Saif Khan Mohammed

Per-Antenna Constant Envelope Precoding for Large Multi-User MIMO Systems

We consider the multi-user MIMO broadcast channel with M single-antenna users and N transmit antennas under the constraint that each antenna emits signals having constant envelope (CE). The motivation for this is that CE signals facilitate the use of power-efficient RF power amplifiers. Analytical and numerical results show that, under certain mild conditions on the channel gains, for a fixed M, an array gain is achievable even under the stringent per-antenna CE constraint. Essentially, for a fixed M, at sufficiently large N the total transmitted power can be reduced with increasing N while maintaining a fixed information rate to each user. Simulations for the i.i.d. Rayleigh fading channel show that the total transmit power can be reduced linearly with increasing N (i.e., an O(N) array gain). We also propose a precoding scheme which finds near-optimal CE signals to be transmitted, and has O(MN) complexity. Also, in terms of the total transmit power required to achieve a fixed desired information sum-rate, despite the stringent per-antenna CE constraint, the proposed CE precoding scheme performs close to the sum-capacity achieving scheme for an average-only total transmit power constrained channel.

High-Rate Space–Time Coded Large-MIMO Systems: Low-Complexity Detection and Channel Estimation

In this paper, we present a low-complexity algorithm for detection in high-rate, non-orthogonal space-time block coded (STBC) large-multiple-input multiple-output (MIMO) systems that achieve high spectral efficiencies of the order of tens of bps/Hz. We also present a training-based iterative detection/channel estimation scheme for such large STBC MIMO systems. Our simulation results show that excellent bit error rate and nearness-to-capacity performance are achieved by the proposed multistage likelihood ascent search (M-LAS) detector in conjunction with the proposed iterative detection/channel estimation scheme at low complexities. The fact that we could show such good results for large STBCs like 16×16 and 32×32 STBCs from Cyclic Division Algebras (CDA) operating at spectral efficiencies in excess of 20 bps/Hz (even after accounting for the overheads meant for pilot based training for channel estimation and turbo coding) establishes the effectiveness of the proposed detector and channel estimator. We decode perfect codes of large dimensions using the proposed detector. With the feasibility of such a low-complexity detection/channel estimation scheme, large-MIMO systems with tens of antennas operating at several tens of bps/Hz spectral efficiencies can become practical, enabling interesting high data rate wireless applications.

Uplink Performance of Time-Reversal MRC in Massive MIMO Systems Subject to Phase Noise

Multiuser multiple-input-multiple-output (MIMO) cellular systems with an excess of base station (BS) antennas (Massive MIMO) offer unprecedented multiplexing gains and radiated energy efficiency. Oscillator phase noise is introduced in the transmitter and receiver radio frequency chains and severely degrades the performance of communication systems. We study the effect of oscillator phase noise in frequency-selective Massive MIMO systems with imperfect channel state information. In particular, we consider two distinct operation modes, namely, when the phase noise processes at the M BS antennas are identical (synchronous operation) and when they are independent (nonsynchronous operation) . We analyze a linear and low-complexity time-reversal maximum-ratio combining reception strategy. For both operation modes, we derive a lower bound on the sum-capacity, and we compare their performance. Based on the derived achievable sum-rates, we show that with the proposed receive processing, an O(√M) array gain is achievable. Due to the phase noise drift, the estimated effective channel becomes progressively outdated. Therefore, phase noise effectively limits the length of the interval used for data transmission and the number of scheduled users. The derived achievable rates provide insights into the optimum choice of the data interval length and the number of scheduled users.

On the Optimality of Single-Carrier Transmission in Large-Scale Antenna Systems

A single carrier transmission scheme is presented for the frequency selective multi-user (MU) multiple-input single-output (MISO) Gaussian Broadcast Channel (GBC) with a base station (BS) having M antennas and K single antenna users. The proposed transmission scheme has low complexity and for M ≥ K it is shown to achieve near optimal sum-rate performance at low transmit power to receiver noise power ratio. Additionally, the proposed transmission scheme results in an equalization-free receiver and does not require any MU resource allocation and associated control signaling overhead. Also, the sum-rate achieved by the proposed transmission scheme is shown to be independent of the channel power delay profile (PDP). In terms of power efficiency, the proposed transmission scheme also exhibits an O(M) array power gain. Simulations are used to confirm analytical observations.

Single-User Beamforming in Large-Scale MISO Systems with Per-Antenna Constant-Envelope Constraints: The Doughnut Channel

Large antenna arrays at the transmitter (TX) have recently been shown to achieve remarkable intra-cell interference suppression at low complexity. However, building large arrays in practice, would require the use of power-efficient RF amplifiers, which generally have poor linearity characteristics and hence would require the use of input signals with a very small peak-to-average power ratio (PAPR). In this paper, we consider the single-user Multiple-Input Single-Output (MISO) channel for the case where the TX antennas are constrained to transmit signals having constant envelope (CE). We show that, with per-antenna CE transmission the effective channel seen by the receiver is a SISO AWGN channel with its input constrained to lie in a doughnut-shaped region. For a broad class of fading channels, analysis of the effective doughnut channel shows that under a per-antenna CE input constraint, i) compared to an average-only total TX power constrained MISO channel, the extra total TX power required to achieve a desired information rate is small and bounded, ii) with N TX antennas an O(N) array power gain is achievable, and iii) for a desired information rate, using power-efficient amplifiers with CE inputs would require significantly less total TX power when compared to using highly linear (power-inefficient) amplifiers with high PAPR inputs.

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.

Low-complexity near-ML decoding of large non-orthogonal STBCs using reactive tabu search

Non-orthogonal space-time block codes (STBC) with large dimensions are attractive because they can simultaneously achieve both high spectral efficiencies (same spectral efficiency as in V-BLAST for a given number of transmit antennas) as well as full transmit diversity. Decoding of non-orthogonal STBCs with large dimensions has been a challenge. In this paper, we present a reactive tabu search (RTS) based algorithm for decoding non-orthogonal STBCs from cyclic division algebras (CDA) having large dimensions. Under i.i.d fading and perfect channel state information at the receiver (CSIR), our simulation results show that RTS based decoding of 12 × 12 STBC from CDA and 4-QAM with 288 real dimensions achieves i) 10−3 uncoded BER at an SNR of just 0.5 dB away from SISO AWGN performance, and ii) a coded BER performance close to within about 5 dB of the theoretical MIMO capacity, using rate-3/4 turbo code at a spectral efficiency of 18 bps/Hz. RTS is shown to achieve near SISO AWGN performance with less number of dimensions than with LAS algorithm (which we reported recently) at some extra complexity than LAS.We also report good BER performance of RTS when i.i.d fading and perfect CSIR assumptions are relaxed by considering a spatially correlatedMIMO channelmodel, and by using a training based iterative RTS decoding/channel estimation scheme.

A Low-complexity near-ML performance achieving algorithm for large MIMO detection

In this paper, we present a low-complexity, near maximum-likelihood (ML) performance achieving detector for large MIMO systems having tens of transmit and receive antennas. Such large MIMO systems are of interest because of the high spectral efficiencies possible in such systems. The proposed detection algorithm, termed as multistage likelihood-ascent search (M-LAS) algorithm, is rooted in Hopfield neural networks, and is shown to possess excellent performance as well as complexity attributes. In terms of performance, in a 64 x 64 V-BLAST system with 4-QAM, the proposed algorithm achieves an un-coded BER of 10 3 at an SNR of just about 1 dB away from AWGN-only SISO performance given by Q(radic(SNR)). In terms of coded BER, with a rate-3/4 turbo code at a spectral efficiency of 96 bps/Hz the algorithm performs close to within about 4.5 dB from theoretical capacity, which is remarkable in terms of both high spectral efficiency as well as nearness to theoretical capacity. Our simulation results show that the above performance is achieved with a complexity of just O(NtNr) per symbol, where Nt and Nr denote the number of transmit and receive antennas.

MIMO Precoding With X- and Y-Codes

We consider a slow fading multiple-input multiple-output (MIMO) system with channel state information at both the transmitter and receiver. A well-known precoding scheme is based upon the singular value decomposition (SVD) of the channel matrix, which transforms the MIMO channel into parallel subchannels. Despite having low maximum likelihood decoding (MLD) complexity, this SVD precoding scheme provides a diversity gain which is limited by the diversity gain of the weakest subchannel. We therefore propose X- and Y-Codes, which improve the diversity gain of the SVD precoding scheme but maintain the low MLD complexity, by jointly coding information across a pair of subchannels. In particular, subchannels with high diversity gain are paired with those having low diversity gain. A pair of subchannels is jointly encoded using a 2 × 2 real matrix, which is fixed a priori and does not change with each channel realization. For X-Codes, these rotation matrices are parameterized by a single angle, while for Y-Codes, these matrices are left triangular matrices. Moreover, we propose X-, Y-Precoders with the same structure as X-, Y-Codes, but with encoding matrices adapted to each channel realization. We observed that X-Codes/Precoders are good for well-conditioned channels, while Y-Codes/Precoders are good for ill-conditioned channels.

Impact of Transceiver Power Consumption on the Energy Efficiency of Zero-Forcing Detector in Massive MIMO Systems

We consider the impact of transceiver power consumption on the energy efficiency (EE) of the zero-forcing (ZF) detector in the uplink of massive MIMO systems, where a base station (BS) with M antennas communicates coherently with K single antenna user terminals (UTs). We consider the problem of maximizing the EE with respect to (M, K) for a fixed sum spectral efficiency. Through analysis, we study the impact of system parameters on the optimal EE. System parameters consists of the average channel gain to the users and the power consumption parameters (PCPs) (e.g., power consumed by each RF antenna/ receiver at BS). When the average user channel gain is high or else the BS/UT design is power inefficient, our analysis reveals that it is optimal to have a few BS antennas and a single user, i.e., nonmassive MIMO regime. Similarly, when the channel gain is small or else the BS/UT design is power efficient, it is optimal to have a larger (M, K), i.e., massive MIMO regime. Tight analytical bounds on the optimal EE are proposed for both these regimes. The impact of the system parameters on the optimal EE is studied, and several interesting insights are drawn.