Random Beamforming Research Articles

Combined beamforming with space-time-frequency coding for MIMO–OFDM systems

Multiple antennas can be used in wireless systems to achieve good quality of service and high data rate communication. Recently, efficient space-time-frequency (STF) codes have been developed to improve the diversity gain. This paper aims at performance analysis of multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO–OFDM) system using STF Coding and random beamforming. The proposed approach which combines beamforming with STF code offers improved performance over STF in term of bit error rates (BER). It is also observed that the proposed scheme gives better performance as compared to the combined space-time block code (STBC) with beamforming. Computational complexity of the proposed scheme is also calculated.

Base Station Cooperative Multiuser MIMO Using Block-Diagonalized Random Beamforming with Online Update

This paper proposes applying random (opportunistic) beamforming to base station (BS) cooperative multiuser multiple-input multiple-output (MIMO) transmission. This proposal comprises two parts. First, we propose a block-diagonalized random unitary beamforming matrix. The proposed beamforming matrix achieves better throughput distribution compared to the purely random unitary beamforming matrix when the average path loss based on distance-dependent loss and shadowing loss is largely different among transmitter antennas, which is true in BS cooperative MIMO. Second, we propose an online update algorithm for a random beamforming matrix to improve the throughput compared to the purely random and channel-independent beamforming matrix generation, especially when the number of users is low. Different from conventional approaches, the proposed online update algorithm does not increase the overhead of the reference signal transmission and control delay. Simulation results show the effectiveness of the proposed method using a block-diagonalized random unitary beamforming matrix with online updates in a BS cooperative multiuser MIMO scenario.

Non-Orthogonal Multiple Access Using Intra-Beam Superposition Coding and SIC in Base Station Cooperative MIMO Cellular Downlink

This paper extends our previously proposed non- orthogonal multiple access (NOMA) scheme to the base station (BS) cooperative multiple-input multiple-output (MIMO) cellular downlink for future radio access. The proposed NOMA scheme employs intra-beam superposition coding of a multiuser signal at the transmitter and the spatial filtering of inter-beam interference followed by the intra-beam successive interference canceller (SIC) at the user terminal receiver. The intra-beam SIC cancels out the inter-user interference within a beam. This configuration achieves reduced overhead for the downlink reference signaling for channel estimation at the user terminal in the case of non-orthogonal user multiplexing and also achieves the applicability of the SIC receiver in MIMO downlink. The transmitter beamforming (precoding) matrix is controlled based on open loop-type random beamforming using a block- diagonalized beamforming matrix, which is very efficient in terms of the amount of feedback information from the user terminal. Simulation results show that the proposed NOMA scheme with block-diagonalized random beamforming in BS cooperative multiuser MIMO and the intra-beam SIC achieves better system-level throughput compared to orthogonal multiple access (OMA), which is assumed in LTE-Advanced. We also show that BS cooperative operation along with the proposed NOMA in particular achieves a high cell-edge user throughput gain which implies better user fairness and universal connectivity.

Non-Orthogonal Multiple Access Using Intra-Beam Superposition Coding and Successive Interference Cancellation for Cellular MIMO Downlink

We investigate non-orthogonal multiple access (NOMA) with a successive interference canceller (SIC) in the cellular multiple-input multiple-output (MIMO) downlink for systems beyond LTE-Advanced. Taking into account the overhead for the downlink reference signaling for channel estimation at the user terminal in the case of non-orthogonal multiuser multiplexing and the applicability of the SIC receiver in the MIMO downlink, we propose intra-beam superposition coding of a multiuser signal at the transmitter and the spatial filtering of inter-beam interference followed by the intra-beam SIC at the user terminal receiver. The intra-beam SIC cancels out the inter-user interference within a beam. Regarding the transmitter beamforming (precoding), in general, any kind of beamforming matrix determination criteria can be applied to the proposed NOMA method. In the paper, we assume open loop-type random beamforming, which is very efficient in terms of the amount of feedback information from the user terminal. Furthermore, we employ a weighted proportional fair (PF)-based resource (beam of each frequency block and power) allocation for the proposed method. Simulation results show that the proposed NOMA method using the intra-beam superposition coding and SIC simultaneously achieves better sum and cell-edge user throughput compared to orthogonal multiple access (OMA), which is widely used in 3.9 and 4G mobile communication systems.

Angle-threshold random beamforming scheme for multi-antenna system

Codebook-based multiple input multiple output (MIMO) beamforming can significantly improve the system spectral efficiency with limited feedback and gets widely adopted. However, this scheme has a drawback of heavy feedback load that the sum feedback rate can be a bottleneck for the communication system, especially when the number of users is large. In this paper, a new scheme using pseudo-random beamforming vectors and angle based threshold in the feedback process is proposed. In the proposed scheme, both the base-station and the users have no need to store a codebook. In each access procedure, the base-station generates a pseudo-random beamforming vector, and each user calculates the angle between the beamforming vectors and its channel state information (CSI) vector. If the angle is less than a predefined angle-threshold, the user feeds back its channel quality indicators (CQI), otherwise it keep silence. Compared with the codebook based scheme, the proposed scheme can largely reduce the sum feedback rate with negligible throughput loss. In particular, when the system has a constraint on the total sum feedback rate in uplink channel, the proposed scheme can increase the system throughput significantly.

On the Energy Efficiency–Spectral Efficiency Tradeoff in Random Beamforming

Energy efficiency (EE) and spectral efficiency (SE) are among the most important metrics in wireless systems. The relationship between EE and SE has attracted more attention recently. In this letter, we derive a closed-form approximation of the EE-SE tradeoff in a multi-antenna random beamforming system under a realistic power consumption model. Based on the approximate EE-SE tradeoff, the EE-maximum SE and the corresponding transmit power are obtained in closed form with the help of Lambert W function. We also derive the optimal number of transmit antennas to maximize the EE when the value of SE is given. These results are helpful to gain analytical insights on choosing proper system parameters, e.g., the transmit power and the number of transmit antennas, to meet the demand of green communication. Simulation results validate the accuracy of our proposed closed-form approximation.

Throughput analysis of multi‐antenna cognitive broadcast networks

In this study, the authors analyse the throughput of random beamforming (RBF) for a multi-antenna cognitive radio (CR) broadcast network. Using extreme value theory, the asymptotic average throughput of a single-beam RBF and a multiple-beam RBF are derived from the limiting distribution of the sample maximum of received signal-to-noise ratio (signal-to-interference-plus-noise ratio) with maximal ratio combiner at the secondary user. It is shown that the throughput of the single-beam RBF scales as logarithm of the number of users, which stands in contrast to the double logarithm of the number of users in non-CR networks. They also found that the single-beam RBF is always much preferable to the multi-beam RBF on the throughput in the CR networks, which is opposite to the previous results in the non-CR networks. Simulation results show that the author's approximated expressions match with the simulation results very well.

A Novel Mode Switching Scheme Utilizing Random Beamforming for Opportunistic Energy Harvesting

Since radio signals carry both energy and information at the same time, a unified study on simultaneous wireless information and power transfer (SWIPT) has recently drawn a significant attention for achieving wireless powered communication networks. In this paper, we study a multiple-input single-output (MISO) multicast SWIPT network with one multi-antenna transmitter sending common information to multiple single-antenna receivers simultaneously along with opportunistic wireless energy harvesting at each receiver. From the practical consideration, we assume that the channel state information (CSI) is only known at each respective receiver but is unavailable at the transmitter. We propose a novel receiver mode switching scheme for SWIPT based on a new application of the conventional random beamforming technique at the multi-antenna transmitter, which generates artificial channel fading to enable more efficient energy harvesting at each receiver when the received power exceeds a certain threshold. For the proposed scheme, we investigate the achievable information rate, harvested average power and power outage probability, as well as their various trade-offs in quasi-static fading channels. Compared to a reference scheme of periodic receiver mode switching without random transmit beamforming, the proposed scheme is shown to be able to achieve better rate-energy trade-offs when the harvested power target is sufficiently large. Particularly, it is revealed that employing one single random beam for the proposed scheme is asymptotically optimal as the transmit power increases to infinity, and also performs the best with finite transmit power for the high harvested power regime of most practical interests, thus leading to an appealing low-complexity implementation. Finally, we compare the rate-energy performances of the proposed scheme with different random beam designs.

Degrees of Freedom for a MIMO Gaussian $K$-Way Relay Channel: Successive Network Code Encoding and Decoding

This paper studies a network information flow problem for a multiple-input multiple-output (MIMO) Gaussian wireless network with K users and a single intermediate relay having M antennas. In this network, each user sends a multicast message to all other users while receiving K-1 independent messages from the other users via an intermediate relay. This network information flow is termed a MIMO Gaussian K-way relay channel. For this channel, it is shown that the optimal sum degrees of freedom (sum-DoF) is KM/K-1, assuming that all nodes have global channel knowledge and operate in full-duplex. A converse argument is derived by cut-set bounds. The achievability is shown by a repetition coding scheme with random beamforming in encoding and a zero-forcing method combined with self-interference cancelation in decoding. Furthermore, under the premise that all nodes have local channel state information at the receiver only and operate in half-duplex mode, it is shown that a total K/2 DoF is achievable when M=K-1. The key to showing this result is a novel encoding and decoding scheme, which creates a set of network code messages with a chain structure during the multiple access phase and performs successive interference cancelation using side-information for the broadcast phase. One major implication of the derived results is that efficient exploitation of the transmit message as side-information leads to an increase in the sum-DoF gain in a multiway relay channel with multicast messages.

Asymptotic throughput analysis of random beamforming for multi‐antenna cognitive broadcast networks

Random beamforming (RBF) has received much attention recently in downlink beamforming because of its simple structure, low-feedback load and same throughput scaling as that obtained using dirty paper coding at the transmitter. In this study, the authors analyse the performance of RBF for cognitive downlink multi-antenna system in terms of the throughput of the secondary network. The authors consider a secondary broadcast station with multiple antennas utilising the licensed spectrum of each primary receiver to broadcast information to multiple secondary users (SUs) simultaneously, as long as the interference power inflicted at each primary receiver is less than a predefined threshold. Firstly, they derived the secondary network closed-form throughput approximation of a single-beam RBF by exploiting extreme value order statistics. Then, closed-form approximation for secondary network throughput on multiple-beam RBF is presented. Simulation results verify the validity of the authors approximation results analysis even with fewer SUs.

Multi-Cell Random Beamforming: Achievable Rate and Degrees of Freedom Region

Random beamforming (RBF) is a practically favourable transmission scheme for multiuser multi-antenna downlink systems since it requires only partial channel state information (CSI) at the transmitter. Under the conventional single-cell setup, RBF is known to achieve the optimal sum-capacity scaling law as the number of users goes to infinity, thanks to the multiuser diversity enabled transmission scheduling that virtually eliminates the intra-cell interference. In this paper, we extend the study of RBF to a more practical multi-cell downlink system with single-antenna receivers subject to the additional inter-cell interference (ICI). First, we consider the case of finite signal-to-noise ratio (SNR) at each receiver. We derive a closed-form expression of the achievable sum-rate with the multi-cell RBF, based upon which we show an asymptotic sum-rate scaling law as the number of users goes to infinity. Next, we consider the high-SNR regime and for tractable analysis assume that the number of users in each cell scales in a certain order with the per-cell SNR. Under this setup, we characterize the achievable degrees of freedom (DoF) for the single-cell case with RBF. Then we extend the analysis to the multi-cell RBF case by characterizing the DoF region. It is shown that the DoF region characterization provides useful guideline on how to design a cooperative multi-cell RBF system to achieve optimal throughput tradeoffs among different cells. Furthermore, our results reveal that the multi-cell RBF scheme achieves the "interference-free DoF" region upper bound for the multi-cell system, provided that the per-cell number of users has a sufficiently large scaling order with the SNR. Our result thus confirms the optimality of multi-cell RBF in this regime even without the complete CSI at the transmitter, as compared to other full-CSI requiring transmission schemes such as interference alignment.

Random Beamforming with Heterogeneous Users and Selective Feedback: Individual Sum Rate and Individual Scaling Laws

This paper investigates three open problems in random beamforming based communication systems: the scheduling policy with heterogeneous users, the closed form sum rate, and the randomness of multiuser diversity with selective feedback. By employing the cumulative distribution function based scheduling policy, we guarantee fairness among users as well as obtain multiuser diversity gain in the heterogeneous scenario. Under this scheduling framework, the individual sum rate, namely the average rate for a given user multiplied by the number of users, is of interest and analyzed under different feedback schemes. Firstly, under the full feedback scheme, we derive the closed form individual sum rate by employing a decomposition of the probability density function of the selected user's signal-to-interference-plus-noise ratio. This technique is employed to further obtain a closed form rate approximation with selective feedback in the spatial dimension. The analysis is also extended to random beamforming in a wideband OFDMA system with additional selective feedback in the spectral dimension wherein only the best beams for the best-L resource blocks are fed back. We utilize extreme value theory to examine the randomness of multiuser diversity incurred by selective feedback. Finally, by leveraging the tail equivalence method, the multiplicative effect of selective feedback and random observations is observed to establish the individual rate scaling.

Achieving Secure Transmission with Equivalent Multiplicative Noise in MISO Wiretap Channels

In this letter, we verify that equivalent multiplicative noise, which is generally introduced by random beamforming security scheme, can also guarantee available secrecy rate in MISO wiretap channels. The multiplicative noise is transformed into additive one via a logarithmic operation which is further demonstrated to be information preserving. Then the achievable secrecy rate is quantitatively characterized when the amplitude and phase of the multiplicative noise are independently generated and follow lognormal and uniform distributions, respectively. Finally, power allocation between the multiplicative noise and the desired signal is optimized and discussed by numerical simulation when the eavesdropping channel is known.

SINR and Throughput Analysis for Random Beamforming Systems with Adaptive Modulation

In this paper, we derive the exact probability distribution of post-scheduling signal-to-interference-plus-noise ratio (SINR) considering both user feedback and scheduling. We also develop an optimized adaptive modulation scheme in orthogonal random beamforming systems with M transmit antennas and K single-antenna users. The exact probability distributions of each user's feedback SINR and the exact post-scheduling SINR are derived rigorously by direct integration and multinomial distribution. It is also shown that the derived cumulative distribution function (CDF) of the post-scheduling SINR happens to be identical to the the existing approximate CDF for SINR higher than 0 dB. The closed form expressions of system performance, such as average spectral efficiency (ASE) and average bit error ratio (A-BER), are derived using the CDF of the post-scheduling SINR. The optimal SINR thresholds that maximize the ASE with a target A-BER constraint are solved using the derived closed form CDF and a Lagrange multiplier. Key contributions of this paper include the derivation of the exact CDF of post-scheduling SINR by direct integration, and its application to an optimized adaptive modulation based on a Lagrange multiplier. Simulations show the correspondence between theoretical and empirical CDF's, and the performance improvement of the proposed adaptive modulation method in terms of ASE.

A Random Beamforming Technique for Omnidirectional Coverage in Multiple-Antenna Systems

A random beamforming (RBF) technique is proposed to achieve omnidirectional coverage for broadcast channels in multiple-antenna systems. In the proposed scheme, the time and frequency resources for communication are divided into many time-frequency blocks (TFBs). A random pattern is employed on each TFB, with the average power in all directions over many TFBs being equal. The design criteria and detailed design of the random pattern sequence are given. We propose a basic RBF scheme and an Alamouti-enhanced scheme, as well as the corresponding structures of the transmitter and the receiver. Simulations are carried out for an eight-element unitary linear array with half-waveform separation in a fast-fading channel, showing that the proposed scheme greatly outperforms the cyclic delay diversity scheme and is robust to calibration errors and failures of radio-frequency chains.

Power Management in Multiuser Adaptive Modulation Transmission under QoS Requirements

A transmitter power management mechanism is presented in this paper where Multiple-Input Multiple-Output (MIMO) Multiuser Random Beamforming with Adaptive Modulation strategy is performed by the system. The objective of the proposed mechanism is quality of service (QoS) satisfaction for the scheduled user. The QoS is represented by the application demanded data rate and symbol error rate. The power outage problem is considered and a practical method to minimize the outage probability is proposed. The obtained results are encouraging as they show a great decrease in the system power budget. The multiuser system capability is also exploited to achieve larger power saving values and smaller probability of power outage by scheduling the user with the best channel characteristics at each time instant. The amount of saved power and the power outage probability are both presented through closed-form expressions. These theoretical results are compared to computer simulations, which show very good agreement in performance.

Secrecy sum-rate for orthogonal random beamforming with opportunistic scheduling

We employ orthogonal random beamforming (ORBF) for the worst-case multi-user downlink scenario where each user is wiretapped by one eavesdropper. Two opportunistic scheduling techniques that ensure confidentiality by exploiting multi-user diversity are investigated; the first technique (optimal) requires limited feedback of the effective signal-to-interference ratio (SIR) from all the users and the eavesdroppers while the second technique (suboptimal) incorporates SIR knowledge from only the legitimate users. By using extreme value theory, we derive the achievable SIR-based secrecy sum-rate and the associated scaling laws for both scheduling techniques.

Greedy Beam Selection with Limited Feedback for Orthogonal Random Beamforming

Greedy Beam Selection with Limited Feedback for Orthogonal Random Beamforming

Joint Optimization of User Set Selection and Transmit Power Allocation for Orthogonal Random Beamforming in Multiuser MIMO Systems

When the number of users is finite, the performance improvement of the orthogonal random beamforming (ORBF) scheme is limited in high signal-to-noise ratio regions. In this paper, to improve the performance of the ORBF scheme, the user set and transmit power allocation are jointly determined to maximize sum rate under the total transmit power constraint. First, the transmit power allocation problem is expressed as a function of a given user set. Based on this expression, the optimal user set with the maximum sum rate is determined. The suboptimal procedure is also presented to reduce the computational complexity, which separates the user set selection procedure and transmit power allocation procedure.

Random Beamforming Over Quasi-Static and Fading Channels: A Deterministic Equivalent Approach

In this work, we study the performance of random isometric precoders over quasi-static and correlated fading channels. We derive deterministic approximations of the mutual information and the signal-to-interference-plus-noise ratio (SINR) at the output of the minimum-mean-square-error (MMSE) receiver and provide simple provably converging fixed-point algorithms for their computation. Although these approximations are only proven exact in the asymptotic regime with infinitely many antennas at the transmitters and receivers, simulations suggest that they closely match the performance of small-dimensional systems. We exemplarily apply our results to the performance analysis of multi-cellular communication systems, multiple-input multiple-output multiple-access channels (MIMO-MAC), and MIMO interference channels. The mathematical analysis is based on the Stieltjes transform method. This enables the derivation of deterministic equivalents of functionals of large-dimensional random matrices. In contrast to previous works, our analysis does not rely on arguments from free probability theory which enables the consideration of random matrix models for which asymptotic freeness does not hold. Thus, the results of this work are also a novel contribution to the field of random matrix theory and applicable to a wide spectrum of practical systems.