Capacity of a mobile multiple-antenna communication link inRayleigh flat fading

We analyze a mobile wireless link comprising M transmitter and N receiver antennas operating in a Rayleigh flat-fading environment. The propagation coefficients between pairs of transmitter and receiver antennas are statistically independent and unknown; they remain constant for a coherence interval of T symbol periods, after which they change to new independent values which they maintain for another T symbol periods, and so on. Computing the link capacity, associated with channel coding over multiple fading intervals, requires an optimization over the joint density of T·M complex transmitted signals. We prove that there is no point in making the number of transmitter antennas greater than the length of the coherence interval: the capacity for M>T is equal to the capacity for M=T. Capacity is achieved when the T×M transmitted signal matrix is equal to the product of two statistically independent matrices: a T×T isotropically distributed unitary matrix times a certain T×M random matrix that is diagonal, real, and nonnegative. This result enables us to determine capacity for many interesting cases. We conclude that, for a fixed number of antennas, as the length of the coherence interval increases, the capacity approaches the capacity obtained as if the receiver knew the propagation coefficients     

Gaussian codes and weighted nearest neighbor decoding in fading multiple-antenna channels

We investigate the fading multiple-antenna channel. The decoder is assumed to possess imperfect channel fading information. A modified nearest neighbor decoder with an innovative weighting factor is introduced and an expression for the generalized mutual information (GMI), the achievable rate, is obtained. We show that under certain conditions the achievable rate is equivalent to that of a fading multiple-antenna Gaussian channel where fading is known to the receiver and is equal to the channel estimation, and where noise is due to both the channel noise and the channel estimation error. We show that for our communication scheme, the minimum mean square error (MMSE) channel estimator is optimal in the sense that it achieves the highest value of GMI, and hence the highest communication rate. Additionally, a training based multiple-input multiple-output (MIMO) scheme in a block-fading channel is investigated and it is shown that the number of degrees of freedom depends on the signal-to-noise ratio (SNR).     

Efficient use of side information in multiple-antenna datatransmission over fading channels

We derive performance limits for two closely related communication scenarios involving a wireless system with multiple-element transmitter antenna arrays: a point-to-point system with partial side information at the transmitter, and a broadcast system with multiple receivers. In both cases, ideal beamforming is impossible, leading to an inherently lower achievable performance as the quality of the side information degrades or as the number of receivers increases. Expected signal-to-noise ratio (SNR) and mutual information are both considered as performance measures. In the point-to-point case, we determine when the transmission strategy should use some form of beamforming and when it should not. We also show that, when properly chosen, even a small amount of side information can be quite valuable. For the broadcast scenario with an SNR criterion, we find the efficient frontier of operating points and show that even when the number of receivers is larger than the number of antenna array elements, significant performance improvements can be obtained by tailoring the transmission strategy to the realized channel     

多天线的发送分集系统中多用户分集的研究

研究了如何通过选择发送天线和天线组合来提高整个多用户多天线系统的性能。本文分别讨论了STOBC、选择式发送分集、相位加权等各种发送信号结构下系统的调度性能。和其它发送信号结构相比,STOBC对于调度性能有着很大危害。信道反馈信息越多,调度性能就越好。不同的发送天线选择和组合策略得到不同的性能。本文讨论了三种选择策略:max-max, max-sum和max-min。max-max的调度性能优于其它两种策略。因此,发送信号的结构和选择策略都严重影响着多用户分集。     

Capacity of a mobile multiple-antenna wireless link with isotropically random Rician fading

We analyze the capacity of a multiple-antenna wireless link with M antennas at the transmitter and N antennas at the receiver in a Rician fading channel when the channel is unknown at both the transmitter and the receiver. The Rician model is a nonstandard model with a Rayleigh component and an isotropically random rank-one specular component. The Rayleigh and specular components remain constant for T symbol periods, after which they change to completely independent realizations, and so on. To maximize mutual information over the joint density of T/spl middot/M complex transmitted signals it is sufficient to maximize over a joint density of min{T,M} real transmitted signal magnitudes. The capacity-achieving signal matrix is equal to the product of two independent matrices, a T/spl times/T isotropically random unitary matrix and a T/spl times/M real nonnegative diagonal matrix. If M>T, optimum signaling uses only T out of the M transmit antennas. We derive a novel lower bound on capacity which enables us to compute achievable rate regions for many cases. This lower bound is also valid for the case of purely Rayleigh-fading channels, where it has not been feasible, in general, to compute capacity, or mutual information. Our numerical results also indicate that the Rayleigh model is surprisingly robust: under our Rician model, up to half of the received energy can arrive via the specular component without significant reduction in capacity compared with the purely Rayleigh case.     

Impact of scattering on the capacity, diversity, and propagation range of multiple-antenna channels

The impact of scattering condition and array configuration on performances are inseparable in early analyses of multiple-antenna systems. An array-independent scattering model is introduced where three basic scattering mechanisms are modeled. Performance results become more intrinsic property of the scattering channel itself. For linear arrays of length L in an environment of total angle spread |/spl Omega/|, the ergodic capacity is shown to increase linearly with L|/spl Omega/| for large arrays. When antenna arrays reduce to practical sizes, the capacity scaling depends on the signal-to-noise ratio (SNR) as well. This implies that the number of antennas used should also depend on the SNR. In terms of outage capacity, the tradeoff between spatial multiplexing gain and diversity gain is shown to be very sensitive to the underlying scattering mechanisms. Finally, as |/spl Omega/| varies with the propagation range, the tradeoff among multiplexing gain, diversity gain, and propagation range is studied.     

Lower capacity bound for MIMO correlated fading channels with keyhole

It is well known that the existence of spatial fading correlation and keyhole effects severely reduces the capacity of multiple-input and multiple-output (MIMO) channels. In this letter, for correlated Rayleigh frequency-flat fading channels with keyholes, a tight lower capacity bound is given in a closed form. For the uncorrelated case, the lower bound can be proved to be tight asymptotically. The tightness of this bound for both correlated and uncorrelated channels is demonstrated by numerical examples.     

Performance analysis of space-time block codes over keyhole Nakagami-m fading channels

In multiple-input-multiple-output (MIMO) fading environments, degenerate channel phenomena, called keyholes or pinholes, may exist under the realistic assumption that the spatial fading is uncorrelated at the transmitter and the receiver, but the channel has a rank-deficient transfer matrix. In this paper, we analyze the exact average symbol error rate (SER) of orthogonal space-time block codes (STBCs) with M-PSK and M-QAM constellations over Nakagami-m fading channels in the presence of the keyhole. We derive the moment generating function (MGF) of instantaneous signal-to-noise ratio (SNR) after space-time block decoding (signal combining) in such channels. Using a well-known MGF-based analysis approach, we express the average SER of the STBC in the form of single finite-range integrals whose integrand contains only the derived MGF. Numerical results show that the keyhole significantly degrades the SER performance of the STBC from idealistic behaviors in independent identically distributed MIMO channels.     

Level crossing rate and average fade duration of the double nakagami-m random process and application in MIMO keyhole fading channels

We present novel exact expressions and accurate closed-form approximations for the level crossing rate (LCR) and the average fade duration (AFD) of the double Nakagami-m random process. These results are used to study the second order statistics of multiple input multiple output (MIMO) keyhole fading channels with space-time block coding. Numerical and computer simulation examples validate the accuracy of the presented mathematical analysis and show the tightness of the proposed approximations.     

频率选择性信道下多天线系统的空间线性预编码设计

研究了频率选择性信道下多天线系统的空间线性发射预编码设计问题.针对有循环前缀的块传输系统,通过理论分析指出,在频率选择性信道下设计空间预编码可以等效成现有的在频域为多个相邻频点设计相同的空间预编码,并可以通过凸优化方法对最优方案进行数值求解.为了降低计算复杂度,提出了一种以信道容量上界最大为目标的次优预编码算法.在进行等功率分配时,这种次优方法退化为现有的特征波束形成(EBF).针对非块传输系统,分析了EBF算法存在的问题,提出了一种基于串行搜索的EBF算法.仿真分析表明,这种方法在高信噪比下的性能明显优于EBF算法.     

Capacity of MIMO channels: asymptotic evaluation under correlated fading

This paper investigates the asymptotic uniform power allocation capacity of frequency nonselective multiple-input multiple-output channels with fading correlation at either the transmitter or the receiver. We consider the asymptotic situation, where the number of inputs and outputs increase without bound at the same rate. A simple uniparametric model for the fading correlation function is proposed and the asymptotic capacity per antenna is derived in closed form. Although the proposed correlation model is introduced only for mathematical convenience, it is shown that its shape is very close to an exponentially decaying correlation function. The asymptotic expression obtained provides a simple and yet useful way of relating the actual fading correlation to the asymptotic capacity per antenna from a purely analytical point of view. For example, the asymptotic expressions indicate that fading correlation is more harmful when arising at the side with less antennas. Moreover, fading correlation does not influence the rate of growth of the asymptotic capacity per receive antenna with high E/sub b//N/sub 0/.     

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     

Capacity of AM-PSK on partially coherent fading channels

This paper presents numerical capacity curves for two discrete complex channels: (1) a slow-fading Rayleigh channel with discrete carrier tracking by a phase-locked loop (PLL), where the PLL SNR is proportional to the fading amplitude squared, and (2) a fast-fading Rician channel with carrier phase estimation for the line-of-sight path only. Both channel models assume independent fading of successively received symbols. Capacity calculations are performed for equiprobable signaling with 8-ary and 16-ary amplitude-modulated phase-shift-keyed (AM-PSK) constellations. On the Rayleigh channel, the AM-PSK constellations give gains between 2 and 9 dB over PSK, at SNRs between 5 and 40 dB. For the Rician channel, AM-PSK gives a capacity gain over PSK of up to 0.75 bit at high SNR     

Layered space-time codes over Ricean fading channels by reducing the correlation of spatial shaping pulses

In this paper, an asynchronous layered space-time architecture is proposed to realize the spatial multiplexing over the Ricean multiple-input multiple-output (MIMO) channels. Based on reducing the correlation of spatial shaping pulses between the multiplexed streams, this approach can be used to solve the problem of detection in the ill-conditioned channel matrix. It is shown that at the receiver, the reduction of the correlation enables the requirement on the number of the receive antennas to be removed by the zero forcing (ZF) detector compared with the conventional synchronous layered space-time architecture. First, this paper presents how to exploit the correlation of spatial shaping pulses between the multiplexed streams. Then deriving the exact closed-form expression of error rate for the proposed scheme, this paper finds that the maximum possible diversity gain can be achieved based on the independent layered architecture by the ZF detector at the cost of limited multiplexing gain.     

On achievable performance of spatial diversity fading channels

Channel time-variation and frequency selectivity [causing intersymbol interference (ISI)] are two major impairments in transmission for a wireless communication environment. Spatial diversity on the transmitter or the receiver side has been traditionally used to combat multipath fading. Previous results indicate significant gains in using multiple transmitter and receiver antenna diversity. By deriving the mutual information and cutoff rate we characterize the gains on these channels. We show that gains linear in the number of antennas can be achieved either when the signal-to-noise ratio (SNR) becomes very large or when the number of antennas becomes large. We show that some of these gains can be achieved by lower complexity linear receiver structures. By evaluating the cutoff rate for phase-shift keying (PSK) constellations we further quantify the gains of using spatial diversity at both the transmitter and the receiver. Next, we examine the expected mutual information for slowly fading ISI channels where the channel is assumed to be block time-invariant. We then examine the impact of fast channel time variation (time variation within a transmission block) on multicarrier transmission schemes. We derive the average mutual information for orthogonal frequency-division multiplexing (OFDM) in time-varying ISI environments. Using this we examine the impact of transmitter and receiver diversity on OFDM transmission over time-varying ISI channels. We also study the effect of time variation on OFDM packet-size design     

Capacity analysis of M-SC receivers over TWDP fading channels

An expression for the probability distribution function (PDF) of the signal-to-noise ratio of a selection combining receiver in two-wave with diffuse power fading channel is derived. Using this PDF expression, the capacity for the different adaptive transmission techniques employing selection combining (SC) are obtained. The study presents the effects of the ratio of total dominant signal power to the scattered signal power on the system capacity. The change in the capacity of the system with the diversity order for a SC receiver in the fading channel is also presented.     

Performance analysis of multiple-antenna cooperative networks under Weibull fading

In wireless communications, cooperative relaying is well-known to enhance the overall system performance, but implementation and cost constraints stand against its wide deployment. This paper investigates the performance of cooperative relays with and without multiple antennas under independent and identically distributed (i.i.d.) Weibull faded channels in a two-hop wireless network. We consider the Weibull fading channel model due to its flexibility in describing the radio propagation environment more than the classical Rayleigh model. Our study relies on applying selection combining (SC) along with threshold decode and forward (TDF) protocol at the cooperative relays as a good compromise between cost and performance. In addition, maximal ratio combining (MRC) is used at the destination. We derive analytical expressions for the end-to-end (E2E) error performance of the network under such scenario and provide simulation results to confirm the validity of the obtained analytical expressions.     

Capacity of correlated nakagami-m fading channels with diversity combining techniques

We derive closed-form expressions for the capacity of dual-branch maximal ratio combining, equal gain combining, selection combining, and switch and stay combining (SSC) diversity systems over correlated Nakagami-m fading channels. Because the final capacity expressions contain infinite series, we truncate the series and present upper bounds on the truncation errors. We also derive an expression that can be used to numerically determine the optimum adaptive switching threshold for the capacity of a dual-branch SSC system over correlated Nakagami-m fading channels. However, a closed-form expression for the optimum adaptive switching threshold is derived for the case of independent branches. The corresponding expressions for Rayleigh fading are obtained as a special case of Nakagami-m fading. Finally, numerical examples are presented for illustration.