Instantaneous Signal-to-noise Ratio Research Articles

Lightweight User Grouping with Flexible Degrees of Freedom in Virtual MIMO

Virtual MIMO (Multiple Input Multiple Output) groups multiple single-antenna mobile devices to form an antenna array, offering higher degrees of freedom and improved spatial diversity gain as a real MIMO does, yet with much lower costs. In this paper, we focus on the user grouping problem in uplink transmission from multiple single-antenna users to one multiple-antenna base station. State-of-the-art solutions mostly target two single-antenna users, solving a pairing problem. Having more than two uplink users in a grouping has yet to be addressed. Intuitively, a higher number of users in a VMIMO group offers better spectrum efficiency, and thus more throughput gains could be expected; the group dynamics however becomes higher too, making fairness harder to be achieved with reasonable computation overhead. To address these challenges, we present a novel solution that decomposes the VMIMO user grouping into two steps. We lighten the computations in user grouping by using instantaneous signal to noise ratio (SNR) as selection criteria, and combining it with proportional fairness for larger groups of users. Lightweight computation in using instantaneous SNR in our solution allows faster grouping and feasible scheduling for a large number of users, as well as fast decision on the efficiency of the number of users in each group. We have evaluated our solution under different network configurations, and the results demonstrate that it achieves much higher data throughput as compared to existing solutions and also well preserves fairness.

Performance Analysis of Scheduled Cognitive Radio Systems With MIMO Transmission

In this paper, we investigate the performance analysis of cognitive radio (CR) multiple-input-multiple-output (MIMO) systems, including the scheduled transmit antenna selection (TAS) with maximal ratio combining (MRC) and the scheduled space-time block coding (STBC). Here, the scheduled MIMO systems transmit data of a user to provide the maximum instantaneous postprocessing signal-to-noise ratio (SNR) at the CR receiver. For the closed-form performance analysis, we derive approximated probability density functions (pdfs) of the instantaneous postprocessing SNR at the receiver for the scheduled TAS with MRC and the scheduled STBC systems, respectively. Based on the results, we derive the approximated closed-form expressions of the average postprocessing SNR and ergodic capacity for the scheduled CR systems with MIMO transmission. Through the analysis, we provide the achievable average postprocessing SNR and ergodic capacity of the proposed scheduled systems as a function of the peak interference power constraint. In addition, we present the impact of imperfect channel state information (CSI) on the ergodic capacity for the scheduled TAS with MRC and the scheduled STBC systems through arbitrary order statistics, respectively.

Adaptive Cooperative Decode-and-Forward Transmission with Power Allocation Under Interference Constraint

In this paper, we examine an adaptive decode-and-forward cooperative protocol under interference constraint. In the proposed protocol, relying on the obtained instantaneous signal-to-noise ratios (SNRs), a direct link or relay link is used to transmit data from the secondary source to the secondary destination. In addition, once the relay link is used, the secondary source and relay must adapt their transmit power to maximize the instantaneous SNR of this link. To evaluate the performance of the proposed protocol, we derive closed-form lower-bound and upper-bound expressions for the outage probability over Rayleigh fading channel. Finally, various Monte-Carlo simulations are presented to verify our analysis and compare the performance of the proposed protocol with that of the direct transmission protocol in underlay cognitive network.

Performance of Full CSI Selection Combining for Cooperative Diversity Systems

Cooperative diversity achieves enhanced data rates and throughput using distributed spatial diversity techniques. We consider a cooperative diversity system comprising of a source, a relay, and a destination, with decode and forward (DF) protocol at the relay. The drawback of conventional instantaneous signal-to-noise ratio (SNR) based selection combining is that it fails to use the instantaneous SNR of the source-relay channel at the destination while selecting the best channel from source-destination and relay-destination channels. Full channel state information (CSI) selection combining, which effectively utilizes the instantaneous SNR of the source-relay channel at the destination, is used to overcome this drawback. The exact end-to-end symbol error probability (SEP) of full CSI selection combining for this DF system, with M-ary phase-shift keying in a flat Rayleigh fading environment, is derived. The analysis is validated through simulations. The diversity gain analysis is also studied for this scheme. Further, we compare the full CSI selection combining scheme with some other existing schemes. Numerical results show that full CSI selection combining has performance similar to that of instantaneous SEP based selection combining, but offers SNR gain over instantaneous SNR based selection combining, max-min selection, and selection cooperation.

Two-Way Amplify-and-Forward Relaying with Gaussian Imperfect Channel Estimations

In this letter, we study the effect of channel estimation errors on the reception reliability of two-way relaying. For a network with two users that exchange information with each other through multiple amplify-and-forward relays, we investigate a single-relay selection scheme. Since the communication is two-way, the selection scheme aims at optimizing the worse performance of the two communication tasks between the pair of users. The signal-to-noise ratio (SNR) at the users' nodes of the relaying network is formulated and upper bounded. Then, the probability density function (PDF) of the upper bounded SNRs are determined. Subsequently, expressions for the error probabilities are obtained. Furthermore, an approximate PDF of the output instantaneous SNRs are derived, based on which simple and general asymptotic expressions for the error probabilities are presented and discussed. Numerical and simulation results are provided to verify the analysis and compare the performance of the two-way relaying network for different operating conditions and scenarios.

A Jointly Optimized VariableM-QAM and Power Allocation Scheme for Image Transmission

We introduce an improved image transmission scheme over wireless channels with flat Rayleigh fading. The proposed scheme jointly optimizes bit power and modulation level to maximize the peak signal-to-noise ratio (PSNR) of the reconstructed image and hence improves the perceptual quality of the received image. In this optimization process, the significance of bits with regard to the overall quality of the image is exploited. The optimality of the proposed algorithm is demonstrated using the Lagrange method and verified through an iterative offline exhaustive search algorithm. For practical implementation, a look-up table is used at the transmitter for assigning the bit power and modulation level to each bit stream according to the received signal-to-noise ratio (SNR) observed at the receiver. The proposed scheme has low complexity since the look-up table is computed offline, only once, and used for any image which makes it suitable for devices with limited processing capability. Analytical and simulation results show that the proposed scheme with jointly optimized bit power and variable modulation level provides an improvement in PSNR of about 10 to 20 dB over fixed power fixed modulation (16-QAM). A further reduction in complexity is achieved by using the average signal-to-noise ratio rather than the instantaneous SNR in selecting the system parameters.

Optimization of cooperative spectrum sensing with sensing user selection in cognitive radio networks

Cooperative spectrum sensing (CSS) can improve the spectrum sensing performance by introducing spatial diversity in cognitive radio networks (CRNs). However, such cooperation also introduces the delay for reporting sensing data. Conventional cooperation scheme assumes that the cooperative secondary users (SUs) report their local sensing data to the fusion center sequentially. This causes the reporting delay to increase with the number of the cooperative SUs, and ultimately affects the performance of CSS. In this article, we consider the reporting delay and formulate the optimization problem of CSS with sensing user selection to maximize the average throughput of the CRN in both the additive white Gaussian noise (AWGN) environment and the Rayleigh fading environment. It is shown that selecting all the SUs within the CRN to cooperate might not achieve the maximal average throughput. In particular, for the AWGN environment, the sensing user selection scheme is equivalent to selecting the optimal number of cooperative SUs due to all the SUs having the same instantaneous detection signal-to-noise ratio (SNR). For the Rayleigh fading environment, the maximal average throughput is achieved by selecting a certain number of cooperative SUs with the highest instantaneous detection SNRs to cooperate. Finally, computer simulations are presented to demonstrate that the average throughput of the CRN can be maximized through the optimization.

A Precise Approximation for Performance Evaluation of Amplify-and-Forward Multihop Relaying Systems

The instantaneous end-to-end received signal-to-noise ratio (SNR) in K-hop amplify-and-forward (AF) relaying systems is commonly upper bounded by 1/k of the harmonic mean of the individual per-hop instantaneous SNRs. It is shown that performance results in Nakagami-m fading of AF multihop relaying systems obtained based on this upper bound are not tight for small values of SNR or for larger values of the Nakagami parameter and, depending on certain channel conditions, these bounds may become looser as the number of hops increases. A new approximation to the instantaneous end-to-end received SNR is introduced in the form of a scaled version of the harmonic mean of the individual per-hop SNRs. The scaling factor is determined based on the average link SNRs. Performance results evaluated using the proposed approximation are more accurate than all performance bounds previously reported in the literature, even though they are obtained with the same computational complexity. Numerical results show that the approximate performance results are very close to the exact results especially in small SNR regimes or for larger values of the Nakagami parameter.

Performance of Dual-Hop Multi-Antenna Systems with Fixed Gain Amplify-and-Forward Relay Selection

The performance of amplify-and-forward relaying in Rayleigh channels is explored for a dual-hop transmission system in which a transmission source selects one of several relays based upon instantaneous SNR (signal to noise ratio) to transmit a data packet to a destination receiver. Both source and receiver devices have multiple antennas, employing beamforming for transmission and MRC (maximal ratio combining) for reception. The chosen relay performs fixed gain forwarding. Closed form solutions for several performance measures are derived for this practical system, and the system is studied in terms of outage probability and symbol error rate which are verified through simulation. Several implementation alternatives are explored to note performance trade-offs, particularly between number of antennas and number of relays.

Opportunistic cooperation and optimal power allocation for wireless sensor networks

Cooperative communications is a promising technology to improve the performance of wireless sensor networks. In this paper, a dual-hop wireless cooperative network with opportunistic amplify-and-forward relaying is investigated over independent and non-identically distributed Nakagami-m fading channels. Due to the complicated form of the probability density function of the instantaneous signal-to-noise ratio (SNR), the symbol error rate and outage probability expressions are difficult to obtain in closed form. Taking advantage of Maclaurin series expansion of the probability density function of the output instantaneous SNR, we present the asymptotic symbol error rate and outage probability expressions at medium and high SNR regions, and the optimal power allocation scheme between the source and opportunistic relay is also proposed to minimize the outage probability. Simulation results demonstrate that the derived symbol error rate and outage probability matches well with the Monte-Carlo simulations. In addition, it is verified that the optimal power allocation scheme outperforms the equal power allocation scheme in terms of outage probability.

Delay Analysis of Cooperative Truncated HARQ With Opportunistic Relaying

In this paper, we evaluate the delay experienced by Poisson arriving packets for cooperative truncated hybrid automatic repeat request (HARQ) with opportunistic relaying. We derive the theoretical expressions of the expected waiting time and the packet's sojourn time in the queue of truncated opportunistic cooperative ARQ, HARQ I with and without packet combining (PC), and HARQ II with code combining (CC). The analysis is valid for block Nakagami- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> fading channels and any number of relays for both amplify-and-forward (AF) and decode-and-forward (DF) relaying. In opportunistic AF cooperative HARQ, packet retransmission is done by the relay offering the highest instantaneous signal-to-noise ratio (SNR) of the relaying link (source-relay-destination). In opportunistic DF cooperative HARQ, retransmission is done by the relay offering the highest instantaneous SNR of the relay-destination link among the relays that have correctly decoded the transmitted packet by the source. If no relay has correctly decoded, the retransmission is made by the source. Simulation results are also provided to verify the tightness of the derived expressions. The results indicate a significant improvement of packet delivery delays when compared with the absence of cooperation.

Prony and Polynomial Approximations for Evaluation of the Average Probability of Error Over Slow-Fading Channels

A novel and simple semianalytical method for evaluating the average probability of transmission error for digital communication systems that operate over slow-fading channels is presented. The proposed method applies a sum of exponentials fit known as the Prony approximation to the conditional probability of error. Hence, knowledge of the moment-generating function of the instantaneous signal-to-noise ratio (SNR) at the detector input can be used to obtain the average probability of error. Numerical results show that knowledge of the conditional probability of error at only a small number of points and the sum of only two exponentials are sufficient to achieve very high accuracy; the relative approximation error of the exact average probability of error is less than 6% in most of the cases considered. Furthermore, a piecewise polynomial approximation of the conditional probability of error is investigated as an alternative to the sum of exponentials fit. In this case, knowledge of the partial moments of the instantaneous SNR at the detector input can be used to obtain the average probability of error. Numerical results indicate that, to achieve good accuracy, the method based on the polynomial approximation requires that the product of the polynomial degree and the number of approximation subintervals be larger than 10.

Threshold Selection for SNR-based Selective Digital Relaying in Cooperative Wireless Networks

This paper studies selective relaying schemes based on signal-to-noise-ratio (SNR) to minimize the end-to-end (e2e) bit error rate (BER) in cooperative digital relaying systems using BPSK modulation. In the SNR-based selective relaying, the relay either retransmits or remains silent depending on the SNRs of the source-relay, relay-destination, and source-destination links. Different models assuming the availability of different sets of instantaneous and average SNR information at the relay are studied. For each model, the optimal strategy to minimize the e2e BER is a different threshold rule on the source-relay SNR, if the link SNRs are uncorrelated in time and space. Approximations for the optimal threshold values that minimize the e2e BER and the resulting performance are derived analytically for BPSK modulation. Using the derived threshold the e2e BER can be reduced significantly compared to simple digital relaying. By studying the performance under different models, it is shown that knowledge of the instantaneous source-destination SNR at the relay can be exploited. The gain from this knowledge is higher when the average source-destination SNR is large. However, knowledge of the instantaneous relay-destination SNR at the relay does not change performance significantly.

Performance Analysis of UWB Autocorrelation Receivers Over Nakagami-Fading Channels

We study the performance of the autocorrelation receiver (AcR) with the transmitted-reference (TR) signaling scheme in the multipath UWB channel, where the fading of each resolvable multipath component is characterized by: 1) Nakagami distribution; 2) arbitrary fading parameter; and 3) arbitrary average power. The analysis, compared to conventional Rake receivers, is complicated by the fact that the instantaneous signal-to-noise ratio (SNR) at the AcR output is a nonlinear function of the instantaneous SNR at the receiver input, the latter given by the sum of the SNRs of each resolvable multipath component. Based on the derivation of exact and approximated expressions for the probability density function (pdf) of the output SNR, we evaluate several indicators of the receiver performance, such as: 1) average SNR; 2) amount of fading; 3) outage probability; and 4) average bit-error probability (BEP); all are given in a closed-form. Remarkably, we show that the pdf of the output SNR can be modeled as a gamma distributed random variable, which allows us to write the average BEP in terms of the well-known hypergeometrical Gaussian function. An approximate, yet accurate, expression of the integration time minimizing the average BEP is also derived.

Capacity analysis for a multiuser cross-layer downlink model in the presence of fading and interference

A system model that employs beamforming at the physical (PHY) layer and different scheduling algorithms at the medium access control (MAC) layer is used in a downlink environment where two users are served simultaneously. The effect of the scheduling algorithms on the system performance is assessed in terms of total system capacity. The scheduling algorithms considered, choose users either randomly, or on the basis of their instantaneous signal-to-noise ratio (SNR) and/or their angular location around the base station. A semi-analytical framework for the capacity analysis is also presented. The results obtained from the numerical model are shown to be consistent with those based on the semi-analytical framework. It is shown that explicitly taking into consideration at the MAC layer the angular location of mobile users around the base station along with instantaneous SNR for the selection of users that are served simultaneously leads to an improved system capacity. This improvement is the result of reduced interference that simultaneously served users cause on each other. The results show that joint addressing of the PHY and MAC layer issues in an integrated cross-layer framework is important for achieving maximal system performance.

Minimum Selection GSC in Independent Rayleigh Fading

We analyze the error performance of minimum selection generalized selection combining (MS-GSC), in which the minimum number of diversity branches are selected such that their combined signal-to-noise ratio (SNR) is above a given threshold. A flat Rayleigh fading channel with independent and distinctly distributed branch SNRs is considered. By transforming the ordered instantaneous branch SNRs to their differences, we derive the distribution of the number of selected branches in closed form. We then modify the derivation of this distribution to get the characteristic function (cf.) of the combiner output SNR. This cf. is used to obtain the symbol error probability for different coherent digital modulation schemes.

Antenna selection for multiple-antenna transmission systems: performance analysis and code construction

This correspondence studies antenna selection for wireless communications systems that employ multiple transmit and receive antennas. We assume that (1) the channel is characterized by quasi-static Rayleigh flat fading, and the subchannels fade independently, (2) the channel state information (CSI) is exactly known at the receiver, (3) the selection is available only at the receiver, and it is based on the instantaneous signal-to-noise ratio (SNR) at each receive antenna, and (4) space-time codes are used at the transmitter. We analyze the performance of such systems by deriving explicit upper bounds on the pairwise error probability (PEP). This performance analysis shows that (1) by selecting the set of antennas that observe the largest instantaneous SNR, one can achieve the same diversity gain as the one obtained by using all the receive antennas, provided that the underlying space-time code has full spatial diversity, and (2) in the case of rank-deficient space-time codes, the diversity gain may be dramatically reduced when antenna selection is used. However, we emphasize that in both cases the coding gain is reduced with antenna selection compared to the full complexity system. Based on the upper bounds derived, we describe code design principles suitable for antenna selection. Specifically, for systems with two transmit antennas, we design space-time codes that perform better than the known ones when antenna selection is employed. Finally, we present numerical examples and simulation results that validate our analysis and code design principles.

Analysis of hybrid selection/maximal-ratio combining in correlated Nakagami fading

We present an analysis of a hybrid selection/maximal-ratio combining diversity system over an evenly correlated slow frequency-nonselective Nakagami fading channel, where the correlation coefficient between any pair of the diversity branch gain amplitudes is the same, and all average branch signal-to-noise ratios (SNRs) are equal. In this system, the L branches with the largest instantaneous SNR out of N available branches are selected and combined using maximal-ratio combining. From the joint characteristic function (cf) of the instantaneous branch SNRs, we obtain an expression for the cf of the combiner output SNR as a series of elementary cfs. The expression can be conveniently used to obtain the symbol error probability of coherent detection of different M-ary modulation schemes. We illustrate our methodology using M-ary phase-shift keying as an example.

Optimum spreading bandwidth for selective RAKE reception over Rayleigh fading channels

Building on the developments in the performance analysis of generalized selection combining (GSC), this paper examines the optimum spreading bandwidth for a fixed-complexity GSC diversity receiver operating over independent identically distributed Rayleigh paths. For this purpose, the study considers three performance criteria: (1) average combined signal-to-noise ratio (SNR) at the GSC output; (2) average bit error probability (BEP); and (3) outage probability of the instantaneous combined SNR at the GSC output. For the average BEP criterion, results are presented for both coherent and noncoherent combining. For the average combined SNR and some instances of the average BEP optimization problem, an accurate approximate estimate of this optimum bandwidth in the form of a solution of a transcendental equation is provided. In other cases, where the optimization is not easily tractable in an analytic fashion, a numeric-search procedure is used to find this optimum bandwidth for different performance criteria and system parameters of interest. Finally, simplified rule-of-thumb-type formulas are also presented as a good reference for picking the optimum spreading bandwidth given a set of system parameters and a particular performance criterion of interest.

SNR of generalized diversity selection combining with nonidentical Rayleigh fading statistics

A closed-form expression for the average signal-to-noise-ratio (SNR) of generalized diversity selection combining, using the m largest (in instantaneous SNR) diversity signals, for arbitrary m, assuming that the Rayleigh fading statistics on each diversity branch are identically, independently distributed (i.i.d.), already exists in the literature. In this paper, a similar closed-form expression, but for nonidentically distributed statistics, is derived, This expression specializes to known results, such as the average SNRs of maximal-ratio combining with either i.i.d. or non-i.i.d. diversity statistics and that of conventional selection combining (CSC) with i.i.d. diversity statistics. In addition, it provides, for the first time, a simple closed-form solution to the combined SNR of CSC with non-i.i.d. diversity statistics. Further, the closed-form solution for the SNR of selecting the m, largest diversity signals has negligible computational complexity.