Line-of-sight (LoS) millimeter wave (mmWave) multiple-input multiple-output (MIMO) is a promising approach for providing the ultra-high speed point to point links required for wireless backhaul in picocellular networks. The combination of large bandwidth and spatial multiplexing can sustain 100+ Gbps links over 10s to 100s of meters, while the antenna form factors required for providing the necessary spatial degrees of freedom remain small due to the small carrier wavelength. However, the large bandwidth makes the system susceptible to geometric misalignments: relatively small misalignments can cause multi-symbol delay spread across the receiver aperture. Furthermore, as the signaling bandwidth approaches the limits of hardware (i.e., analog-to-digital converter (ADC)) capabilities, the temporal oversampling typically used to overcome intersymbol interference becomes infeasible. In this paper, we investigate an architecture for joint space-time equalization with spatial oversampling by introducing additional receive antennas while maintaining symbol-rate sampling. We consider linear space-time equalization, controlling complexity by employing an adaptive time window at each receiver. We illustrate tradeoffs between the size of the adaptive window and the spatial oversampling factor via analysis and simulation for a 4-stream, 128 Gbps, 100 m LoS link at 130 GHz with both horizontal and vertical misalignment of the 2D planar arrays. For example, we show, via a signal space analysis accompanied by simulation results, that error floors can be avoided via 2X spatial oversampling and a temporal window of 5.

A key goal of next generation networks is to scale hardware design and signal processing algorithms to mmWave and THz arrays with a large number of elements. Imperfect manufacturing and limitations of circuit design introduce variations in the gain and relative phase offset of transmit and receive array elements that must be compensated prior to beam formation for either communication or sensing. We propose a novel method for calibrating large arrays in the field by exploiting the sparsity of the spatial channel. While conventional calibration methods are susceptible to multipath components in the wireless channel, our approach is shown to be robust to multipath interference if the measurements are gathered from a sufficiently diverse set of locations.

Millimeter wave MIMO combines the benefits of compact antenna arrays with a large number of elements and massive bandwidths, so that fully digital beamforming has the potential of supporting a large number of simultaneous users withper userdata rates of multiple gigabits/sec (Gbps). In this paper, we develop an analytical model for the impact of nonlinearities in such a system, and illustrate its utility in providing hardware design guidelines regarding two key challenges: the low available precision of analog-to-digital conversion at high sampling rates, and nonlinearities in ultra-high speed radio frequency (RF) and baseband circuits. We consider linear minimum mean square error (LMMSE) reception for a multiuser MIMO uplink, and provide performance guarantees based on two key concepts: (a) summarization of the impact of per-antenna nonlinearities via a quantity that we term the “intrinsic SNR”, (b) using linear MMSE performance in an ideal system without nonlinearities to bound that in our non-ideal system. For our numerical results, we employ nominal parameters corresponding to outdoor picocells operating at a carrier frequency of 140 GHz, with a data rate of 10 Gbps per user.

This paper investigates the effect of oscillator phase noise on a multiuser millimeter wave (mmWave) massive MIMO uplink as we scale up the number of base station antennas, fixing the load factor, defined as the ratio of the number of simultaneous users to the number of base station antennas. We consider a modular approach in which the base station employs an array of subarrays, or “tiles.” Each tile supports a fixed number of antennas, and can therefore be implemented using a separate radio frequency integrated circuit (RFIC), with synchronization across tiles accomplished by employing a phased locked loop in each tile to synthesize an on-chip oscillator at the carrier frequency by locking on to a common lower frequency reference clock. Assuming linear minimum mean squared error (LMMSE) multiuser detection, we provide an analytical framework that can be used to specify the required power spectral density (PSD) mask for phase noise for a target system performance. Our analysis for the phase noise at the output of the LMMSE receiver indicates two distinct effects: self-noise for each user which is inversely proportional to the number of tiles, and cross-talk between users which is insensitive to the number of tiles, and is proportional to the load factor. These analytical predictions, verified by simulations for a 140 GHz system targeting a per-user data rate of 10 Gbps, show that tiling is a robust approach for scaling. Numerical results for our proposed design approach yield relatively relaxed specifications for phase noise PSD masks.

Picocellular architectures are essential for providing the spatial reuse required to satisfy the ever-increasing demand for mobile data. A key deployment challenge is to provide backhaul connections with sufficiently high data rate. Providing wired support (e.g., using optical fiber) to pico base stations deployed opportunistically on lampposts and rooftops is impractical, hence wireless backhaul becomes an attractive approach. A multihop mesh network comprised of directional millimeter (mm) wave links is considered here for this purpose. Such networks are well suited for scaling backhaul data rates due to the abundance of spectrum in the mm wave bands, and the ability to form highly directional, electronically steerable beams. The backhaul design problem is formulated as one of joint routing and resource allocation, accounting for mutual interference across simultaneously active links. A computationally tractable formulation is developed by leveraging the localized nature of interference and the provable existence of a sparse optimal allocation. Numerical results are provided for topologies modeling urban and suburban settings.

We investigate distributed beamforming from a cluster of N cooperating transmitters to a distant destination over a wideband dispersive channel. Feedback from the destination is critical for enabling this. In order to develop protocols that scale to arbitrarily large numbers of cooperating nodes, we restrict attention to aggregate feedback broadcast from the destination to the entire transmit cluster, rather than per-transmitter channel feedback as in conventional feedback-based MIMO systems. We first show that naive application of a one-bit feedback algorithm developed for narrowband channels to each subcarrier in an OFDM system does achieve beamforming gain on each subcarrier, but results in an effective channel at the destination with severe phase discontinuities across frequency, which is not amenable to standard receive channel estimation algorithms. We then show that it is possible to enforce smoothness of phase across frequency by augmenting the feedback to 2 bits per subcarrier, which enables modeling and estimation of the effective channel as sparse in the time domain. Our preliminary results show that, even when the SNR per node is well below the threshold for reliable demodulation, it is possible to bootstrap using the N-fold power pooling gain obtained from incoherent combining of the signals from multiple transmitters, and to attain a significant fraction of the N2-fold beamforming gain using the proposed algorithm. We also discuss a number of open issues, recognizing that this is only a first step in developing scalable, wideband, distributed MIMO systems.

Distributed transmit beamforming with N cooperating nodes, each with fixed transmit power, provides a received power scaling with N2, corresponding to a “power pooling” gain of N and a beamforming gain of N. Prior work has shown that the optimal beamforming solution can be attained using a decentralized, iterative algorithm based on one bit (per iteration) feedback broadcast from the receiver to the transmitters. The algorithm is provably convergent in a noiseless setting, and is the basis for several successful prototypes. In this paper, we develop a framework for providing analytical insight into the effect of receiver noise, with the following key question in mind: can we bootstrap the algorithm from the incoherent power-pooled solution to operate in a regime in which the received SNR per node can be made arbitrarily small as we scale up the number of nodes N? Our analytical computations, validated by simulations, yield a somewhat negative answer: while the power-pooling gain guarantees a linear increase in received power with N, the per-node SNR cannot be scaled down with N if we wish to attain a quadratic increase in received power. Specifically, the fraction of the ideal beamforming gain attained using the one-bit algorithm is asymptotically independent of N, and depends only on the per-node SNR. However, the one-bit algorithm provides significant performance gains in practical regimes with a moderate number of cooperating nodes: the per-node SNR required for attaining a substantial fraction of the beamforming gain is low enough (e.g., - 5dB for 65% of the beamforming gain) to provide significant extension in operation regimes, while providing aggregate SNRs which permit reliable communication at high spectral efficiency: for example, starting from -5 dB per-node SNR, we obtain about 11 dB aggregate SNR with 10 cooperating nodes, and 17 dB SNR with 20 cooperating nodes.