Optimum power control over fading channels

We study optimal constant-rate coding schemes for a block-fading channel with strict transmission delay constraint, under the assumption that both the transmitter and the receiver have perfect channel-state information. We show that the information outage probability is minimized by concatenating a standard “Gaussian” code with an optimal power controller, which allocates the transmitted power dynamically to the transmitted symbols. We solve the minimum outage probability problem under different constraints on the transmitted power and we derive the corresponding power-allocation strategies. In addition, we propose an algorithm that approaches the optimal power allocation when the fading statistics are not known. Numerical examples for different fading channels are provided, and some applications discussed. In particular, we show that minimum outage probability and delay-limited capacity are closely related quantities, and we find a closed-form expression for the delay-limited capacity of the Rayleigh block-fading channel with transmission over two independent blocks. We also discuss repetition diversity and its relation with direct-sequence or multicarrier spread-spectrum transmission. The optimal power-allocation strategy in this case corresponds to selection diversity at the transmitter. From the single-user point of view considered in this paper, there exists an optimal repetition diversity order (or spreading factor) that minimizes the information outage probability for given rate, power, and fading statistics     

Capacity of multiple-antenna systems with both receiver and transmitter channel state information

The capacity of multiple-antenna systems operating in Rayleigh flat fading is considered under the assumptions that channel state information (CSI) is available at both transmitter and receiver, and that the transmitter is subjected to an average power constraint. First, the capacity of such systems is derived for the special case of multiple transmit antennas and a single receive antenna. The optimal power-allocation scheme for such a system is shown to be a water-filling algorithm, and the corresponding capacity is seen to be the same as that of a system having multiple receive antennas (with a single transmitter antenna) whose outputs are combined via maximal ratio combining. A suboptimal adaptive transmission technique that transmits only over the antenna having the best channel is also proposed for this special case. It is shown that the capacity of such a system under the proposed suboptimal adaptive transmission scheme is the same as the capacity of a system having multiple receiver antennas (with a single transmitter antenna) combined via selection combining. Next, the capacity of a general system of multiple transmitter and receiver antennas is derived together with an equation that determines the cutoff value for such a system. The optimal power allocation scheme for such a multiple-antenna system is given by a matrix water-filling algorithm. In order to eliminate the need for cumbersome numerical techniques in solving the cutoff equation, approximate expressions for the cutoff transmission value are also provided. It is shown that, compared to the case in which there is only receiver CSI, large capacity gains are available with optimal power and rate adaptation schemes. The increased capacity is shown to come at the price of channel outage, and bounds are derived for this outage probability.     

Optimal power control over multiple time-scale fading channels with service outage constraints

This paper considers the power-control problem for a fading channel in an information-theoretic framework. We derive power-control schemes to optimize ergodic capacity, outage capacity, and capacity with a service outage constraint. The novelty in the paper lies in the use of a two-time-scale fading process and its implications for the channel-state information available at the transmitter.     

Capacity of correlated MIMO Rayleigh channels

Abstract-This paper presents some exact results on the capacity of multiple-input-multiple-output (MIMO) channels subject to correlated Rayleigh fading when perfect channel state information (CSI) is known at the receiver. The authors focus on the semicorrelated scenario in which correlation exists either at the transmitter or at the receiver., They consider two cases: 1) the transmitter does not have any CSI and as such allocates power equally among transmitter antennas and 2) the transmitter only knows the statistical distribution of the channel. The first case derives the moment generating function (MGF) of the mutual information (MI) and then deduces from this MGF the mean MI. The authors also study the cumulative distribution function (CDF) of the MI, which can serve as an upper bound to the outage probability under the capacity versus outage formulation when the channel is nonergodic. The second case studies the capacity achieved by optimum power-loading and beamforming schemes based on covariance feedback. Numerical results illustrate that the full capacity of MIMO systems can be preserved even for relatively high values of correlation coefficients.     

Exponential Diversity Achieving Spatio–Temporal Power Allocation Scheme for Fading Channels

In this paper, we analyze optimal (in space and time) adaptive power transmission policies for fading channels when the channel-state information (CSI) at the transmitter (CSIT) and the receiver (CSIR) is available. The transmitter has a long-term (time) average power constraint. There can be multiple antennas at the transmitter and at the receiver. The channel experiences Rayleigh fading. We consider beamforming and space-time coded systems with perfect/imperfect CSIT and CSIR. The performance measure is the bit error rate (BER). We show that in both coded and uncoded systems, our power allocation policy provides exponential diversity order if perfect CSIT is available. We also show that, if the quality of CSIT degrades then the exponential diversity is retained in the low SNR region but we get only polynomial diversity in the high SNR region. Another interesting conclusion is that in case of imperfect CSIT and CSIR, knowledge of CSIT at the receiver is very important. Finally, for the optimal power control policy of the uncoded system we find the error-exponents which provide the rate versus diversity-order tradeoff for this policy. This tradeoff is of an entirely different nature than the well-known Zheng-Tse tradeoff.     

Performance analysis of adaptive loading OFDM under Rayleigh fading

In this paper, we investigate the performance of adaptive loading orthogonal frequency-division multiplexing (OFDM) under Rayleigh fading with maximal ratio-combining (MRC) diversity at the receiver. We assume that channel-state information is available at both the transmitter and the receiver. Closed-form expressions for the lower bound on the average capacity of OFDM transmission under Rayleigh fading are provided for ideal MRC diversity. Simple approximate expressions for the average capacity of the Rayleigh-fading channel are also provided for the high signal-to-noise ratio (SNR) case. In the second part of this paper, a maximum-rate adaptive-loading strategy is derived for uncoded quadrature-amplitude-modulation modulated OFDM. Simple lower bound expressions and high-SNR approximations are provided for the average spectral efficiency of the maximum-rate adaptive-loaded uncoded OFDM under Rayleigh-fading channel conditions. According to the results, the performance of the uncoded adaptive-loading OFDM is about 8.5 dB inferior to the capacity bound at 10/sup -5/ symbol error probability under frequency-selective Rayleigh fading.     

Fading correlations in wireless MIMO communication systems

We investigate the effects of fading correlations on wireless communication systems employing multiple antennas at both the receiver and the transmitter side of the link, so called multiple-input multiple-output (MIMO) systems. It turns out that the amount of transmitter sided channel knowledge plays an important part when dealing with fading correlations. Furthermore, the possible availability of time diversity in a time-selective channel can have essential influence on performance. To study the influence of time-selectivity, the concept of sample-mean outage is introduced and applied to information theoretic measures, like capacity or cutoff rate. It will be shown, that in some cases correlated fading may offer better performance than uncorrelated fading permits, which is due to exploitable antenna gain, that will also be defined in a general form for MIMO systems.     

MIMO系统信道容量研究

针对单用户MIMO系统信道的容量特性展开研究。首先详细推导了无衰落信道下信道容量表达式,然后重点分析了瑞利衰落信道下,接收端已知信道状态信息,发射端已知信道状态分布时的容量特性。最后分别针对瑞利衰落信道下,采用发射分集、接收分集以及BLAST传输结构的系统容量进行仿真。仿真结果表明:给定发射功率,独立的瑞利衰落信道条件下,MIMO系统容量随最小天线数目的增加而线性增加,极大地提高了系统容量。     

Secrecy outage performance analysis of MIMO underlay cognitive radio networks with delayed CSI and transmitter antenna selection

Cognitive radio network is an emerging solution to deal with spectrum scarcity and to utilize the radio spectrum in opportunistic and efficient manner. Secure data transmission is one of the important issues in these kind of networks. This work studies the secrecy outage performance of a multiple-input multiple-output underlay cognitive wiretap radio network system over Rayleigh fading channel with delayed channel state information. This work considers that the secondary transmitter is equipped with multiple antennas and confidential information is transmitted from to multiantenna receiver in the presence of multiantenna eavesdropper. Further, the transmit antenna selection scheme is considered at secondary transmitter to reduce the complexity of antenna selection and to make it more practicable. To improve the quality of signal, this work considers maximal ratio combining (MRC) at secondary receiver, while selection combining and MRC techniques are utilized at the eavesdropper. The closed form expression for exact, asymptotic, and intercept secrecy outage probability has been derived, and the simulation is done for the validation of analytical results. The derived results reveal deterioration of channel secrecy performance with outdated channel state information, and the eavesdropper with outdated channel state information has also an adverse effect. Moreover, the diversity order that can be achieved in underlay cognitive radio network with outdated channel state information is unity.     

Capacity and optimal resource allocation for fading broadcastchannels .II. Outage capacity

For pt.I see ibid., vol.47, no.3, p.1083-1102 (2002). We study three 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 capacity region with outage. In this paper, we derive the outage capacity regions of fading broadcast channels, assuming that both the transmitter and the receivers have perfect channel side information. These capacity regions and the associate optimal resource allocation policies are obtained for code division (CD) with and without successive decoding, for time division (TD), and for frequency division (FD). We show that in an M-user broadcast system, the outage capacity region is implicitly obtained by deriving the outage probability region for a given rate vector. Given the required rate of each user, we find a strategy which bounds the outage probability region for different spectrum-sharing techniques. The corresponding optimal power allocation scheme is a multiuser generalization of the threshold-decision rule for a single-user fading channel. Also discussed is a simpler minimum common outage probability problem under the assumption that the broadcast channel is either not used at all when fading is severe or used simultaneously for all users. Numerical results for the different outage capacity regions are obtained for the Nakagami-m (1960) fading model     

Communication on the Grassmann manifold: a geometric approach tothe noncoherent multiple-antenna channel

We study the capacity of multiple-antenna fading channels. We focus on the scenario where the fading coefficients vary quickly; thus an accurate estimation of the coefficients is generally not available to either the transmitter or the receiver. We use a noncoherent block fading model proposed by Marzetta and Hochwald (see ibid. vol.45, p.139-57, 1999). The model does not assume any channel side information at the receiver or at the transmitter, but assumes that the coefficients remain constant for a coherence interval of length T symbol periods. We compute the asymptotic capacity of this channel at high signal-to-noise ratio (SNR) in terms of the coherence time T, the number of transmit antennas M, and the number of receive antennas N. While the capacity gain of the coherent multiple antenna channel is min{M, N} bits per second per Hertz for every 3-dB increase in SNR, the corresponding gain for the noncoherent channel turns out to be M* (1 - M*/T) bits per second per Hertz, where M*=min{M, N, [T/2]}. The capacity expression has a geometric interpretation as sphere packing in the Grassmann manifold     

Error probability of coded STBC systems in block fading environments

In this letter, a union bound on the error probability of coded multi-antenna systems over block fading channels is derived. The bound is based on uniform interleaving of the coded sequence prior to transmission over the channel. Using this argument the distribution of error bits over the fading blocks is computed and the corresponding pair wise error probability (PEP) is derived. We consider coded systems that concatenate a binary code with a space-time block code (STBC). Coherent detection is assumed with perfect and imperfect channel state information (CSI) at the receiver, where imperfect CSI is obtained using pilot-aided estimation. Under channel estimation environments, the tradeoff between channel diversity and channel estimation is investigated and the optimal channel memory is approximated analytically. Results show that the performance degradation due to channel memory decreases as the number of transmit antennas is increased. Moreover, the optimal channel memory increases with increasing the number of transmit antennas.     

Capacity of fading channels with channel side information

We obtain the Shannon capacity of a fading channel with channel side information at the transmitter and receiver, and at the receiver alone. The optimal power adaptation in the former case is “water-pouring” in time, analogous to water-pouring in frequency for time-invariant frequency-selective fading channels. Inverting the channel results in a large capacity penalty in severe fading     

Gallager?s Exponent for MIMO Channels: A Reliability-Rate Tradeoff

In this paper, we derive Gallager's random coding error exponent for multiple-input multiple-output (MIMO) Rayleigh block-fading channels, assuming no channel-state information (CSI) at the transmitter and perfect CSI at the receiver. This measure gives insight into a fundamental tradeoff between the communication reliability and information rate of MIMO channels, enabling to determine the required codeword length to achieve a prescribed error probability at a given rate below the channel capacity. We quantify the effects of the number of antennas, channel coherence time, and spatial fading correlation on the MIMO exponent. In addition, the general formulae for the ergodic capacity and the cutoff rate in the presence of spatial correlation are deduced from the exponent expressions. These formulae are applicable to arbitrary structures of transmit and receive correlation, encompassing all the previously known results as special cases of our expressions.     

On the capacity of OFDM-based spatial multiplexing systems

This paper deals with the capacity behavior of wireless orthogonal frequency-division multiplexing (OFDM)-based spatial multiplexing systems in broad-band fading environments for the case where the channel is unknown at the transmitter and perfectly known at the receiver. Introducing a physically motivated multiple-input multiple-output (MIMO) broad-band fading channel model, we study the influence of physical parameters such as the amount of delay spread, cluster angle spread, and total angle spread, and system parameters such as the number of antennas and antenna spacing on ergodic capacity and outage capacity. We find that, in the MIMO case, unlike the single-input single-output (SISO) case, delay spread channels may provide advantages over flat fading channels not only in terms of outage capacity but also in terms of ergodic capacity. Therefore, MIMO delay spread channels will in general provide both higher diversity gain and higher multiplexing gain than MIMO flat fading channels     

On the Capacity of Time-Varying Channels With Periodic Feedback

The capacity of time-varying channels with periodic feedback at the transmitter is evaluated. It is assumed that the channel-state information (CSI) is perfectly known at the receiver and is fed back to the transmitter at the regular time intervals. The system capacity is investigated in two cases: 1) finite-state Markov channel, and 2) additive white Gaussian noise channel with time-correlated fading. In the first case, it is shown that the capacity is achievable by multiplexing multiple codebooks across the channel. In the second case, the channel capacity and the optimal adaptive coding is obtained. It is shown that the optimal adaptation can be achieved by a single Gaussian codebook, while adaptively allocating the total power based on the side information at the transmitter.     

多天线频谱共享认知网络保密中断概率分析

针对单输入多输出认知无线电网络,研究了瑞利衰落信道下采用最大比合并时保密中断性能。在所研究的系统中,次用户发射机发送机密信息给另一个次用户接收机,次用户接收机配备多个天线并且采用最大比例合并多个接收信号。同时,拥有多个天线窃听者也采用最大比合并方案偷听次用户发射机和次用户接收机之间传送的信息。频谱共享下次用户发射机工作时必须保证主用户的服务质量。推导了保密中断概率的精确表达式,分析了系统保密中断概率渐近性能。仿真结果验证了分析的正确性。     

Limited feedback unitary precoding for orthogonal space-time block codes

Orthogonal space-time block codes (OSTBCs) are a class of easily decoded space-time codes that achieve full diversity order in Rayleigh fading channels. OSTBCs exist only for certain numbers of transmit antennas and do not provide array gain like diversity techniques that exploit transmit channel information. When channel state information is available at the transmitter, though, precoding the space-time codeword can be used to support different numbers of transmit antennas and to improve array gain. Unfortunately, transmitters in many wireless systems have no knowledge about current channel conditions. This motivates limited feedback precoding methods such as channel quantization or antenna subset selection. This paper investigates a limited feedback approach that uses a codebook of precoding matrices known a priori to both the transmitter and receiver. The receiver chooses a matrix from the codebook based on current channel conditions and conveys the optimal codebook matrix to the transmitter over an error-free, zero-delay feedback channel. A criterion for choosing the optimal precoding matrix in the codebook is proposed that relates directly to minimizing the probability of symbol error of the precoded system. Low average distortion codebooks are derived based on the optimal codeword selection criterion. The resulting design is found to relate to the famous applied mathematics problem of subspace packing in the Grassmann manifold. Codebooks designed by this method are proven to provide full diversity order in Rayleigh fading channels. Monte Carlo simulations show that limited feedback precoding performs better than antenna subset selection.     

LDPC-based space-time coded OFDM systems over correlated fadingchannels: Performance analysis and receiver design

We consider a space-time coded (STC) orthogonal frequency-division multiplexing (OFDM) system with multiple transmitter and receiver antennas over correlated frequency- and time-selective fading channels. It is shown that the product of the time-selectivity order and the frequency-selectivity order is a key parameter to characterize the outage capacity of the correlated fading channel. It is also observed that STCs with large effective lengths and ideal built-in interleavers are more effective in exploiting the natural diversity in multiple-antenna correlated fading channels. We then propose a low-density parity-check (LDPC)-code-based STC-OFDM system. Compared with the conventional space-time trellis code (STTC), the LDPC-based STC can significantly improve the system performance by exploiting both the spatial diversity and the selective-fading diversity in wireless channels. Compared with the previously proposed turbo-code-based STC scheme, LDPC-based STC exhibits lower receiver complexity and more flexible scalability. We also consider receiver design for LDPC-based STC-OFDM systems in unknown fast fading channels and propose a novel turbo receiver employing a maximum a posteriori expectation-maximization (MAP-EM) demodulator and a soft LDPC decoder, which can significantly reduce the error floor in fast fading channels with a modest computational complexity. With such a turbo receiver, the proposed LDPC-based STC-OFDM system is a promising solution to highly efficient data transmission over selective-fading mobile wireless channels     

多中继与多用户选择的中继系统安全性能分析

为了考察使用多中继选择与多用户选择的放大转发（AF）中继系统的物理层安全性能,推导了其在瑞利衰落信道上和联合发送天线选择/接收最大比合并天线分集下的非零安全容量概率和安全中断概率的精确表达式以及在高信噪比下的渐近安全中断概率解析表达式。AF中继系统的非零安全容量概率和安全中断概率的数值计算和仿真结果相吻合,验证了以上理论分析的正确性;分析结果表明,其安全分集增益为源节点发射天线数、最优中继节点接收天线数、中继节点数的三者乘积与最优中继节点发射天线数、最优用户接收天线数、用户数三者乘积之间的最小值,且与窃听信道无关。