Aniruddha Das

NDA SNR estimation: CRLBs and EM based estimators

Signal to noise ratio (SNR) estimation is an important problem in many communication systems. SNR often needs to be estimated in the presence of unknown transmitted data symbols in a non data aided (NDA) manner. In this paper we derive a methodology to calculate the Cramer-Rao lower bound (CRLB) of NDA SNR estimation in an additive white Gaussian noise (AWGN) channel for any symmetric constellation. In particular, the CRLB is evaluated and presented for QPSK, 8PSK, 16QAM, 32QAM, 16APSK and 32APSK constellations. We also present an Expectation-Maximization (EM) algorithm based iterative estimator, valid for any arbitrary constellation, which performs very close to the CRLBs at all SNRs of practical interest and discuss issues regarding this iterative algorithm such as initialization and convergence speed.

SNR and Noise Variance Estimation for MIMO Systems

Accurate signal-to-noise ratio (SNR) and noise variance estimation are extremely important aspects of receiver design in multiple-input multiple-output (MIMO) systems. Typically, these parameters are estimated using known pilot/training symbols. However, significant improvements may be made by using both the known pilot symbols as well as the unknown data symbols. In this paper, we address SNR and noise variance estimation of MIMO systems for both a data aided (DA) model, a non-data aided (NDA) model, as well as a mixed model that uses known and unknown data symbols. The Cramér-Rao lower bound (CRLB) and modified Cramér-Rao lower bound (MCRLB) for MIMO SNR and MIMO noise variance estimation are determined for digital constellations such as BPSK, QPSK, 8PSK, and 16QAM. Maximum-likelihood estimators are derived in closed form for the DA model. For the NDA model, closed form approximations are derived in addition to iterative expectation-maximization (EM) algorithm based estimators, all of which are demonstrated to perform very close to the CRLB.

Remote non-linearity detection via burst power dithering and EM based SNR Estimation

A new approach to detect the onset of saturation (1dB output compression point) at remote terminals is proposed in this paper. The proposed approach dithers the transmit power of periodic ranging bursts by a known amount and then estimates the received difference in Signal to Noise Ratio (SNR) and uses this metric to indicate whether the operating point of the Power Amplifier is in the linear range or not. The Expectation-Maximization (EM) Algorithm is used to achieve the ML estimate of the received SNR and is compared to the Cramer-Rao Lower Bound (CRLB). Application of this algorithm to a commercial satellite broadband system as well as simplifications to the algorithm to make it easier for implementation on FPGAs, are also discussed.

MIMO Systems with Intentional Timing Offset

The performance of MIMO systems with intentional timing offset between the transmitters has recently been the focus of study of different researchers. In these schemes, a nonzero (but known) symbol timing offset is introduced between the signals transmitted from the different transmitters to improve the performance of MIMO systems. This leads to a reduction in Interantenna Interference (IAI), and it is shown that an advanced receiver can utilize this information to extract significant performance gains. In this paper, we show that this transmission scheme may be used in conjunction with different kinds of receivers including ZF, MMSE, and sequence detection-based receivers. We also consider the design of novel pulse shapes that reduce the IAI at the expense of slightly higher intersymbol interference (ISI) and show that additional gains may be achieved.

Adaptive Non Orthogonal MFSK

M-ary frequency shift keying (MFSK) using one or more orthogonal tones per symbol has been in use in non-coherent systems for quite some time. We present an alternate system for non-coherent systems using non-orthogonal tones, spread non-uniformly throughout the bandwidth, which outperforms the equivalent orthogonal tone system. We demonstrate that from a theoretical capacity point of view, the same bit rate could be achieved by the proposed system with as much as 2.5 dB lower signal-to-noise ratio (SNR). For some practical configurations we demonstrate as much as 2 dB of gain. We present the performance with maximum-likelihood (ML) receivers as well as least-squares (LS) receivers as well as lower complexity receivers based on compressed sensing (CS). We also demonstrate that such a non-orthogonal system may be used to increase the spectral efficiency of the overall system by adapting the spectral efficiency in response to the link SNR. Such an adaptive non-orthogonal MFSK system requires estimation of the SNR (or Es/N0), and we present both the Cramér-Rao lower bound (CRLB) as well as maximum-likelihood (ML) estimators, which attain the CRLB for both data-aided (DA) SNR estimation as well as non-data-aided (NDA) SNR estimation.

Impact of receiver structure and timing offset on MIMO spatial multiplexing

Multiple antenna enhancements via symbol timing relative offsets (MAESTRO) was recently introduced as a scheme to improve the performance of a V-BLAST like multi-antenna system by introducing sub-symbol timing offsets between the transmit antennas. In this paper we address the role of receiver structure on performance and investigate the optimal choice of the time offset parameter. A similar timing offset V-BLAST scheme was also introduced by Shao et al., where the authors use a zero-forcing (ZF) receiver and conclude the system outperforms V-BLAST only for small block sizes. We show that the zero-forcing (ZF) receiver suggested by Shao et al. is deficient and is the main reason for some of the drawbacks observed by them. The optimal ZF receiver is derived, and along with the linear MMSE receiver, is shown to exhibit no such weaknesses. The problem of optimal offset is also examined and the optimal offset for a 2 times 2 MIMO system derived.

NDA SNR estimation for 32APSK in AWGN

32-amplitude and phase-shift-keying (32APSK) is one of the modulation schemes proposed in the 2nd generation digital video broadcasting over satellite (DVB-S2) standard. This paper presents a non-data-aided (NDA) SNR estimation scheme for 32APSK using the expectation-maximization (EM) algorithm. Two variants of the EM algorithm are presented, first with an arbitrary initialization and a second version that is initialized by modifying an existing (sub-optimal) SNR estimation technique. We demonstrate a significantly faster convergence with the latter form of initialization. We compare the performance of this estimator to the Cramer-Rao lower bound (CRLB) of NDA SNR estimation and show that the estimator performs very close to the CRLB over all SNRs of practical interest even for block sizes of 100 symbols. The estimator has also been implemented on FPGAs and we show that the fixed point implementation also performs very close to the theoretical limit.