Performance of downlink massive MIMO in Ricean fading channels with ZF precoder

We investigate the achievable sum rate and energy efficiency of zero-forcing precoded downlink massive multiple-input multiple-output systems in Ricean fading channels. A simple and accurate approximation of the average sum rate is presented, which is valid for a system with arbitrary rank channel means. Based on this expression, the optimal power allocation strategy maximizing the average sum rate is derived. Moreover, considering a general power consumption model, the energy efficiency of the system with rank-1 channel means is characterized. Specifically, the impact of key system parameters, such as the number of users N, the number of BS antennas M, Ricean factor K and the signal-to-noise ratio (SNR) ρ are studied, and closed-form expressions for the optimal ρ and M maximizing the energy efficiency are derived. Our findings show that the optimal power allocation scheme follows the water filling principle, and it can substantially enhance the average sum rate in the presence of strong line-of-sight effect in the low SNR regime. In addition, we demonstrate that the Ricean factor K has significant impact on the optimal values of M, N and ρ.

Energy efficiency analysis of rank-1 Ricean fading MIMO channels

This paper studies the energy efficiency (EE) of a point-to-point rank-1 Ricean fading multiple-input-multiple-output (MIMO) channel. In particular, a tight lower bound and an asymptotic approximation for the EE of the considered MIMO system are presented, under the assumption that the channel is unknown at the transmitter and perfectly known at the receiver. Moreover, the effects of different system parameters, namely, transmit power, spectral efficiency (SE), and number of transmit and receive antennas, on the EE are analytically investigated. An important observation is that, in the high signal-to-noise ratio regime and with the other system parameters fixed, the optimal transmit power that maximizes the EE increases as the Ricean-K factor increases. On the contrary, the optimal SE and the optimal number of transmit antennas decrease as K increases.

Full-Duplex Spectrum Sharing in Cooperative Single Carrier Systems

We propose cyclic prefix single carrier full-duplex transmission in amplify-and-forward cooperative spectrum sharing networks to achieve multipath diversity and full-duplex spectral efficiency. Integrating full-duplex transmission into cooperative spectrum sharing systems results in two intrinsic problems: 1) the residual loop interference occurs between the transmit and the receive antennas at the secondary relays and 2) the primary users simultaneously suffer interference from the secondary source (SS) and the secondary relays (SRs). Thus, examining the effects of residual loop interference under peak interference power constraint at the primary users and maximum transmit power constraints at the SS and the SRs is a particularly challenging problem in frequency selective fading channels. To do so, we derive and quantitatively compare the lower bounds on the outage probability and the corresponding asymptotic outage probability for max–min relay selection, partial relay selection, and maximum interference relay selection policies in frequency selective fading channels. To facilitate comparison, we provide the corresponding analysis for half-duplex. Our results show two complementary regions, named as the signal-to-noise ratio (SNR) dominant region and the residual loop interference dominant region, where the multipath diversity and spatial diversity can be achievable only in the SNR dominant region, however the diversity gain collapses to zero in the residual loop interference dominant region.

Secure Transmission in Cooperative Relaying Networks with Multiple Antennas

We investigate the secrecy performance of dualhop amplify-and-forward (AF) multi-antenna relaying systems over Rayleigh fading channels, by taking into account the direct link between the source and destination. In order to exploit the available direct link and the multiple antennas for secrecy improvement, different linear processing schemes at the relay and different diversity combining techniques at the destination are proposed, namely, 1) Zero-forcing/Maximal ratio combining (ZF/MRC), 2) ZF/Selection combining (ZF/SC), 3) Maximal ratio transmission/MRC (MRT/MRC) and 4) MRT/Selection combining (MRT/SC). For all these schemes, we present new closed-form approximations for the secrecy outage probability. Moreover, we investigate a benchmark scheme, i.e., cooperative jamming/ZF (CJ/ZF), where the secrecy outage probability is obtained in exact closed-form. In addition, we present asymptotic secrecy outage expressions for all the proposed schemes in the high signal-to-noise ratio (SNR) regime, in order to characterize key design parameters, such as secrecy diversity order and secrecy array gain. The outcomes of this paper can be summarized as follows: a) MRT/MRC and MRT/SC achieve a full diversity order of M + 1, ZF/MRC and ZF/SC achieve a diversity order of M, while CJ/ZF only achieves unit diversity order, where M is the number of antennas at the relay. b) ZF/MRC (ZF/SC) outperforms the corresponding MRT/MRC (MRT/SC) in the low SNR regime, while becomes inferior to the corresponding MRT/MRC (MRT/SC) in the high SNR. c) All of the proposed schemes tend to outperform the CJ/ZF with moderate number of antennas, and linear processing schemes with MRC attain better performance than those with SC.

Secrecy Performance of Wirelessly Powered Wiretap Channels

This paper considers a wirelessly powered wiretap channel, where an energy constrained multi-antenna information source, powered by a dedicated power beacon, communicates with a legitimate user in the presence of a passive eavesdropper. Based on a simple time-switching protocol where power transfer and information transmission are separated in time, we investigate two popular multi-antenna transmission schemes at the information source, namely maximum ratio transmission (MRT) and transmit antenna selection (TAS). Closed-form expressions are derived for the achievable secrecy outage probability and average secrecy rate for both schemes. In addition, simple approximations are obtained at the high signal-to-noise ratio (SNR) regime. Our results demonstrate that by exploiting the full knowledge of channel state information (CSI), we can achieve a better secrecy performance, e.g., with full CSI of the main channel, the system can achieve substantial secrecy diversity gain. On the other hand, without the CSI of the main channel, no diversity gain can be attained. Moreover, we show that the additional level of randomness induced by wireless power transfer does not affect the secrecy performance in the high SNR regime. Finally, our theoretical claims are validated by the numerical results.

Beamforming and interference cancellation in D2D communication underlaying cellular networks

This paper presents an analytical performance investigation of both beamforming (BF) and interference cancellation (IC) strategies for a device-to-device (D2D) communication system underlaying a cellular network with an M-antenna base station (BS). We first derive new closed-form expressions for the ergodic achievable rate for BF and IC precoding strategies with quantized channel state information (CSI), as well as, perfect CSI. Then, novel lower and upper bounds are derived which apply for an arbitrary number of antennas and are shown to be sufficiently tight to the Monte-Carlo results. Based on these results, we examine in detail three important special cases including: high signal-to-noise ratio (SNR), weak interference between cellular link and D2D link, and BS equipped with a large number of antennas. We also derive asymptotic expressions for the ergodic achievable rate for these scenarios. Based on these results, we obtain valuable insights into the impact of the system parameters, such as the number of antennas, SNR and the interference for each link. In particular, we show that an irreducible saturation point exists in the high SNR regime, while the ergodic rate under IC strategy is verified to be always better than that under BF strategy. We also reveal that the ergodic achievable rate under perfect CSI scales as log2M, whilst it reaches a ceiling with quantized CSI.

Achievable sum-rate of multiuser massive MIMO downlink in ricean fading channels

We investigate the achievable ergodic sum-rate of multi-user multiple-input multiple-output systems in Ricean fading channels. We first derive a lower bound on the average signal-to-leakage-and-noise ratio by utilizing the Mullen's inequality, which is then used to analyze the effect of channel mean information on the achievable sum-rate. With these results, a novel statistical-eigenmode space-division multipleaccess downlink transmission scheme is proposed. For this scheme, we derive an exact closed-form expression for the achievable ergodic sum-rate. Our results show that the achievable ergodic sum-rate converges to a saturation value in the high signal-to-noise ratio (SNR) region and reaches to a lower limit value in the lower Ricean K-factor range. In addition, we present tractable upper and lower bounds, which are shown to be tight for any SNR and Ricean K-factor value. Finally, the theoretical analysis is validated via numerical simulations.

TRIPPy: Trailed Image Photometry in Python

Photometry of moving sources typically suffers from a reduced signal-to-noise ratio (S/N) or flux measurements biased to incorrect low values through the use of circular apertures. To address this issue, we present the software package, TRIPPy: TRailed Image Photometry in Python. TRIPPy introduces the pill aperture, which is the natural extension of the circular aperture appropriate for linearly trailed sources. The pill shape is a rectangle with two semicircular end-caps and is described by three parameters, the trail length and angle, and the radius. The TRIPPy software package also includes a new technique to generate accurate model point-spread functions (PSFs) and trailed PSFs (TSFs) from stationary background sources in sidereally tracked images. The TSF is merely the convolution of the model PSF, which consists of a moffat profile, and super-sampled lookup table. From the TSF, accurate pill aperture corrections can be estimated as a function of pill radius with an accuracy of 10 mmag for highly trailed sources. Analogous to the use of small circular apertures and associated aperture corrections, small radius pill apertures can be used to preserve S/Ns of low flux sources, with appropriate aperture correction applied to provide an accurate, unbiased flux measurement at all S/Ns.

Beamforming and interference cancellation schemes for D2D communications

We investigate device-to-device (D2D) communication underlaying cellular networks with M-antenna base stations. We consider both beamforming (BF) and interference cancellation (IC) strategies under quantized channel state information (CSI), as well as, perfect CSI. We derive tight closed-form approximations of the ergodic achievable rate which hold for arbitrary transmit power, location of users and number of antennas. Based on these approximations, we derive insightful asymptotic expressions for three special cases namely high signal-to-noise (SNR), weak interference, and large M. In particular, we show that in the high SNR regime a ceiling effect exists which depends on the received signal-to-interference ratio and the number of antennas. Moreover, the achievable rate scales logarithmically with M. The ergodic achievable rate is shown to scale logarithmically with SNR and the antenna number in the weak interference case. When the BS is equipped with large number of antennas, we find that the ergodic achievable rate under quantized CSI reaches a saturated value, whilst it scales as log2M under perfect CSI.

Energy efficiency optimization in hardware-constrained large-scale MIMO systems

Large-scale multiple-input multiple-output (MIMO) communication systems can bring substantial improvement in spectral efficiency and/or energy efficiency, due to the excessive degrees-of-freedom and huge array gain. However, large-scale MIMO is expected to deploy lower-cost radio frequency (RF) components, which are particularly prone to hardware impairments. Unfortunately, compensation schemes are not able to remove the impact of hardware impairments completely, such that a certain amount of residual impairments always exists. In this paper, we investigate the impact of residual transmit RF impairments (RTRI) on the spectral and energy efficiency of training-based point-to-point large-scale MIMO systems, and seek to determine the optimal training length and number of antennas which maximize the energy efficiency. We derive deterministic equivalents of the signal-to-noise-and-interference ratio (SINR) with zero-forcing (ZF) receivers, as well as the corresponding spectral and energy efficiency, which are shown to be accurate even for small number of antennas. Through an iterative sequential optimization, we find that the optimal training length of systems with RTRI can be smaller compared to ideal hardware systems in the moderate SNR regime, while larger in the high SNR regime. Moreover, it is observed that RTRI can significantly decrease the optimal number of transmit and receive antennas.

Investigation of the chemical origin and evidential value of differences in the SERS spectra of blue gel inks

Highly swellable polymer films doped with Ag nanoparticle aggregates (poly-SERS films) have been used to record very high signal:noise ratio, reproducible surface-enhanced (resonance) Raman (SER(R)S) spectra of in situ dried ink lines and their constituent dyes using both 633 and 785 nm excitation. These allowed the chemical origins of differences in the SERRS spectra of different inks to be determined. Initial investigation of pure samples of the 10 most common blue dyes showed that the dyes which had very similar chemical structures such as Patent Blue V and Patent Blue VF (which differ only by a single OH group) gave SERRS spectra in which the only indications that the dye structure had been changed were small differences in peak positions or relative intensities of the bands. SERRS studies of 13 gel pen inks were consistent with this observation. In some cases inks from different types of pens could be distinguished even though they were dominated by a single dye such as Victoria Blue B (Zebra Surari) or Victoria Blue BO (Pilot Acroball) because their predominant dye did not appear in other inks. Conversely, identical spectra were also recorded from different types of pens (Pilot G7, Zebra Z-grip) because they all had the same dominant Brilliant Blue G dye. Finally, some of the inks contained mixtures of dyes which could be separated by TLC and removed from the plate before being analysed with the same poly-SERS films. For example, the Pentel EnerGel ink pen was found to give TLC spots corresponding to Erioglaucine and Brilliant Blue G. Overall, this study has shown that the spectral differences between different inks which are based on chemically similar, but nonetheless distinct dyes, are extremely small, so very close matches between SERRS spectra are required for confident identification. Poly-SERS substrates can routinely provide the very stringent reproducibility and sensitivity levels required. This, coupled with the awareness of the reasons underlying the observed differences between similarly coloured inks allows a more confident assessment of the evidential value of inks SERS and should underpin adoption of this approach as a routine method for the forensic examination of inks.

Effect of channel aging on the sum rate of uplink massive MIMO systems

This paper investigates the achievable sum-rate of uplink massive multiple-input multiple-output (MIMO) systems considering a practical channel impairment, namely, aged channel state information (CSI). Taking into account both maximum ratio combining (MRC) and zero-forcing (ZF) receivers at the base station, we present tight closed-form lower bounds on the sum-rate for both receivers, which provide efficient means to evaluate the sum-rate of the system. More importantly, we characterize the impact of channel aging on the power scaling law. Specifically, we show that the transmit power of each user can be scaled down by 1/√(M), which indicates that aged CSI does not affect the power scaling law; instead, it causes only a reduction on the sum rate by reducing the effective signal-to-interference-and-noise ratio (SINR).

I/Q imbalance in two-way AF relaying: Performance analysis and detection mode switch

This paper studies the impact of in-phase and quadrature-phase imbalance (IQI) in two-way amplify-and-forward (AF) relaying systems. In particular, the effective signal-to-interference-plus-noise ratio (SINR) is derived for each source node, considering four different linear detection schemes, namely, uncompensated (Uncomp) scheme, maximal-ratio-combining (MRC), zero-forcing (ZF) and minimum mean-square error (MMSE) based schemes. For each proposed scheme, the outage probability (OP) is investigated over independent, non-identically distributed Nakagami-m fading channels, and exact closed-form expressions are derived for the first three schemes. Based on the closed-form OP expressions, an adaptive detection mode switching scheme is designed for minimizing the OP of both sources. An important observation is that, regardless of the channel conditions and transmit powers, the ZF-based scheme should always be selected if the target SINR is larger than 3 (4.77dB), while the MRC-based scheme should be avoided if the target SINR is larger than 0.38 (-4.20dB).

I/Q imbalance in two-way AF relaying: Power allocation and performance analysis

We investigate the performance of dual-hop two-way amplify-and-forward (AF) relaying in the presence of inphase and quadrature-phase imbalance (IQI) at the relay node. In particular, the effective signal-to-interference-plus-noise ratio (SINR) at both sources is derived. These SINRs are used to design an instantaneous power allocation scheme, which maximizes the minimum SINR of the two sources under a total transmit power constraint. The solution to this optimization problem is analytically determined and used to evaluate the outage probability (OP) of the considered two-way AF relaying system. Both analytical and numerical results show that IQI can create fundamental performance limits on two-way relaying, which cannot be avoided by simply improving the channel conditions.