eye diagram simulation, and constellation diagram simulation. The OFDM MIMO ZF system was required an Eb / No value more than 25 dB to achieve BER 10-4 while the OFDM MIMO STBC system only required an Eb / No value of 10.5 dB to achieve BER 10-4. The eye pattern generated by the OFDM MIMO ZF system was more closed and the dispersion of constellation signals away from the ideal point while OFDM MIMO STBC system displayed a more open eye pattern and the dispersion of its constellation signal closer to the ideal point. It indicated more ISI occurs in the OFDM MIMO ZF system than that in OFDM MIMO STBC system.

This paper investigates the maximal ratio combining (MRC) performance of an amplify and forward (AF) relay system in Nakagami-m fading environments. The study considers a general scenario with distinct m fading parameters for the following three links, source to relay link, and source to destination link and relay to destination link. We derive new closed form expressions for the statistics of important performance metrics, including the moment generating function, outage probability, higher order moments of equivalent signal to noise ratio (SNR), ergodic capacity, and average symbol error probability (SEP) of common modulation types. In particular, we focus on analytical SEP expressions in the context of an additive white generalized Gaussian noise (AWGGN). As an active area of research, generalized noise receives much attention for its flexible model. However, analytical performance of modulation scheme in generalized noise type has not been found in open literature for AF relaying with MRC despite its practical usefulness. Without the help of analytical solutions, the SEP in generalized noise can only be obtained by a large number of repeated simulation experiments. Therefore, we present the general SEP expression by using special Fox’s H function. Simulation results verify the accuracy of our theoretical analysis and show that the diversity order of MRC criterion linearly depends upon Nakagami parameters of three links.

Cooperative communications can exploit the distributed spatial diversity to improve the multiple-link performance. In this paper, the average symbol error probability (SEP) is carefully investigated for the three-node relaying structure, in which the relaying protocol is amplify-and-forward, and the modulation scheme can be N-PSK or N-QAM. We first exploit the optimistic condition to derive the lower bound of SEP. This is the generalization of the existing Anghel-Kaveh formulation. Then, the upper bound is also provided based on the exponential approximation to the Bessel function. This bound turns out to be tighter than the Anghel-Kaveh upper bound. Numerical results are provided to confirm the analytical analysis.

Precoding for Multiuser Spatial Multiplexing MIMO Downlink

This letter presents a study on statistical and symbol error performance analysis of the two-hop orthogonal frequency division multiplexing (OFDM) relay link with amplify-and-forward (AF) protocol and subcarrier mapping (SCM) scheme. Closed-form expressions for probability density function (PDF) and symbol error probability (SEP) of the signal-to-noise ratio (SNR) for the kth mapped subcarrier pair link (k-MSPL) are provided. Our asymptotic SEP analysis reveals that the traditional SCM which can maximize the capacity can not improve the average SEP for uncoded OFDM system, however the average SEP can be decreased significantly by dropping several worst links.

Using a spatial multiplexing transmission scheme can improve the data rate in multiple-input–multiple-output (MIMO) relaying systems, while making signal detection more difficult at receivers. Aiming at lowering the computational complexity of the receiver, this paper proposes a maximum likelihood combining (MLC) algorithm for spatial multiplexing MIMO amplify-and-forward (AF) relaying systems in a Rayleigh flat-fading environment, which is implemented before maximum likelihood (ML) detection. The combining signal and equivalent channel are opportunely designed based on the ML rule in the MLC algorithm. We also formulate the diversity gain of the systems that employ the MLC algorithm mathematically, induced by the Chernoff bound of pairwise error probability (PEP). An upper bound on the symbol error probability (SEP) for the MLC algorithm with multiple modulations is also given, based on the derived bound of PEP. Moreover, the complexities of ML receivers adopting the MLC algorithm and the conventional vector combining (VC) algorithm are analyzed. Numerical simulations indicate that systems with the MLC algorithm achieve the same performance while consuming lower computational complexity compared to that with the VC algorithm.

This paper analyzes the performance of multicarrier index modulation (MCIM) with greedy detection (GD) in a dual hop, multiple decode and forward (DF) relay network. We propose a novel partial relay selection (PRS) technique combined with index modulation and its energy detection. For performance analysis, we derive novel closed form solutions for both the average pairwise error probability (PEP) and the average symbol error probability (SEP) at the relays and destination over Nakagami-m fading channels. Unlike the information theoretical works, with presence of positive detection error in the relays, the derived expressions provide a useful insight into the error performance of PRS based MCIM in a multiple DF relay network under various fading conditions. Also, we address the impacts of both relays and different rates of sub-carrier index activation.

In this work, we derive exact closed-form expressions for the average symbol error probability (SEP) of arbitrary rectangular quadrature amplitude modulation (QAM) when used along with orthogonal space-time block coding (OSTBC) over independent but not necessarily identically distributed multiple-input multiple-output (MIMO) Nakagami-m fading channels. The derived SEP expressions account for diversity branches which may exhibit identical or distinctive power levels while their associated Nakagami indexes can take arbitrary real values not less than 1/2. Our work extends previous results pertaining to the performance analysis of OSTBC using M-ary rectangular QAM over Rayleigh fading channels and M-ary square QAM over Nakagami-m fading channels. For a MIMO diversity system with n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> transmit and n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> receive antennas and a corresponding set of arbitrary real-valued Nakagami indexes, our rectangular QAM SEP results are expressed in terms of Lauricella's multivariate hypergeometric functions F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(L)</sup> and F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(L + 1)</sup> where L = n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sub> n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> is the total number of diversity branches.

Channel feedback for multi-user (MU)-multiple-input multiple-output (MIMO) has been widely studied and some results have been got with random vector quantization scheme. However, while the low rate fixed codebook feedbacks are adopted, the performance of zero forcing (ZF) MU-MIMO will decrease as the unpredictable inter-user interference is introduced because of quantized channel state information (CSI). To decrease inter-user interference in low rate fixed codebook feedback, an enhanced user selection switch (USS) feedback scheme for ZF MU-MIMO is proposed in this article. In USS feedback, the extra USS information is added after quantized CSI and received signal-to-noise ratio feedback. The USS information indicates inter-user interference and it can be used in user selection procedure to avoid large inter-user interference. Simulation results show that the proposed USS feedback scheme is efficient to solve the problems of unpredictable inter-user interference in conventional feedback scheme with low rate codebook in ZF MU-MIMO.

Factory automation is one of the most challenging use cases for 5G-and-beyond mobile networks due to strict latency, availability and reliability constraints. In this work, an indoor factory scenario is considered, and distributed multiple- input multiple-output (MIMO) schemes are investigated in order to enable reliable communication to the actuators (ACs) active in the factory. Different levels of coordination among the access points serving the ACs and several beamforming schemes are considered and analyzed. To enforce system reliability, a max-min power allocation (MPA) algorithm is proposed, aimed at improving the signal to interference plus noise ratio (SINR) of the ACs with the worst channel conditions. Extensive system simulations are performed in a realistic scenario, which includes a new path-loss model based on recent measurements in factory scenarios, and, also, the presence of non-Gaussian impulsive noise. Numerical results show that distributed MIMO schemes with zero-forcing (ZF) beamforming and MPA have the potential of providing SINR gains in the order of tens of dB with respect to a centralized MIMO deployment, as well as that the impulsive noise can strongly degrade the system performance and thus requires specific detection and mitigation techniques.

In this paper, we present a new beamforming scheme for a downlink of multiuser multiple-input multiple- output (MIMO) communication systems. Recently, a block- diagonalization (BD) algorithm has been proposed for the multiuser MIMO downlink where both a base station and each user have multiple antennas. However, the BD algorithm is not efficient when the number of supported streams per user is smaller than that of receive antennas. Since the BD method utilizes the nullspace based on the channel matrix without considering the receive combining, the degree of freedom for beamforming cannot be fully exploited at the transmitter. In this paper, we optimize the receive beamforming vector under a zero forcing (ZF) constraint, where all inter-user interference is driven to zero. We propose an efficient algorithm to find the optimum receive vector by an iterative procedure. The proposed algorithm requires two phase values feedforward information for the receive combining vector. Also, we present another algorithm which needs only one phase value by using a decomposition of the complex general unitary matrix. Simulation results show that the proposed beamforming scheme outperforms the conventional BD algorithm in terms of error probability and obtains the diversity enhancement by utilizing the degree of freedom at the base station.