Achievable Rates with Imperfect Transmitter Side Information Using a Broadcast Transmission Strategy

rdquoWe investigate the performance of the broadcast approach for various fading distributions, which correspond to different models of partial transmit channel state information (CSI). The first model considered is the quantized limited feedback. In this model, the receiver can send as feedback only a finite number of bits describing the fading gain. We derive the optimal power allocation for the broadcast approach for the quantized feedback model. For a Rayleigh fading channel, numerical results here show that if the feedback word can be longer than one bit, the broadcasting gain becomes negligible, due to diminished channel uncertainty. The second partial transmit CSI model is a stochastic Gaussian model with mean and variance information, which is commonly used for modeling the channel estimation error. In a single-input single-output (SISO) channel, this model also corresponds to the Ricean fading distribution, for which we derive maximal achievable broadcasting rates. We further consider a multiple-input single-output (MISO) channel, and derive the optimal power allocation strategy in a broadcast approach. Numerical results here show that uniform power allocation is preferable over beamforming power allocation in the region where broadcasting gain over single level coding is non-negligible.     

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.     

Optimized Transmission for Fading Multiple-Access and Broadcast Channels With Multiple Antennas

In mobile wireless networks, dynamic allocation of resources such as transmit powers, bit-rates, and antenna beams based on the channel state information of mobile users is known to be the general strategy to explore the time-varying nature of the mobile environment. This paper looks at the problem of optimal resource allocation in wireless networks from different information-theoretic points of view and under the assumption that the channel state is completely known at the transmitter and the receiver. In particular, the fading multiple-access channel (MAC) and the fading broadcast channel (BC) with additive Gaussian noise and multiple transmit and receive antennas are focused. The fading MAC is considered first and a complete characterization of its capacity region and power region are provided under various power and rate constraints. The derived results can be considered as nontrivial extensions of the work done by Tse and Hanly from the case of single transmit and receive antenna to the more general scenario with multiple transmit and receive antennas. Efficient numerical algorithms are proposed, which demonstrate the usefulness of the convex optimization techniques in characterizing the capacity and power regions. Analogous results are also obtained for the fading BC thanks to the duality theory between the Gaussian MAC and the Gaussian BC.     

Capacity Results for Block-Stationary Gaussian Fading Channels With a Peak Power Constraint

A peak-power-limited single-antenna block-stationary Gaussian fading channel is studied, where neither the transmitter nor the receiver knows the channel state information, but both know the channel statistics. This model subsumes most previously studied Gaussian fading models. The asymptotic channel capacity in the high signal-to-noise ratio (SNR) regime is first computed, and it is shown that the behavior of the channel capacity depends critically on the channel model. For the special case where the fading process is symbol-by-symbol stationary, it is shown that the codeword length must scale at least logarithmically with SNR in order to guarantee that the communication rate can grow logarithmically with SNR with decoding error probability bounded away from one. An expression for the capacity per unit energy is also derived. Furthermore, it is shown that the capacity per unit energy is achievable using temporal on–off signaling with optimally allocated on symbols, where the optimal on-symbol allocation scheme may depend on the peak power constraint.      

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.     

和速率约束下衰落高斯MIMO广播信道的和功率优化

 本文研究了在系统和速率一定的条件下有着高斯噪声的衰落MIMO广播信道和功率最小化问题.该问题通常存在于无线通信系统动态资源分配中,是和功率约束下衰落MIMO下行链路和速率最大化的互补问题.首先利用MIMO MAC和MIMO BC的对偶性,将问题描述和转化为凸最优化问题,在此基础上,利用子梯度法和二分法,设计了相应的快速迭代的多用户注水算法,用于计算基站的发射功率.理论分析和数值仿真结果表明,该算法全局有效地收敛于最小的和功率.     

Gaussian degraded relay channel with lossy state reconstruction

We consider a state reconstruction problem where the additive state process to a Gaussian degraded relay channel (GRC) is to be reconstructed at the receiver subject to some distortion/fidelity constraints. The state process we consider is Gaussian, independent and identically distributed (i.i.d.) and known a priori at the encoder as well as the relay. The receiver has to perform a lossy estimation of the state process, to within some prescribed distortion tolerance under a squared error distortion criterion. The setting also involves communicating messages across to the receiver, in addition to the estimation. Naturally, there is a tension between communication rate and state reconstruction fidelity. We are interested in the optimal trade-off between the distortion incurred at the receiver versus the rate at which messages can be communicated. We provide a complete characterization of the optimal rate versus distortion performance. The main contribution of the paper is a characterization of the fundamental limits of achievable rate versus distortion pairs in the Gaussian degraded relay model under consideration.     

The capacity region of broadcast channels with intersymbolinterference and colored Gaussian noise

We derive the capacity region for a broadcast channel with intersymbol interference (ISI) and colored Gaussian noise under an input power constraint. The region is obtained by first defining a similar channel model, the circular broadcast channel, which can be decomposed into a set of parallel degraded broadcast channels. The capacity region for parallel degraded broadcast channels is known. We then show that the capacity region of the original broadcast channel equals that of the circular broadcast channel in the limit of infinite block length, and we obtain an explicit formula for the resulting capacity region. The coding strategy used to achieve each point on the convex hull of the capacity region uses superposition coding on some or all of the parallel channels and dedicated transmission on the others. The optimal power allocation for any point in the capacity region is obtained via a multilevel water-filling. We derive this optimal power allocation and the resulting capacity region for several broadcast channel models     

A Unified Framework for Layered Transmission Over Fading and Packet Erasure Channels

We consider layered transmission of a successively refinable source over a quasi-static fading channel. We establish a duality relationship between this problem and that of packet transmission over erasure channels and use it to share solution techniques in both domains. For a Gaussian source and the fading channel, a low-complexity, optimal algorithm is proposed, and it is shown that the corresponding dual for packet erasure channels has a linear complexity as opposed to the quadratic complexity of the best known optimal algorithms in the literature. For non-Gaussian sources, the optimal rate allocation problem for fading channels is solved using the dual solution for erasure channels. It is also shown that a single-layer system is optimal for fading channels if the goal is to maximize the rate. Numerical results for multiple antenna Rayleigh fading channels are presented for Gaussian sources and practical image coders. It is shown that a few number of layers significantly improves the performance. Finally, we numerically show that for practical operating conditions, optimizing the asymptotic measure of distortion exponent is not enough when there are more than one transmit or receive antennas.     

Resource Allocation for Wireless Fading Relay Channels: Max-Min Solution

Resource allocation is investigated for fading relay channels under separate power constraints at the source and relay nodes. As a basic information-theoretic model for fading relay channels, the parallel relay channel is first studied, which consists of multiple independent three-terminal relay channels as subchannels. Lower and upper bounds on the capacity are derived, and are shown to match, and thus establish the capacity for the parallel relay channel with degraded subchannels. This capacity theorem is further demonstrated via the Gaussian parallel relay channel with degraded subchannels, for which the synchronized and asynchronized capacities are obtained. The capacity-achieving power allocation at the source and relay nodes among the subchannels is partially characterized for the synchronized case and fully characterized for the asynchronized case. The fading relay channel is then studied, which is based on the three-terminal relay channel with each communication link being corrupted by a multiplicative fading gain coefficient as well as an additive Gaussian noise term. For each link, the fading state information is assumed to be known at both the transmitter and the receiver. The source and relay nodes are allowed to allocate their power adaptively according to the instantaneous channel state information. The source and relay nodes are assumed to be subject to separate power constraints. For both the full-duplex and half-duplex cases, power allocations that maximize the achievable rates are obtained. In the half-duplex case, the power allocation needs to be jointly optimized with the channel resource (time and bandwidth) allocation between the two orthogonal channels over which the relay node transmits and receives. Capacities are established for fading relay channels that satisfy certain conditions.     

Adaptive source-channel subband video coding for wireless channels

This paper presents a general framework for combined source-channel coding within the context of subband coding. The unequal importance of subbands in reconstruction of the source is exploited by an appropriate allocation of source and channel coding rates for the coding and transmission of subbands over a noisy channel. For each subband, the source coding rate as well as the level of protection (quantified by the channel coding rate) are jointly chosen to minimize the total end-to-end mean-squared distortion suffered by the source. This allocation of source and channel coding rates is posed as a constrained optimization problem, and solved using a generalized bit allocation algorithm. The optimal choice of source and channel coding rates depends on the state of the physical channel. These results are extended to transmission over fading channels using a finite state model, where every state corresponds to an additive white Gaussian noise (AWGN) channel. A coding strategy is also developed that minimizes the average distortion when the channel state is unavailable at the transmitter. Experimental results are provided that demonstrate application of these combined source-channel coding strategies on video sequences     

Isotropic fading vector broadcast Channels:The scalar upper bound and loss in degrees of freedom

We propose a scalar upper bound on the capacity region of the isotropic fading vector broadcast channel in terms of the capacity region of a scalar fading broadcast channel. The scalar upper bound is applicable to the broad class of isotropic fading broadcast channels regardless of the distribution of the users' channel magnitudes, the distribution of the additive noise experienced by each user, or the amount of channel knowledge available at the receiver. Using this upper bound, we prove the optimality of the Alamouti scheme in a broadcast setting, extend the recent results on the capacity of nondegraded, fading scalar broadcast channels to nondegraded fading vector broadcast channels, and determine the capacity region of a fading vector Gaussian broadcast channel with channel magnitude feedback. We also provide an example of a Rayleigh-fading broadcast channel with no channel state information available to the receiver (CSIR), where the bound on the capacity region obtained by a naive application of the scalar upper bound is provably loose, because it fails to account for the additional loss in degrees of freedom due to lack of channel knowledge at the receiver. A tighter upper bound is obtained by separately accounting for the loss in degrees of freedom due to lack of CSIR before applying the scalar upper bound.     

On source coding, channel coding and spreading tradeoffs in a DS-CDMA system operating over frequency selective fading channels with narrowband interference

For a fixed total bandwidth expansion factor, we consider the problem of optimal bandwidth allocation among the source coder, the channel coder, and the spread-spectrum unit for a direct-sequence code-division multiple-access system operating over a frequency-selective fading channel with narrowband interference. Assuming a Gaussian source with the optimum scalar quantizer, and a binary convolutional code with soft-decision decoding, and further assuming that the self-interference is negligible, we obtain both a lower and an upper bound on the end-to-end average source distortion. The joint three-way constrained optimization of the source code rate, the channel code rate, and the spreading factor can be simplified into an unconstrained optimization problem over two variables. Upon fixing the channel code rate, we show that both upper and lower bound-based distortion functions are convex functions of the source code rate. Because an explicit solution for the optimum source code rate, i.e., one that minimizes the average distortion, is difficult to obtain, computer-based search techniques are employed. Numerical results are presented for the optimum source code rate and spreading factor, parameterized by the channel code rate and code constraint length. The optimal bandwidth allocation, in general, depends on the system and the channel conditions, such as the total number of active users, the average jammer-to-signal power ratio, and the number of resolved multipath components together with their power delay profile.     

Capacity Region and Optimum Power Control Strategies for Fading Gaussian Multiple Access Channels With Common Data

A Gaussian multiple access channel (MAC) with common data is considered. Capacity region when there is no fading is known in an implicit form. We provide an explicit characterization of the capacity region and provide a simpler encoding/decoding scheme than that mentioned in work by Slepian and Wolf. Next, we give a characterization of the ergodic capacity region when there is fading, and both the transmitters and the receiver know the channel perfectly. Then, we characterize the optimum power allocation schemes that achieve arbitrary rate tuples on the boundary of the capacity region. Finally, we provide an iterative method for the numerical computation of the ergodic capacity region and the optimum power control strategies.     

Outage analysis of the hybrid free-space optical and radio-frequency channel

We study the hybrid free-space optical (FSO) and radio-frequency (RF) channel from an information theoretic perspective. Since both links operate at vastly different carrier frequencies, we model the hybrid channel as a pair of parallel channels. Moreover, since the FSO channel signals at a higher rate than the RF channel, we incorporate this key feature in the parallel channel model. Both channels experience fading due to scintillation, which is slow compared to typical signalling rates. Under this framework, we study the fundamental limits of the hybrid channel. In particular, we analyse the outage probability in the large signal-to-noise ratio (SNR) regime, and obtain the outage diversity or SNR exponent of the hybrid system. First we consider the case when only the receiver has perfect channel state information (CSIR case), and obtain the exponents for general scintillation distributions. These exponents relate key system design parameters to the asymptotic outage performance and illustrate the benefits of using hybrid systems with respect to independent FSO or RF links. We next consider the case when perfect CSI is known at both the receiver and transmitter, and derive the optimal power allocation strategy that minimises the outage probability subject to peak and average power constraints. The optimal solution involves non-convex optimisation, which is intractable in practical systems. We therefore propose a suboptimal algorithm that achieves significant power savings (on the order of tens of dBs) over uniform power allocation. We show that the suboptimal algorithm has the same diversity as the optimal power allocation strategy.     

Multiaccess fading channels. I. Polymatroid structure, optimalresource allocation and throughput capacities

In multiaccess wireless systems, dynamic allocation of resources such as transmit power, bandwidths, and rates is an important means to deal with the time-varying nature of the environment. We consider the problem of optimal resource allocation from an information-theoretic point of view. We focus on the multiaccess fading channel with Gaussian noise, and define two notions of capacity depending on whether the traffic is delay-sensitive or not. We characterize the throughput capacity region which contains the long-term achievable rates through the time-varying channel. We show that each point on the boundary of the region can be achieved by successive decoding. Moreover, the optimal rate and power allocations in each fading state can be explicitly obtained in a greedy manner. The solution can be viewed as the generalization of the water-filling construction for single-user channels to multiaccess channels with arbitrary number of users, and exploits the underlying polymatroid structure of the capacity region     

Progressive source coding for a power constrained Gaussian channel

We consider the progressive transmission of a lossy source across a power constrained Gaussian channel using binary phase-shift keying modulation. Under the theoretical assumptions of infinite bandwidth, arbitrarily complex channel coding, and lossless transmission, we derive the optimal channel code rate and the optimal energy allocation per transmitted bit. Under the practical assumptions of a low complexity class of algebraic channel codes and progressive image coding, we numerically optimize the choice of channel code rate and the energy per bit allocation. This model provides an additional degree of freedom with respect to previously proposed schemes, and can achieve a higher performance for sources such as images. It also allows one to control bandwidth expansion or reduction     

Multiplexing Video on Multiuser Broadcast Channels

We propose a framework to address the problem of broadcasting a multiplicity of video sequences over a multiuser broadcast channel. The approach is intended to be general, without assumptions about specific video-coding or modulation techniques. However, we do assume the channel is Gaussian and exhibits quasi-static Rayleigh fading. Under the proposed framework, the algorithms seek to minimize the total distortion of multiple sequences broadcast simultaneously. To suit different applications, both greedy and long-term distortion metrics are considered. A salient aspect of this work is support for real-time video transport, hence delay and buffer constraints need to be accounted for. Under these constraints, the algorithms compute a jointly optimal source-rate and transmit-power allocation for all users under a power constraint. It turns out that problem can be formulated efficiently as a geometric program, which can be solved in different ways. In particular, we investigate a class of primal-dual convex algorithms. The complexity of the optimization is seen to scale well with the number of users. For the purpose of comparison, an orthogonal multiplexing scheme is also considered. Numerical results with H.264-coded video show that significant coding gains can be obtained.