SNR Gain Research Articles

Low-Latency Burst Error Detection and Correction in Decision-Feedback Equalization

This article describes low latency, zero overhead DFE burst error correction technique. Without any encoder or decoder latency, the proposed technique makes use of the existing pre-cursor ISI to detect and correct errors on a burst of data. The implemented proof-of-concept 2-tap DFE prototype in 65nm CMOS operates at 16 Gb/s and compensates 32 dB loss consuming 58 mW only. With an additional 18 mW, the receiver enables error correction capability that translates to 2-to-6 dB SNR gain depending on the pre-cursor magnitude. Experimental results demonstrate that for lossy channels where pre-cursor is 60% or higher of main, this error correction outperforms RS(528, 514) without any overhead and with much lower latency and power consumption.

Uplink SCMA Codebook Reuse Transmission and Reception Scheme

Sparse code multiple access (SCMA) is a new non-orthogonal multiple access scheme suitable for 5G communication, which can effectively improve spectrum efficiency and support massive connections. Multiple users in the SCMA system realize the sharing of the same time-frequency resources by mapping data into codewords of a special code book (Code Book, CB). A typical SCMA system increases the spectrum utilization to 150%. In order to further improve the system spectrum utilization and increase the number of user connections, this paper proposes an uplink SCMA codebook reuse transmission and reception scheme (CB-Reuse-SCMA), which reuse a codebook to multiple users. The base station allocates <i>β</i> users to each codebook at the same time, so that <i>β</i> users use the same codebook to transmit uplink information. On the receiver of the base station, an improved Logarithmic Message Passing Algorithm (Log-MPA) is designed for multi-user detection, so that the base station can correctly detect the data of <i>β</i> users who reuse the same codebook. Simulation results show that at the time <i>β</i> = 2, the proposed scheme increased the spectrum utilization to 300%; at the time <i>β</i> = 3, the proposed scheme increased the spectrum utilization to 450%. Compared with the traditional SCMA scheme where the user has an exclusive codebook, the proposed scheme improves the spectrum utilization to <i>β</i> × 150% through codebook reuse at the expense of a small amount of SNR gain, which improves the throughput and user connection by <i>β</i> times number.

Distributed Learning Assisted Fronthaul Compression for Multi-Antenna C-RAN

This paper investigates the uplink reception in the cloud radio access network (C-RAN), sometimes called centralized-RAN. C-RAN is an architecture for cellular networks which consists of many remote radio units (RRUs) connected to a central processor (CP). Due to the prohibitive complexity of computations, the most efficient uplink C-RAN schemes are challenging to be implemented in practical systems. Using deep neural networks (DNNs), we propose a new and low complex method for uplink C-RAN subject to some quantization rules. This is the first work that uses DNNs to mimic the C-RAN system to the best of our knowledge. Our architecture’s objective, called QDNet, is to jointly optimize the processing done at the RRUs, which considers the quantization constraints and the processing done at the CP side. Inspired by the projected gradient descent algorithm, QDNet is designed as a distributed DNN with sparse connections. The performance of QDNet is compared to current solutions such as the zero-forcing (ZF) equalizer and the sphere decoder (SD). In some scenarios, experiment results show that our scheme achieves 2 dB SNR gain over the linear ZF with the same or lower computational complexity. It also achieves near-optimal performance compared to the SD algorithm, especially for low-to-moderate fronthaul link capacity and many RRUs in the C-RAN system.

The sparsity of the response of a quasi-distributed fiber optic sensing system allows ‘overclocking’ its interrogation

The response of a quasi-distributed fiber optic sensing system to a short interrogation pulse can be considered as a sparse signal in the time domain. This attribute can be exploited to enhance its performance beyond the commonly accepted limits. The work described here is analogous to some compressed sensing systems, which can be adequately sampled at sub-Nyquist rates, based on knowledge of their sparsity in the spectral domain. Equivalently, it is shown here how the sparsity of the impulse-response of a Quasi-Distributed Acoustic Sensing (Q-DAS) system can be exploited to interrogate it at rates well above the limit dictated by the total duration of its impulse response. An additional improvement in performance is achieved by using a Perfect Periodic Auto-correlation (PPA) code, rather than a pulse, for interrogation of the system. Cross-correlating the raw response of the Q-DAS system with the original code retains the sparsity of the response and provides significant gain in SNR without losing spatial resolution. Experimentally, the method was utilized to implement a 76 km long acoustic sensing system and successfully detected 250 kHz ultrasound signal. This was achieved by interrogating the system at a rate of 971 kHz which is 737 times the inherent limit dictated by the duration of the impulse-response of the system.

Mismatched Filters for Incoherent Pulse Compression in Laser Radar

A pulsed laser system is considered for long-range target detection. Single-pulse power received from a target may be low compared to the noise and background clutter power. Due to long-range and short laser wavelength, multi-pulse coherent processing is not possible, so incoherent detection is employed. Incoherent pulse compression sums received power from numerous pulses to increase SNR while maintaining single pulse range resolution. Following Levanon, aperiodic burst waveforms of on-off Keying (OOK) modulated transmitted pulses are derived from binary codes with optimal auto-correlation minimum integrated sidelobe level and minimum peak sidelobe level codes. Pulse compression uses real, continuous mismatched filters of lengths equal to or greater than the OOK code length. Filter values minimize a weighted sum of ISL and filter output power, the latter to increase SNR gain relative to that of a single pulse. Weighting can be adjusted to lower ISL for multiple target discrimination or to increase SNR gain for dim targets. A simple evolutionary modulation of the initial OOK code exchanges pairs of dissimilar samples to keep the number of on samples from decreasing and improves ISL performance. A very fast filter calculation is employed that permits an exploration of a wide variation in parameters.

Probabilistic Shaping for the Optical Phase Conjugation Channel

Probabilistic constellation shaping is studied and developed for optical phase conjugation (OPC)-based nonlinearity compensation of Kerr nonlinearities in optical fiber links. The mid-link OPC scenario is considered for dispersion compensated systems. It is demonstrated in simulations and experimentally that transmission strategies optimal for classical additive white Gaussian noise (AWGN) channels can be sub-optimal for these systems without nonlinearity compensation. On the contrary, when nonlinearity compensation is applied with mid-link OPC, the channel noise is demonstrated to be Gaussian and AWGN-like transmission strategies thus remain effective. A channel-agnostic probability mass function (PMF) optimization algorithm is proposed for the input constellation in order to further improve the shaping gains in both scenarios. Operating arbitrary PMFs on arbitrary channels is enabled by a channel-agnostic digital signal processing (DSP) chain. After ≈2000 km of transmission, mid-link OPC is demonstrated to provide ≈1 dB of gain in effective SNR, which translates to ≈0.4 bits/QAM symbol of gain in achievable information rate. The gain is then increased by an extra 0.2 bits/QAM symbol by applying probabilistic shaping.

Deep learning based digital backpropagation demonstrating SNR gain at low complexity in a 1200 km transmission link.

A deep learning (DL) based digital backpropagation (DBP) method with a 1 dB SNR gain over a conventional 1 step per span DBP is demonstrated in a 32 GBd 16QAM transmission across 1200 km. The new DL-DPB is shown to require 6 times less computational power over the conventional DBP scheme. The achievement is possible due to a novel training method in which the DL-DBP is blind to timing error, state of polarization rotation, frequency offset and phase offset. An analysis of the underlying mechanism is given. The applied method first undoes the dispersion, compensates for nonlinear effects in a distributed fashion and reduces the out of band nonlinear modulation due to compensation of the nonlinearities by having a low pass characteristic. We also show that it is sufficient to update the elements of the DL network using a signal with high nonlinearity when dispersion or nonlinearity conditions changes. Lastly, simulation results indicate that the proposed scheme is suitable to deal with impairments from transmission over longer distances.

Hierarchical Distribution Matching for Probabilistic Amplitude Shaping.

Probabilistic amplitude shaping—implemented through a distribution matcher (DM)—is an effective approach to enhance the performance and the flexibility of bandwidth-efficient coded modulations. Different DM structures have been proposed in the literature. Typically, both their performance and their complexity increase with the block length. In this work, we present a hierarchical DM (Hi-DM) approach based on the combination of several DMs of different possible types, which provides the good performance of long DMs with the low complexity of several short DMs. The DMs are organized in layers. Each upper-layer DM encodes information on a sequence of lower-layer DMs, which are used as “virtual symbols”. First, we describe the Hi-DM structure, its properties, and the encoding and decoding procedures. Then, we present three particular Hi-DM configurations, providing some practical design guidelines, and investigating their performance in terms of rate loss and energy loss. Finally, we compare the system performance obtained with the proposed Hi-DM structures and with their single-layer counterparts: a SNR gain is obtained by a two-layer Hi-DM based on constant composition DMs (CCDM) compared to a single-layer CCDM with same complexity; a gain and a significant complexity reduction are obtained by a Hi-DM based on minimum-energy lookup tables compared to a single-layer DM based on enumerative sphere shaping with same memory requirements.

Golden Coded GFDM for 5G Communication

The 5th Generation (5G) of wireless communication will be heterogeneous to support various traffic types and applications. Generalized Frequency Division Multiplexing (GFDM) is a 5G non-orthogonal waveform contender that offers scalable and spectrally compliant air interface which addresses the needs of 5G requirements. To aid the demand of high-capacity and reliable transmission, multiple antenna techniques are relied upon. In this work, the 5G modulation scheme GFDM is combined with a full rate Space–Time Block Code (STBC) with nonvanishing determinant called Golden Codes to exploit the diversity to the fullest. The proposed work is implemented in a real-time SDR test-bed called Wireless Open Access Research Platform (WARP). The proposed work is compared with 4G OFDM modulation in both Golden Coded and Uncoded case. The performance is assessed in terms of BER and Capacity/Bandwidth resolution. From the investigations, it is seen that the BER performance of Golden Coded GFDM outperforms the Uncoded GFDM by 3 dB SNR gain and attains a near-equal performance as OFDM. Also, it is evident from the analysis that, there is a 3.5 bps/Hz gain in capacity when compared to OFDM.

Signal-domain Kalman filtering: An approach for maneuvering target surveillance with wideband radar

As unmanned aerial vehicles (UAVs), owing to their low cost and wide variety of applications, become increasingly indispensable to modern society, and monitoring their illegal use through multichannel radar tracking has drawn widespread attention. Unfortunately, traditional tracking methods face challenges due to the UAV target with high-maneuverability and low-observability. In addition, the traditional measurements suffer some significant information loss because of their treatments like thresholding, clustering and peak sampling, which decreases tracking performance. In order to track UAV precisely, we propose a novel UAV tracking method based on the joint estimation of range and direction of arrival (DOA) in this paper. A complex-valued reference signal is introduced by coherently integrating in sliding windows to obtain SNR gain and preserve the complete structure and motion information of UAV. Besides motion state, the complex-valued reference signal is also utilized to predict the current return signal based on dynamic equation, and then a Bayes based method is derived to jointly estimate the range and DOA errors by comparing reference signal and return signal. In order to adapt to the maneuverable feature, a precise measurement model for motion variables is constructed to realize tracking combined with Kalman filter. Due to the utilization of the complex-valued reference signal and the precise measurement model, the proposed method has outstanding performance in the scene of low SNR and high maneuverability. In addition, there is no any information loss when the raw data is used to realize estimating and tracking. Finally, simulated and real-measured experiments confirm its remarkable performance.

Diffusion-prepared 3D gradient spin-echo sequence for improved oscillating gradient diffusion MRI.

Oscillating gradient (OG) enables the access of short diffusion times for time-dependent diffusion MRI (dMRI); however, it poses several technical challenges for clinical use. This study proposes a 3D oscillating gradient-prepared gradient spin-echo (OGprep-GRASE) sequence to improve SNR and shorten acquisition time for OG dMRI on clinical scanners. The 3D OGprep-GRASE sequence consisted of global saturation, diffusion encoding, fat saturation, and GRASE readout modules. Multiplexed sensitivity-encoding reconstruction was used to correct the phase errors between multiple shots. We compared the scan time and SNR of the proposed sequence and the conventional 2D-EPI sequence for OG dMRI at 30-90-mm slice coverage. We also examined the time-dependent diffusivity changes with OG dMRI acquired at frequencies of 50 Hz and 25 Hz and pulsed-gradient dMRI at diffusion times of 30 ms and 60 ms. The OGprep-GRASE sequence reduced the scan time by a factor of 1.38, and increased the SNR by 1.74-2.27 times compared with 2D EPI for relatively thick slice coverage (60-90 mm). The SNR gain led to improved diffusion-tensor reconstruction in the multishot protocols. Image distortion in 2D-EPI images was also reduced in GRASE images. Diffusivity measurements from the pulsed-gradient dMRI and OG dMRI showed clear diffusion-time dependency in the white matter and gray matter of the human brain, using both the GRASE and EPI sequences. The 3D OGprep-GRASE sequence improved scan time and SNR and reduced image distortion compared with the 2D multislice acquisition for OG dMRI on a 3T clinical system, which may facilitate the clinical translation of time-dependent dMRI.

Automatic detection of underwater propeller signals using cyclostationarity analysis

The second order Cyclostationarity Analysis (CA) is gaining attention for detection and classification of marine vehicles driven by propellers in broadband passive sonar systems, in which the Detection of Envelope Modulation On Noise (DEMON) is a standard tool for the same purpose. In this paper both CA and DEMON are discussed in the form of discrete digital formulae. It is shown that the three cyclo-spectra obtained by the DEMON analysis, the coherent integration of the Cyclic Modulation Spectra (CMS) and the coherent integration of the Cyclic Modulation Coherence (CMC) are equivalent to each other when the same frequency band and duration are chosen for calculating all of them. This equivalence is further explained based on the physical characteristic of cyclic modulation (also called amplitude modulation), that is, the same harmonic of cyclic modulation at different carrier frequencies is in-phase. For detection and/or classification of propeller signals a Coherent Integration and Quadratic Detection Law (CIQDL) is proposed to construct cyclo-spectra from the CMS and CMC. The performance of the thus constructed cyclo-spectra are compared with that of cyclo-spectra constructed using the Quadratic Detection Law (QDL). The SNR gain of the CIQDL over the QDL is derived theoretically and the gain is always larger than unity, indicating that the CIQDL outperforms the QDL. Both simulation and sea-trial data are used to demonstrate the in-phase characteristic. The performances of the CIQDL and the QDL are also quantitatively assessed using both simulation and sea-trial data.

Imaging characteristics of intravascular spherical contrast agents for grating-based x-ray dark-field imaging \u2013 effects of concentrations, spherical sizes and applied voltage

This study investigates the x-ray scattering characteristics of microsphere particles in x-ray-grating-based interferometric imaging at different concentrations, bubble sizes and tube voltages (kV). Attenuation (ATI), dark-field (DFI) and phase-contrast (PCI) images were acquired. Signal-to-noise (SNR) and contrast-to-noise ratios with water (CNRw) and air as reference (CNRa) were determined. In all modalities, a linear relationship between SNR and microbubbles concentration, respectively, microsphere size was found. A significant gain of SNR was found when varying kV. SNR was significantly higher in DFI and PCI than ATI. The highest gain of SNR was shown at 60 kV for all media in ATI and DFI, at 80 kV for PCI. SNR for all media was significantly higher compared to air and was slightly lower compared to water. A linear relationship was found between CNRa, CNRw, concentration and size. With increasing concentration and decreasing size, CNRa and CNRw increased in DFI, but decreased in PCI. Best CNRa and CNRw was found at specific combination of kV and concentration/size. Highest average CNRa and CNRw was found for microspheres in ATI and PCI, for microbubbles in DFI. Microspheres are a promising contrast-media for grating-based-interferometry, if kV, microsphere size and concentration are appropriately combined.

Solution for the Problems in RADAR Systems from SNR Gain Expressions and Blackout Likelihood Detection for Aviation Systems

Issues confronted in Radar frameworks at SDSC are, It is exceptionally troublesome for them to track an flying machine and discover its point, run and rise. With the existing ACSs, being incapable to provide the required information capacity. Since this misfortune of communication takes put between the ground station to the discuss station, discuss crashes may happen. Thus to dodge these kind of issues, modern proposed framework is defined. The full Duplex and Half Duplex systems can be combined to form a Hybrid Duplex Systems (HBD-ACS). In the existing Half duplex system, there was a crux in the spectrum mainly in the aeronautical industry. Hence the new HBD-ACS in proposed which eliminates the progressive interference. Progressive interference detector includes two methods namely, expressions of SNR gain and blackout probability. The Full duplex system may consists of the leftover interference. Hence to eliminate this, Interference Ignorant detector and SIC detector are used. Hence from the HBD-ACS, the diversity gain will be non-zero and the interference can be limited.

BER Performance of Signal Detection for Massive Multi User Spatial Modulation Systems

Massive spatial modulation (MSM) is considered as an attractive technique for multi antenna wireless communications. That is because, it gives higher energy efficiency and spectral efficiency than small scale multiple-input multiple-output (MIMO) systems. Massive SM-MIMO utilizes multiple transmit antennas for each user with only one transmit radio frequency (RF) chain and hundreds of receive antennas at base station (BS) with small number of RF chain. Where, each user can activate any one of its transmit antennas and the index of active transmit antenna (TA) can convey to information bits in addition to the information bits conveyed through classical modulation symbols (e.g. 16QAM). Owing to large number of TAs at the user and small number of RF chains at BS, multi user signal detection becomes challenging problem. To solve this matter, a joint grouped SM transmission scheme at users and group subspace pursuit (GSP) based signal detection at BS can be proposed to improve the signal detection performance. Owing to joint transmission scheme, SM signals in same transmission group exhibit group sparsity. Also, spatial signal composed of multiple users’ SM signals exhibits distributed sparsity. By utilizing these sparse features, the proposed GSP based signal detection can detect SM signals more reliability than other detection techniques. Additionally, the cyclic prefix single carrier (CPSC) is utilized to withstand the multipath channels. Simulation results prove that BER performance of the proposed GSP based signal detection outperforms classical SP based signal detection by 8 dB SNR gain at BER = 10−2. This gain can be improved by 2 dB by increasing the number of transmit antenna.

A multi spin echo pulse sequence with optimized excitation pulses and a 3D cone readout for hyperpolarized 13 C imaging.

PurposeImaging tumor metabolism in vivo using hyperpolarized [1‐13C]pyruvate is a promising technique for detecting disease, monitoring disease progression, and assessing treatment response. However, the transient nature of the hyperpolarization and its depletion following excitation limits the available time for imaging. We describe here a single‐shot multi spin echo sequence, which improves on previously reported sequences, with a shorter readout time, isotropic point spread function (PSF), and better signal‐to‐noise ratio.MethodsThe sequence uses numerically optimized spectrally selective excitation pulses set to the resonant frequencies of pyruvate and lactate and a hyperbolic secant adiabatic refocusing pulse, all applied in the absence of slice selection gradients. The excitation pulses were designed to be resistant to the effects of B0 and B1 field inhomogeneity. The gradient readout uses a 3D cone trajectory composed of 13 cones, all fully refocused and distributed among 7 spin echoes. The maximal gradient amplitude and slew rate were set to 4 G/cm and 20 G/cm/ms, respectively, to demonstrate the feasibility of clinical translation.ResultsThe pulse sequence gave an isotropic PSF of 2.8 mm. The excitation profiles of the optimized pulses closely matched simulations and a 46.10 ± 0.04% gain in image SNR was observed compared to a conventional Shinnar–Le Roux excitation pulse. The sequence was demonstrated with dynamic imaging of hyperpolarized [1‐13C]pyruvate and [1‐13C]lactate in vivo.ConclusionThe pulse sequence was capable of dynamic imaging of hyperpolarized 13C labeled metabolites in vivo with relatively high spatial and temporal resolution and immunity to system imperfections.

A hybrid method for artifact removal of visual evoked EEG

BackgroundThe visual evoked Electroencephalogram (EEG) signals are useful indicators to explore the hidden neural circuitry in human brain. But these signals are highly contaminated with a plethora of artifacts arising from power interference, eye, muscle and cardiac movements. Since the interference components include neural activity also, the existing techniques result in the distortion of the underlying cerebral signals. New MethodTo address the aforementioned problem, the current study proposes a hybrid method for denoising the visually evoked EEG responses. According to the proposed method, a cascade combination of digital filters, Independent Component Analysis (ICA) and Transient Artifact Reduction Algorithm (TARA) is utilized to suppress the artifacts. ICA technique automatically eliminates the ocular artifacts. The interference due to the remaining artifacts is removed through TARA. ResultsThe artifact removal ability of the proposed heuristics is evaluated in terms of SNR, correlation coefficient and sample entropy. The ICA results exhibit an increase of 13.47 % in SNR values on simulated signals and 26.66 % on real data. The application of TARA on simulated and real signals results in further SNR gain of 6.98 % and 71.51 % respectively. Significant statistical difference is also observed in this method (p<0.05). Comparison with Existing MethodsThis approach outperforms previous methods based on wavelets, enhanced variants of empirical mode decomposition and earlier versions of total variation denoising. ConclusionICA-TARA effectively eliminates the major artifacts without compromising the interpretation of the underlying neural state in both simulated and real visual evoked EEG.

Design and characterization of receive-only surface coil arrays at 3T with integrated solid high permittivity materials

A receive-only surface coil array for 3 Tesla integrating a high-permittivity material (HPM) with a relative permittivity of 660 was designed and constructed and subsequently its performance was evaluated and compared in terms of transmit field efficiency and specific absorption ratio (SAR) during transmission, and signal-to-noise ratio during reception, with a conventional identically-sized surface coil array. Finite-difference time-domain simulations, bench measurements and in-vivo neck imaging on three healthy volunteers were performed using a three-element surface coil array with integrated HPMs placed around the larynx. Simulation results show an increase in local transmit efficiency of the body coil of ~10-15% arising from the presence of the HPM. The receiver efficiency also increased by approximately 15% close to the surface. Phantom experiments confirmed these results. In-vivo scans using identical transmit power resulted in SNR gains throughout the laryngeal area when compared with the conventional surface coil array. In particular specifically around the carotid arteries an average SNR gain of 52% was measured averaged over the three subjects, while in the spine an average of 20% SNR gain was obtained.

Performance Analysis of Hardware Impairment Aware MMSE Receiver With Channel and CFO Estimation Error Statistics for a Large MIMO-OFDM System

In this treatise, we conceive a hardware impairment aware receiver design of a large multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system, taking into account the error statistics of parameter estimations. The hardware impairment includes the quantization noise, phase noise etc. There are two key contributions in this work. Firstly, consideration of error statistics of residual parameters in the receiver design improves receiver performance. In this work, we propose a linear equalizer based data detector at the receiver for a large MIMO-OFDM system and the parameters of interest are the channel impulse response (CIR) and carrier frequency offset (CFO) along with the hardware impairments awareness both at transmitter and receiver. The design criterion chosen for designing the detector equalizer is based on the linear minimum mean square error (LMMSE) one and it will consider the statistics of estimation error and hardware impairments. However, in any practical communication system, the availability of statistics for these parameter errors is inconceivable. Hence, we propose further to consider the Bayesian Crammer Rao lower bound (BCRLB) as the variance of the error with the key assumption of zero mean. Numerical simulation demonstrates that, consideration of such statistics attains an SNR gain of $2$ dB with respect to a fixed symbol error ratio (SER). It also shows that the SER performance with BCRLB matches very closely with the case, when exact error variance is used. For the second contribution, an extensive theoretical analysis has been performed to evaluate the MSE improvement of data detection with the LMMSE criterion with parameter estimation error statistics consideration in the large MIMO-OFDM system. This theoretical analysis of improved MSE has been conceived with the usage of large dimension random matrix theory and a closed-form expression has been obtained. Numerical simulation demonstrates that the theoretical analysis for MSE improvement matches closely with the simulated one.

Subcarrier Subset Selection-Aided Transmit Precoding Achieves Full-Diversity in Index Modulation

Index modulation (IM) is a recently proposed multi-carrier transmission scheme, which conveys information both by conventional symbols as well as by the specific subcarrier activation patterns conveying them. However, an impediment of IM is that it lacks transmit diversity gain. In this paper, we circumvent this limitation by proposing a limited-feedback assisted IM transmission scheme. Specifically, Euclidean distance based subcarrier subset selection (ED-SSS) is proposed and its attainable transmit diversity order is shown to be $N_c-N_{IM}+1$ , where $N_c$ is the total number of subcarriers in an IM block and $N_{IM}$ is the number of subcarriers used for IM. Furthermore, the ED-SSS is shown to be amenable to low-complexity implementation owing to the orthogonality of its subcarriers. In order to attain the maximum transmit diversity order of $N_c$ , ED-SSS is further extended with the aid of transmit precoding and its transmit diversity order is quantified. The proposed precoding assisted ED-SSS is shown to subsume several of the existing precoding aided IM transmission schemes. Simulation studies are conducted for validating our theoretical claims and also for quantifying the attainable performance gains of the proposed schemes. Specifically, at a BER of $10^{-3}$ an SNR gain as high as 8 dB is observed in case of precoding when compared to its counterpart operating without precoding.