Energy-Spectral Efficiency Trade-off for a Massive SU-MIMO System with Transceiver Power Consumption

We consider a single user (SU) massive MIMO system with multiple antennas at the transmitter (base station) and a single antenna at the user terminal (UT). Taking transceiver power consumption into consideration, for a given spectral efficiency (SE) we maximize the energy efficiency (EE) as a function of the number of base station (BS) antennas $M$, resulting in a closed-form expression for the optimal SE-EE trade-off. It is observed that in contrast to the classical SE-EE trade-off (which considers only the radiated power), with transceiver power consumption taken into account, the EE increases with increasing SE when SE is sufficiently small. Further, for a fixed SE we analyze the impact of varying cell size (i.e., equivalently average channel gain $G_c$) on the optimal EE. We show the interesting result that for sufficiently small $G_c$, the optimal EE decreases as $\mathcal{O}(\sqrt{G_c})$ with decreasing $G_c$. Our analysis also reveals that for sufficiently small SE (or large $G_c$), the EE is insensitive to the power amplifier efficiency.Comment: Submitted to IEEE International Conference on Communications (ICC) 201

Impact of Frequency Selectivity on the Information Rate Performance of CFO Impaired Single-Carrier Massive MU-MIMO Uplink

In this paper, we study the impact of frequency-selectivity on the gap between the required per-user transmit power in the residual CFO scenario (i.e. after CFO estimation/compensation at the base-station (BS) from [6]) and that in the ideal/zero CFO scenario, for a fixed per-user information rate, in single-carrier massive MU-MIMO uplink systems with the TR-MRC receiver. Information theoretic analysis reveals that this gap decreases with increasing frequency-selectivity of the channel. Also, in the residual CFO scenario, an $\mathcal{O}(\sqrt{M})$ array gain is still achievable ($M$ is the number of BS antennas) in frequency-selective channels with imperfect channel estimates.Comment: Submitted to IEEE Wireless Communications Letter

Information Rate Performance of Massive MU-MIMO Uplink with Constant Envelope Pilot-based Frequency Synchronization

In this paper, we consider a constant envelope (CE) pilot-based low-complexity technique for frequency synchronization in multi-user massive MIMO systems. Study of the complexity-performance trade-off shows that this CE-pilot-based technique provides better MSE performance when compared to existing low-complexity high-PAPR pilot-based CFO (carrier frequency offset) estimator. Numerical study of the information rate performance of the TR-MRC receiver in imperfect CSI scenario with this CE-pilot based CFO estimator shows that it is more energy-and-spectrally efficient than existing low-complexity CFO estimator in massive MIMO systems. It is also observed that with this CE-pilot based CFO estimation, an $\mathcal{O}(\sqrt{M})$ array gain is achievable.Comment: Submitted to IEEE Wireless Communication Letter

Constant Envelope Pilot-Based Low-Complexity CFO Estimation in Massive MU-MIMO Systems

In this paper we consider a constant envelope pilot signal based carrier frequency offset (CFO) estimation in massive multiple-input multiple-output (MIMO) systems. The proposed algorithm performs spatial averaging on the periodogram of the received pilots across the base station (BS) antennas. Our study reveals that the proposed algorithm has complexity only linear in $M$ (the number of BS antennas). Further our analysis and numerical simulations also reveal that with fixed number of users and a fixed pilot length, the minimum required transmit pilot power decreases as $\frac{1}{\sqrt{M}}$ with increasing $M$, while maintaining a fixed desired mean squared error (MSE) of CFO estimation.Comment: Submitted to IEEE Globecom 2016 Conferenc

Constant-Envelope Precoding with Time-Variation Constraint on the Transmitted Phase Angles

We consider downlink precoding in a frequency-selective multi-user massive MIMO system with highly efficient but non-linear power amplifiers at the base station (BS). A low-complexity precoding algorithm is proposed, which generates constant-envelope (CE) transmit signals for each BS antenna. To avoid large variations in the phase angle transmitted from each antenna, the difference of the phase angles transmitted in consecutive channel uses is limited to $[-\alpha \pi \,,\, \alpha \pi]$ for a fixed $0 < \alpha \leq 1$. To achieve a desired per-user information rate, the extra total transmit power required under the time variation constraint when compared to the special case of no time variation constraint (i.e., $\alpha=1$), is small for many practical values of $\alpha$. In a i.i.d. Rayleigh fading channel with $80$ BS antennas, $5$ single-antenna users and a desired per-user information rate of $1$ bit-per-channel-use, the extra total transmit power required is less than $2.0$ dB when $\alpha = 1/2$.Comment: Submitted to IEEE Wireless Communication Letter

Improving the Performance of the Zero-Forcing Multiuser MISO Downlink Precoder through User Grouping

We consider the Multiple Input Single Output (MISO) Gaussian Broadcast channel with $N_t$ antennas at the base station (BS) and $N_u$ single-antenna users in the downlink. We propose a novel user grouping precoder which improves the sum rate performance of the Zero-Forcing (ZF) precoder specially when the channel is ill-conditioned. The proposed precoder partitions all the users into small groups of equal size. Downlink beamforming is then done in such a way that, at each user's receiver the interference from the signal intended for users not in its group is nulled out. Intra-group interference still remains, and is cancelled through successive interference pre-subtraction at the BS using Dirty Paper Coding (DPC). The proposed user grouping method is different from user selection, since it is a method for precoding of information to the selected (scheduled) users, and not for selecting which users are to be scheduled. Through analysis and simulations, the proposed user grouping based precoder is shown to achieve significant improvement in the achievable sum rate when compared to the ZF precoder. When users are paired (i.e., each group has two users), the complexity of the proposed precoder is $O(N_u^3) + O(N_u^2 N_t)$ which is the same as that of the ZF precoder.Comment: Submitted to IEEE Transactions on Wireless Communication

Constant-Envelope Multi-User Precoding for Frequency-Selective Massive MIMO Systems

We consider downlink precoding in a frequency-selective multi-user Massive MIMO system with highly efficient but non-linear power amplifiers at the base station (BS). A low-complexity precoding algorithm is proposed, which generates constant-envelope (CE) signals at each BS antenna. To achieve a desired per-user information rate, the extra total transmit power required under the per-antenna CE constraint when compared to the commonly used less stringent total average transmit power constraint, is small.Comment: Submitted to IEEE Wireless Communications Letter

Derivation of OTFS Modulation from First Principles

Orthogonal Time Frequency Space (OTFS) modulation has been recently proposed to be robust to channel induced Doppler shift in high mobility wireless communication systems. However, to the best of our knowledge, none of the prior works on OTFS have derived it from first principles. In this paper, using the ZAK representation of time-domain (TD) signals, we rigorously derive an orthonormal basis of approximately time and bandwidth limited signals which are also localized in the delay-Doppler (DD) domain. We then consider DD domain modulation based on this orthonormal basis, and derive OTFS modulation. To the best of our knowledge, this is the first paper to rigorously derive OTFS modulation from first principles. We show that irrespective of the amount of Doppler shift, the received DD domain basis signals are localized in a small interval of size roughly equal to the inverse time duration along the Doppler domain and of size roughly equal to the inverse bandwidth along the delay domain (time duration refers to the length of the time-interval where the TD transmit signal has been limited). With sufficiently large time duration and bandwidth, there is little interference between information symbols modulated on different basis signals, which allows for joint DD domain equalization of all information symbols. This explains the inherent robustness of DD domain modulation to channel induced Doppler shift when compared with Orthogonal Frequency Division Multiplexing (OFDM). The degree of localization of the DD domain basis signals is inversely related to the time duration of the transmit signal, which explains the trade-off between robustness to Doppler shift and latency.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Time-Domain to Delay-Doppler Domain Conversion of OTFS Signals in Very High Mobility Scenarios

In Orthogonal Time Frequency Space (OTFS) modulation, information symbols are embedded in the delay-Doppler (DD) domain instead of the time-frequency (TF) domain. n order to ensure compatibility with existing OFDM systems (e.g. 4G LTE), most prior work on OTFS receivers consider a two-step conversion, where the received time-domain (TD) signal is firstly converted to a time-frequency (TF) signal (using an OFDM demodulator) followed by post-processing of this TF signal into a DD domain signal. In this paper, we show that the spectral efficiency (SE) performance of a two-step conversion based receiver degrades in very high mobility scenarios where the Doppler shift is a significant fraction of the communication bandwidth (e.g., control and non-payload communication (CNPC) in Unmanned Aircraft Systems (UAS)). We therefore consider an alternate conversion, where the received TD signal is directly converted to the DD domain. The resulting received DD domain signal is shown to be not the same as that obtained in the two-step conversion considered in prior works. The alternate conversion does not require an OFDM demodulator and is shown to have lower complexity than the two-step conversion. Analysis and simulations reveal that even in very high mobility scenarios, the SE achieved with the alternate conversion is invariant of Doppler shift and is significantly higher than the SE achieved with two-step conversion (which degrades with increasing Doppler shift).Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Impact of CFO Estimation on the Performance of ZF Receiver in Massive MU-MIMO Systems

In this paper, we study the impact of carrier frequency offset (CFO) estimation/compensation on the information rate performance of the zero-forcing (ZF) receiver in the uplink of a multi-user massive multiple-input multiple-output (MIMO) system. Analysis of the derived closed-form expression of the per-user information rate reveals that with increasing number of BS antennas $M$, an $\mathcal{O}(\sqrt{M})$ array gain is achievable, which is same as that achieved in the ideal zero CFO scenario. Also it is observed that compared to the ideal zero CFO case, the performance degradation in the presence of residual CFO (after CFO compensation) is the same for both ZF and MRC.Comment: Submitted to IEEE Transactions on Vehicular Technology (TVT) as a correspondence pape