Millimeter wave (mmWave) signals experience orders-of-magnitude more pathloss than the microwave signals currently used in most wireless applications. MmWave systems must therefore leverage large antenna arrays, made possible by the decrease in wavelength, to combat pathloss with beamforming gain. Beamforming with multiple data streams, known as precoding, can be used to further improve mmWave spectral efficiency. Both beamforming and precoding are done digitally at baseband in traditional multi-antenna systems. The high cost and power consumption of mixed-signal devices in mmWave systems, however, make analog processing in the RF domain more attractive. This hardware limitation restricts the feasible set of precoders and combiners that can be applied by practical mmWave transceivers. In this paper, we consider transmit precoding and receiver combining in mmWave systems with large antenna arrays. We exploit the spatial structure of mmWave channels to formulate the precoding/combining problem as a sparse reconstruction problem. Using the principle of basis pursuit, we develop algorithms that accurately approximate optimal unconstrained precoders and combiners such that they can be implemented in low-cost RF hardware. We present numerical results on the performance of the proposed algorithms and show that they allow mmWave systems to approach their unconstrained performance limits, even when transceiver hardware constraints are considered.

Hybrid analog/digital architectures and receivers with low-resolution analog-to-digital converters (ADCs) are two low power solutions for wireless systems with large antenna arrays, such as millimeter wave and massive MIMO systems. Most prior work represents two extreme cases in which either a small number of RF chains with full-resolution ADCs, or low resolution ADC with a number of RF chains equal to the number of antennas is assumed. In this paper, a generalized hybrid architecture with a small number of RF chains and finite number of ADC bits is proposed. For this architecture, achievable rates with channel inversion and SVD based transmission methods are derived. Results show that the achievable rate is comparable to that obtained by full-precision ADC receivers at low and medium SNRs. A trade-off between the achievable rate and power consumption for different numbers of bits and RF chains is devised. This enables us to draw some conclusions on the number of ADC bits needed to maximize the system energy efficiency. Numerical simulations show that coarse ADC quantization is optimal under various system configurations. This means that hybrid combining with coarse quantization achieves better energy-rate trade-off compared to both hybrid combining with full-resolutions ADCs and 1-bit ADC combining.

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