Optimal bandwidth allocation for the data and feedback channels in MISO-FDD systems

In frequency-division duplex (FDD) systems, channel-state information (CSI) is estimated by the receiver and then fed back to the transmitter through a feedback link, which inevitably requires additional bandwidth and power. In this letter, we jointly study optimal bandwidth allocation between the data channel, modeled as a flat-fading multiple-input single-output (MISO) channel, and the feedback channel for maximum average throughput in the data channel using a beamforming scheme. We consider two models of the partial CSI at the transmitter (CSIT): the noisy CSIT, modeled as jointly Gaussian with the actual channel state, and the quantized CSIT. In the first model, we use distortion-rate theory to relate the CSIT accuracy to the feedback-link bandwidth. In the second model, we derive a lower bound on the achievable rate of the data channel based on the ensemble of a set of random quantization codebooks. We show that in the MISO flat-fading channel case, beamforming based on feedback CSI can achieve an average rate larger than the capacity without CSIT under a wide range of mobility conditions.     

On the Expected Rate of Slowly Fading Channels With Quantized Side Information

We study a multiple-layer variable-rate system employing quantized feedback to maximize the expected rate over a single-input single-output slowly fading Gaussian channel. The transmitter uses partial channel-state information, which is obtained via an optimized resolution-constrained feedback link, to adapt the power and to assign code layer rates, subject to different power constraints. To systematically design the system parameters, we develop a simple iterative algorithm that successfully exploits results in the study of parallel broadcast channels. We present the necessary and sufficient conditions for single-layer coding to be optimal, irrespective of the number of code layers that the system can afford. Unlike in the ergodic case, even coarsely quantized feedback is shown to improve the expected rate considerably. Our results also indicate that with as little as one bit of feedback information, the role of multilayer coding reduces significantly     

Limited Feedback Beamforming Over Temporally-Correlated Channels

Feedback of quantized channel state information (CSI), called limited feedback, enables transmit beamforming in multiple-input-multiple-output (MIMO) wireless systems with a small amount of overhead. Due to its efficiency, beamforming with limited feedback has been adopted in several wireless communication standards. Prior work on limited feedback commonly adopts the block fading channel model where temporal correlation in wireless channels is neglected. In this paper, we consider temporally correlated channels and design single-user transmit beamforming with limited feedback. Analytical results concerning CSI feedback are derived by modeling quantized CSI as a first-order finite-state Markov chain. These results include the information rate of the CSI quantizer output, the bit rate a CSI feedback channel is required to support, and the effect of feedback delay on throughput. In particular, based on the theory of Markov chain convergence rate, feedback delay is proved to reduce the throughput gain due to CSI feedback at least exponentially. Furthermore, an algorithm is proposed for CSI feedback compression in time. Combining the results in this work leads to a new method for designing limited feedback beamforming as demonstrated by a design example.     

Optimal transmission strategies and impact of correlation in multiantenna systems with different types of channel state information

We study the optimal transmission strategy of a multiple-input single-output (MISO) wireless communication link. The receiver has perfect channel state information (CSI), while the transmitter has different types of CSI, i.e., either perfect CSI, or no CSI, or long-term knowledge of the channel covariance matrix. For the case in which the transmitter knows the channel covariance matrix, it was recently shown that the optimal eigenvectors of the transmit covariance matrix correspond with the eigenvectors of the channel covariance matrix. However, the optimal eigenvalues are difficult to compute. We derive a characterization of the optimum power allocation. Furthermore, we apply this result to provide an efficient algorithm which computes the optimum power allocation. In addition to this, we analyze the impact of correlation on the ergodic capacity of the MISO system with different CSI schemes. At first, we justify the belief that equal power allocation is optimal if the transmitter is uninformed and the transmit antennas are correlated. Next, we show that the ergodic capacity with perfect CSI and without CSI at the transmitter is Schur-concave, i.e., the more correlated the transmit antennas are, the less capacity is achievable. In addition, we show that the ergodic capacity with covariance knowledge at the transmitter is Schur-convex with respect to the correlation properties. These results completely characterize the impact of correlation on the ergodic capacity in MISO systems. Furthermore, the capacity loss or gain due to correlation is quantified. For no CSI and perfect CSI at the transmitter, the capacity loss due to correlation is bounded by some small constant, whereas the capacity gain due to correlation grows unbounded with the number of transmit antennas in the case in which transmitter knows the channel covariance matrix. Finally, we illustrate all theoretical results by numerical simulations.     

A broadcast approach for a single-user slowly fading MIMO channel

A broadcast transmission strategy for the slowly fading Gaussian multiple-input multiple-output (MIMO) channel is introduced. This broadcast strategy is an extension of the single-input single-output (SISO) broadcast approach. Perfect channel state information (CSI) is assumed known at the receiver end only. This strategy facilitates to adapt the reliably decoded rate to the actual channel state without having any feedback link to the transmitter. Transmission of layered coded information is motivated by the theory of majorization. We derive the basic equations characterizing achievable rates of the strategy. Several ad hoc approximations to the achievable region are considered and their performance is compared with the SISO setting and the ergodic capacity. It has been demonstrated that a single-layer outage approach is reasonably efficient in the MIMO setting in terms of the average reliably decoded rate. A multiple-access channel (MAC) broadcast approach is also applied for the MIMO case, and demonstrated to be relatively efficient.     

On the Capacity and Design of Limited Feedback Multiuser MIMO Uplinks

The theory of multiple-input–multiple-output (MIMO) technology has been well developed to increase fading channel capacity over single-input–single-output (SISO) systems. This capacity gain can often be leveraged by utilizing channel state information at the transmitter and the receiver. Users make use of this channel state information for transmit signal adaptation. In this correspondence, we derive the capacity region for the MIMO multiple access channel (MIMO MAC) when partial channel state information is available at the transmitters, where we assume a synchronous MIMO multiuser uplink. The partial channel state information feedback has a cardinality constraint and is fed back from the basestation to the users using a limited rate feedback channel. Using this feedback information, we propose a finite codebook design method to maximize the sum rate. In this correspondence, the codebook is a set of transmit signal covariance matrices. We also derive the capacity region and codebook design methods in the case that the covariance matrix is rank one (i.e., beamforming). This is motivated by the fact that beamforming is optimal in certain conditions. The simulation results show that when the number of feedback bits increases, the capacity also increases. Even with a small number of feedback bits, the performance of the proposed system is close to an optimal solution with the full feedback.      

On the error exponent for memoryless flat fading channels withchannel-state-information feedback

We derive the random coding error exponent for the time-independent flat fading channel with perfect knowledge of the channel state information (CSI) at both the receiver and the transmitter. That is, the CSI is feedback from the receiver to the transmitter. In such a situation, the transmitter is capable of optimizing the power allocation of the transmitted signal according to the fading state in order to obtain, for our case, the best error exponent. The power scheme obtained here is different from the water-pouring one, which is known to maximize the channel capacity     

On the average rate performance of hybrid-ARQ in quasi-static fading channels

The problem of efficient communication over a scalar quasi-static fading channel is considered. The single-layer transmission (SLT) and multi-layer transmission (MLT) schemes do not require any knowledge of the channel state information (CSI) at the transmitter, but their performance is also limited. It is shown that using Hybrid-ARQ (HARQ) can significantly improve the average rate performance, provided that the rate assignment between different ARQ rounds is carefully chosen. The average rate performance of several HARQ schemes is optimized and compared. In addition, optimal power allocation among retransmissions is derived and shown to further increase the average rate. This power allocation gain is remarkable at low signal-to-noise ratio (SNR), but becomes negligible at high SNR. Comparison of two different types of limited feedback, sequential feedback (ARQ) and one-shot feedback (quantized CSI), is made from several perspectives. Although the optimization problem is formed with respect to the average rate, simulation results give a comprehensive comparison under different metrics, including average rate, outage probability, and the combination of both. Substantial performance improvement is observed with even one ARQ retransmission in all simulations. More importantly, this gain appears to be robust with respect to the fading distributions.     

Transmit antenna selection based strategies in MISO communication systems with low-rate channel state feedback

The performance of multiple-antenna communication systems is known to critically depend on the amount of channel state information (CSI) available at the transmitter. In the low-rate CSI feedback case, an important problem is what kind of information should be submitted to the transmitter in each feedback cycle and what is the optimal transmission strategy in this case. In this paper, we address this problem in the multiple-input single-output (MISO) case by analytically comparing the bit error rate (BER) performance of different low-rate feedback based transmitter strategies involving various combinations of transmit antenna selection, Alamouti's spacetime coding, and adaptive power allocation.     

Power allocation in a transmit diversity system with mean channel gain information

We study the power allocation problem in a transmit diversity wireless system with mean channel gain information. In Rayleigh fading for a given set of mean channel gains and nodes, we seek to find the power allocation that minimizes the outage probability subject to a total power constraint. The optimal solution is shown to be computationally intensive when the number of channels is large. Instead, we derive a simple solution based on the upper bound to the outage probability which can be summarized as equal power allocation with channel selection. Numerical results show that the proposed solution is near-optimal over a wide range of parameter values. The problem addressed and the solution are relevant to a decode-and-forward cooperative relaying system with only partial channel information available to the relays.     

On the Optimality of Beamforming with Quantized Feedback

The ergodic capacity of a fading vector channel with multiple transmit antennas and a single receive antenna is explored. Perfect channel information is assumed to be available at the receiver while the transmitter has only partial knowledge of the direction of the user's channel vector based on quantized feedback. We present necessary and sufficient conditions for the optimality of beamforming in such systems. The conditions are applicable to all quantized feedback scenarios regardless of the channel distribution, number of transmit antennas, number of quantization vectors or transmit power. The optimality conditions are closely related to the iteration conditions of the Lloyd algorithm, revealing an interesting link between the optimality of beamforming and the optimality of the vector quantizers. Using the conditions, we prove the capacity optimality of beamforming for several quantized feedback scenarios such as the antenna-selection scheme. We also point out examples of quantized feedback scenarios where beamforming is not optimal. We find that for the independent identically distributed Rayleigh fading channel with more than a single bit of quantized feedback, there is no capacity benefit from increasing the number of antennas beyond the number of quantization vectors. Extensions of the necessary and sufficient optimality condition to the multiple-input multiple-output case are also provided.     

Capacity and optimal power allocation for fading broadcast channels with minimum rates

We derive the capacity region and optimal power allocation scheme for a slowly fading broadcast channel in which minimum rates must be maintained for each user in all fading states, assuming perfect channel state information at the transmitter and at all receivers. We show that the minimum-rate capacity region can be written in terms of the ergodic capacity region of a broadcast channel with an effective noise determined by the minimum rate requirements. This allows us to characterize the optimal power allocation schemes for minimum-rate capacity in terms of the optimal power allocations schemes that maximize ergodic capacity of the broadcast channel with effective noise. Numerical results are provided for different fading broadcast channel models.     

Statistical channel knowledge-based optimum power allocation for relaying protocols in the high SNR regime

We are concerned with transmit power optimization in a wireless relay network with various cooperation protocols. With statistical channel knowledge (in the form of knowledge of the fading distribution and the path loss information across all the nodes) at the transmitters and perfect channel state information at the receivers, we derive the optimal power allocation that minimizes high signal-to-noise ratio (SNR) approximations of the outage probability of the mutual information (MI) with amplify-and-forward (AF), decode-and-forward (DF) and distributed space-time coded (DSTC) relaying protocols operating over Rayleigh fading channels. We demonstrate that the high SNR approximation-based outage probability expressions are convex functions of the transmit power vector, and the nature of the optimal power allocation depends on whether or not a direct link between the source and the destination exists. Interestingly, for AF and DF protocols, this allocation depends only on the ratio of mean channel power gains (i.e., the ratio of the source-relay gain to the relay-destination gain), whereas with a DSTC protocol this allocation also depends on the transmission rate when a direct link exists. In addition to the immediate benefits of improved outage behavior, our results show that optimal power allocation brings impressive coding gains over equal power allocation. Furthermore, our analysis reveals that the coding gain gap between the AF and DF protocols can also be reduced by the optimal power allocation     

Throughput maximization over slowly fading channels using quantized and erroneous feedback

We design a conceptual transmission scheme that adjusts rate and power of data codewords to send them over a slowly fading channel, when quantized and possibly erroneous channel state information (CSI) is available at the transmitter. The goal is to maximize the data throughput or the expected data rate using a multi-layer superposition coding technique and temporal power control at the transmitter. The main challenge here is to design a CSI quantizer structure for a noisy feedback link. This structure resembles conventional joint source and channel coding schemes, however, with a newly introduced quasi-gray bit-mapping. Our results show that with proper CSI quantizer design, even erroneous feedback can provide performance gains. Also, with an unreliable feedback link, superposition coding provides significant gains when feedback channel is poorly conditioned and channel uncertainty at the transmitter is severe, whereas power control is more effective with more reliable feedback.     

Capacity and optimal resource allocation for fading broadcastchannels .I. Ergodic capacity

In multiuser wireless systems, dynamic resource allocation between users and over time significantly improves efficiency and performance. In this two-part paper, we study three types of capacity regions for fading broadcast channels and obtain their corresponding optimal resource allocation strategies: the ergodic (Shannon) capacity region, the zero-outage capacity region, and the outage capacity region with nonzero outage. We derive the ergodic capacity region of an M-user fading broadcast channel for code division (CD), time division (TD), and frequency division (FD), assuming that both the transmitter and the receivers have perfect channel side information (CSI). It is shown that by allowing dynamic resource allocation, TD, FD, and CD without successive decoding have the same ergodic capacity region, while optimal CD has a larger region. Optimal resource allocation policies are obtained for these different spectrum-sharing techniques. A simple suboptimal policy is also proposed for TD and CD without successive decoding that results in a rate region quite close to the ergodic capacity region. Numerical results are provided for different fading broadcast channels     

Secure Communication Over Fading Channels

The fading broadcast channel with confidential messages (BCC) is investigated, where a source node has common information for two receivers (receivers 1 and 2), and has confidential information intended only for receiver 1. The confidential information needs to be kept as secret as possible from receiver 2. The broadcast channel from the source node to receivers 1 and 2 is corrupted by multiplicative fading gain coefficients in addition to additive Gaussian noise terms. The channel state information (CSI) is assumed to be known at both the transmitter and the receivers. The parallel BCC with independent subchannels is first studied, which serves as an information-theoretic model for the fading BCC. The secrecy capacity region of the parallel BCC is established, which gives the secrecy capacity region of the parallel BCC with degraded subchannels. The secrecy capacity region is then established for the parallel Gaussian BCC, and the optimal source power allocations that achieve the boundary of the secrecy capacity region are derived. In particular, the secrecy capacity region is established for the basic Gaussian BCC. The secrecy capacity results are then applied to study the fading BCC. The ergodic performance is first studied. The ergodic secrecy capacity region and the optimal power allocations that achieve the boundary of this region are derived. The outage performance is then studied, where a long-term power constraint is assumed. The power allocation is derived that minimizes the outage probability where either the target rate of the common message or the target rate of the confidential message is not achieved. The power allocation is also derived that minimizes the outage probability where the target rate of the confidential message is not achieved subject to the constraint that the target rate of the common message must be achieved for all channel states.     

Design Guidelines for Training-Based MIMO Systems With Feedback

In this paper, we study the optimal training and data transmission strategies for block fading multiple-input multiple-output (MIMO) systems with feedback. We consider both the channel gain feedback (CGF) system and the channel covariance feedback (CCF) system. Using an accurate capacity lower bound as a figure of merit that takes channel estimation errors into account, we investigate the optimization problems on the temporal power allocation to training and data transmission as well as the training length. For CGF systems without feedback delay, we prove that the optimal solutions coincide with those for nonfeedback systems. Moreover, we show that these solutions stay nearly optimal even in the presence of feedback delay. This finding is important for practical MIMO training design. For CCF systems, the optimal training length can be less than the number of transmit antennas, which is verified through numerical analysis. Taking this fact into account, we propose a simple yet near optimal transmission strategy for CCF systems, and derive the optimal temporal power allocation over pilot and data transmission.     

基于部分信道信息的自适应资源分配

在保证一定吞吐量前提下,为了降低传输功率,文中提出了一种基于部分信道反馈信息的多用户OFDM系统子载波分配方案。该方案利用少量已反馈子载波的状态信息来线性推导未反馈子载波的信道增益。仿真结果表明,在平坦瑞利信道衰落中,相比传统方式该方案在不增加反馈开销的前提下该方案能够大幅度地改善系统的性能,提高资源利用率。     

空间相关莱斯衰落信道下基于部分信道信息的多用户预编码与调度算法

在空间相关的莱斯衰落信道模型下,针对多用户MIMO(Multiple-Input Multiple-Output)系统潜在的多用户分集增益和空间分集增益,该文提出了一种基于部分信道信息的多用户预编码与调度算法。结合部分瞬时信道信息和统计信息,利用约束最大似然估计对各用户信道矢量进行估计,然后利用估计的各用户信道调度多个用户进行预编码。仿真结果表明,该方案以较少的反馈开销,获得了较大的性能增益。     

The Optimality of Transmit Beamforming: A Unified View

The optimality of transmit beamforming for a multiple antenna system with partial/limited feedback is investigated and a single general necessary and sufficient condition for beamforming to achieve ergodic capacity is derived. The condition obtained is universal - applicable to all partial/limited feedback scenarios in all ergodic fading channel distributions regardless of the number of transmit/receive antennas or transmit power. Using the universal condition we explore the optimality of beamforming for the quantized mean feedback scheme, which unifies previous results for the separate cases of mean feedback and quantized feedback. Numerical results are provided to complement the analysis