M-ary symbol error outage over Nakagami-m fading channels in shadowing environments

This letter addresses the problem of finding a tractable expression for the symbol error outage (SEO) in flat Nakagami-m fading and shadowing channels. We deal with M-ary phase shift keying (M-PSK) and quadrature amplitude modulation (M-QAM) which extends our previous results on BPSK signaling. We propose a new tight approximation of the symbol error probability (SEP) holding for M-PSK and M-QAM signals which is accurate over all signal to noise ratios (SNRs) of interest. We derive a new generic expression for the inverse SEP which facilitates the derivation of a tight approximation of the SEO in a lognormal shadowing environment.     

The Performance of Space-Time Block Codes from Coordinate Interleaved Orthogonal Designs over Nakagami-m Fading Channels

Space-time block codes (STBCs) from coordinate interleaved orthogonal designs (CIODs) offer several advantages including full-diversity and single-symbol decodability. In an effort to assess their performance in quasi-static frequencynonselective i.i.d. Nakagami-m fading channels, we analyze the error rate, outage capacity, and information outage probability. First, based on an accurate closed-form formula for the average symbol pairwise error rate (SPER), we derive tight union upper and lower bounds on the symbol-error rate (SER). Second, we apply Gaussian and Gamma approximations to provide closedform expressions for the outage capacity. Third, using high signal-to-noise ratio (SNR) and moment-matching approximation techniques, we also derive accurate closed-form approximations for the information outage probability (IOP). Finally, we show that STBCs from CIODs provide full-diversity by deriving SERbased and IOP-based asymptotic and instantaneous diversity orders. Monte-Carlo simulations show that the analytical results agree with simulation experiments.     

Invertible bounds for M-QAM in Rayleigh fading

In this letter, we derive tight invertible bounds on the bit-error probability (BEP) for the coherent detection of M-ary quadrature amplitude modulation with Gray code bit mapping in Rayleigh fading channels. These bounds enable us to easily obtain tight lower and upper bounds on the bit-error outage (BEO), i.e., BEP-based outage probability, in a log-normal shadowing environment. As examples of applications, these bounds are used to investigate the BEO and mean spectral efficiency for slow adaptive modulation.     

SEP performance of coherent MPSK over fading channels in the presence of phase/quadrature error and I-Q gain mismatch

This letter presents a joint approach to the symbol-error probability (SEP) of coherent M-ary phase-shift keying in a situation where the phase error, quadrature error, and in-phase-quadrature (I-Q) gain mismatch problems take place all concurrently over an additive white Gaussian noise and arbitrary fading channel. A set of equations that characterizes the conditional SEP on an instantaneous fading signal-to-noise ratio is derived in the form of the Craig representation.     

Outage Performance of Cognitive AF Relay Networks with Imperfect CSI Based on Geometrical Analysis

This paper studies the outage performance of a cognitive Amplify-and-forward (AF) relay network subject to Rayleigh fading.Under the condition of imperfect Channel state information (CSI) estimations of the links from the secondary system to the Primary user (PU),the closed-form upper and lower bounds of the outage probability are derived through a geometrical analysis method.An asymptotic analysis of the outage probability is also derived in the high Signal-to-noise ratio (SNR) regime to gain additional insights on the system.The simulation results corroborate our theoretical analysis,and the effectiveness of the geometrical analysis method is verified with the conventional approach as a benchmark.The asymptotic results are very tight with the analytical lower bound in the high SNR regime.It also can be observed from the simulation results that the impact of the number of relays as well as the imperfect CSI on the outage probability and the diversity order.     

Performance Analysis of Quantized Beamforming MIMO Systems

Multiple-input multiple-output (MIMO) wireless systems can achieve significant diversity and array gain by using single-stream transmit beamforming and receive combining. A MIMO beamforming system with feedback using a codebook based quantization of the beamforming vector allows practical implementation of such a strategy in a single-user scenario. The performance of this system in uncorrelated Rayleigh flat fading channels is studied from the point-of-view of signal-to-noise ratio (SNR) and outage probability. In this paper, lower bounds are derived on the expected SNR loss and the outage probability of systems that have a single receive antenna or two transmit antennas. For arbitrary transmit and receive antennas, approximations for the SNR loss and outage are derived. In particular, the SNR loss in a quantized MIMO beamforming system is characterized as a function of the number of quantization bits and the number of transmit and receive antennas. The analytical expressions are proved to be tight with asymptotically large feedback rate. Simulations show that the bounds and approximations are tight even at low feedback rates, thereby providing a benchmark for feedback system design     

Outage probability of multihop transmission over Nakagami fading channels

We present a general analytical framework for the evaluation of the end-to-end outage probability of multihop wireless communication systems with nonregenerative relays over Nakagami fading channels. It is shown that the presented results can either be exact or tight lower bounds on the performance of these systems depending on the choice of the relay gain. More specifically, we obtain a closed-form expression for the moment generating function of the reciprocal of the end-to-end signal-to-noise ratio (SNR) and we then use this expression to calculate the outage probability via numerical inversion of the Laplace transform. Numerical examples show that regeneration is more crucial at low average SNR and for multihop systems with a large number of hops.     

Bounds on the delay-constrained capacity of UWB communication with a relay node

We derive bounds on the expected capacity and outage capacity of a three-node relay network for UWB communications. We also provide a simple tight approximation for the derived upper bound on the capacity and then using this bound we obtain the outage probability of the network. Numerical results show that a significant improvement in the system capacity and outage probability is obtained by adding a relay node. Moreover, our theoretical results reveal that the diversity gain of a relay channel substantially increases by using UWB links instead of NB links. We also derive these bounds when we have a constraint on the total transmitted power of the source and the relay nodes.     

On the optimum design of unitary cyclic group space-time codes

In this letter, based on the exact pairwise-error probability, we derive the union bound on the symbol-error probability (SEP) of the differential unitary space-time (DUST) modulation employing group codes. Instead of using the rank-and-determinant or Euclidean distance criteria, we optimize the cyclic group codes such that the union bound on the SEP is minimized for a predetermined scenario, taking into account the number of transmit and receive antennas and the operating signal-to-noise ratio (SNR). Our simulation results show that for a wide range of SNRs, the codes with the minimum union bound for a particular SNR outperform the codes designed based on rank-and-determinant or Euclidean distance criteria.     

Performance of Non-coherent MFSK with Selection and Switched Diversity Over Hoyt Fading Channel

A closed-form expression of cumulative distribution function (CDF) of the instantaneous signal to noise ratio (SNR) in Hoyt fading channel is derived. This CDF and associated formulas are then used to find out the error probability of non-coherent M-ary frequency shift keying with multichannel reception. Simple finite-range integral expression for the symbol error probability (SEP) with selection diversity is found through CDF method. Next, closed-form expressions of moment generating functions (MGF) are presented for the switched diversity case and SEP values are calculated using the derived MGFs. Some other performance parameters like, outage probability and average SNR with switched diversity, are provided. In addition, analytic frameworks are presented for calculation of optimum switching thresholds that ensure minimum outage probability or minimum SEP. The analysis is quite general in the sense that it covers switch and stay combining and Rayleigh fading as special cases.     

Asymptotically tight bounds on the capacity and outage probabilityfor QAM transmissions over Rayleigh-faded data channels with CSI

In this article, novel quickly computable analytical upper and lower bounds are presented on the symmetric capacity for flat-faded Rayleigh channels with finite-size quadrature amplitude modulation constellations when perfect channel-state information at the receiving site is available; the proposed bounds are asymptotically tight both for high and low signal-to-noise ratios. Furthermore, an easily computable expression is also provided for a reasonably tight evaluation of the resulting outage probability     

Performance Analysis of Cooperative Diversity Wireless Networks over Nakagami-m Fading Channel

This letter analyzes the performance of cooperative diversity wireless networks using amplify-and-forward relaying over independent, non-identical, Nakagami-m fading channels. The error rate and the outage probability are determined using the moment generating function (MGF) of the total signal-to-noise-ratio (SNR) at the destination. Since it is hard to find a closed form for the probability density function (PDF) of the total SNR, we use an approximate value instead. We first derive the PDF and the MGF of the approximate value of the total SNR. Then, the MGF is used to determine the error rate and the outage probability. We also use simulation to verify the analytical results. Results show that the derived error rate and outage probability are tight lower bounds particularly at medium and high SNR     

空时协作系统的中断概率分析和功率分配研究

提出了选择中继协议下最小化系统中断概率的最优功率分配方案,并给出了最佳功率分配的闭式解。根据协作节点间是否存在交互信息,分别通过对系统中断概率的分析,推出了高信噪比下中断概率的理论界。基于理论界,在功率受限情况下,通过拉格朗日乘数法,得到最优功率分配的闭合解。仿真结果表明,所推理论界在高信噪比下与仿真值近似相等,最优功率分配点的系统性能也要优于其它功率分配点。     

Transmission capacity of wireless ad hoc networks with outage constraints

In this paper, upper and lower bounds on the transmission capacity of spread-spectrum (SS) wireless ad hoc networks are derived. We define transmission capacity as the product of the maximum density of successful transmissions multiplied by their data rate, given an outage constraint. Assuming that the nodes are randomly distributed in space according to a Poisson point process, we derive upper and lower bounds for frequency hopping (FH-CDMA) and direct sequence (DS-CDMA) SS networks, which incorporate traditional modulation types (no spreading) as a special case. These bounds cleanly summarize how ad hoc network capacity is affected by the outage probability, spreading factor, transmission power, target signal-to-noise ratio (SNR), and other system parameters. Using these bounds, it can be shown that FH-CDMA obtains a higher transmission capacity than DS-CDMA on the order of M/sup 1-2//spl alpha//, where M is the spreading factor and /spl alpha/>2 is the path loss exponent. A tangential contribution is an (apparently) novel technique for obtaining tight bounds on tail probabilities of additive functionals of homogeneous Poisson point processes.     

On performance limits of space-time codes: a sphere-packing bound approach

A sphere-packing bound (SPB) on average word-error probability (WEP) is derived to determine the performance limits of space-time codes on Rayleigh block-fading channels under delay and maximum energy constraints. Two other explicit bounds, a looser bound and a tight approximate bound, are also derived to provide more intuition on how the system parameters affect the performance limits. Moreover, it is shown that as the block length grows to infinity, the SPB converges to the outage probability, and the asymptotic behavior of performance limits is determined by the outage probability.     

Multiuser decision-feedback receivers for asynchronous CDMA systemsover a mismatched flat Rayleigh fading channel

In this paper, the design of decision-feedback multiuser (DFM) receivers for asynchronous code-division multiple access (CDMA) systems over a mismatched flat Rayleigh fading channel is studied, and tight upper and lower bounds on the pair-wise symbol-error probability, which has been averaged over the channel fading, time delays, and phase angles, are derived for some of the DFM detection schemes. The performance bounds, which are computed by efficient analytic techniques, can serve as reliable references for CDMA system design. It is shown that the proposed system, which takes into account the effect of mismatched fading on the system design, has some gain over the system where the estimation of fading is assumed to be exact     

Optimal power control in interference-limited fading wirelesschannels with outage-probability specifications

We propose a new method of power control for interference-limited wireless networks with Rayleigh fading of both the desired and interference signals. Our method explicitly takes into account the statistical variation of both the received signal and interference power and optimally allocates power subject to constraints on the probability of fading induced outage for each transmitter/receiver pair. We establish several results for this type of problem. We establish tight bounds that relate the outage probability caused by channel fading to the signal-to-interference margin calculated when the statistical variation of the signal and interference powers is ignored. This allows us to show that well-known methods for allocating power, based on Perron-Frobenius eigenvalue theory, can be used to determine power allocations that are provably close to achieving optimal (i.e., minimal) outage probability. We show that the problems of minimizing the transmitter power subject to constraints on outage probability and minimizing outage probability subject to power constraints can be posed as a geometric program (GP). A GP is a special type of optimization problem that can be transformed to a nonlinear convex optimization problem by a change of variables and therefore solved globally and efficiently by interior-point methods. We also give a fast iterative method for finding the optimal power allocation to minimize the outage probability     

Performance evaluation of cellular mobile radio systems with interference ing of dominant interferers

This paper develops an analytical framework for characterizing the average symbol error rate and outage performance of a smart antenna system in cellular mobile radio environments. Specifically, the carrier-to-interference ratio statistics with N remaining (uncancelled) "weakest" cochannel interference (CCI) signals from a total of N/sub I/ signals are derived, given that both the desired user signal and the CCI signal amplitudes are subjected to Rayleigh, Rice, Nakagami-m, or Nakagami-q fading. General expressions for the outage probability and the average symbol-error rate performance of different digital modulation schemes in the presence of CCI signals are derived. Selected numerical results are presented to demonstrate the utility of the analysis in assessing the selective interference ing performance in different fading environments.     

Outage Performance of Underlay Cognitive Opportunistic Multi-relay Networks in the Presence of Interference from Primary User

In this paper, considering the interferences from primary transmitter to secondary receiver and from secondary transmitter to primary receiver, we derive the upper and lower bounds of outage probability for underlay cognitive opportunistic multi-relay networks. Theoretical and simulation results show the upper and lower bounds converge to the exact outage probability at high interference-to-noise (INR) region. Because the interference from primary transmitter to secondary receiver is considered, an outage floor at high signal-to-noise ratio (SNR) occurs when INR increases proportionally with SNR.     

Performance Analysis of MIMO-MRC in Double-Correlated Rayleigh Environments

We consider multiple-input multiple-output (MIMO) transmit beamforming systems with maximum ratio combining (MRC) receivers. The operating environment is Rayleigh fading with both transmit and receive spatial correlation. We present exact expressions for the probability density function (pdf) of the output signal-to-noise ratio, as well as the system outage probability. The results are based on explicit closed-form expressions which we derive for the pdf and cumulative distribution function of the maximum eigenvalue of double-correlated complex Wishart matrices. For systems with two antennas at either the transmitter or the receiver, we also derive exact closed-form expressions for the symbol-error rate. The new expressions are used to prove that MIMO-MRC achieves the maximum available spatial diversity order, and to demonstrate the effect of spatial correlation. The analysis is validated through comparison with Monte Carlo simulations