Ultra-reliable wireless communication links require the utilization of all diversity sources of a wireless communication channel. Hadani et al. propose a two dimensional discrete symplectic Fourier transform (DSFT) as orthogonal pre-coder for a time-frequency modulation scheme. In this paper we explore general orthogonal precoding (OP) and its performance in timeand frequency-selective channels. We show that iterative parallel interference cancellation (PIC) and iterative channel estimation methods can be used for the detection of OP. A scalar signal model for OP transmission is obtained by PIC. Based on this signal model, we can prove that all constant modulus sequences, e.g. the DSFT basis functions or Walsh-Hadamard sequences, lead to the same performance for OP. We validate our receiver structure by numerical link level simulations of a vehicleto-vehicle communication link with a relative velocity of 0 . . . 200 km/h. We demonstrate that OP achieves a gain of about 4.8 dB if compared to orthogonal frequency division multiplexing at a bit error rate of 10 −4 . Our performance results for coded OP are the best results for a fully documented receiver architecture, published so far.

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Massive multiple-input multiple-output (MIMO) systems are of high interest for ultrareliable low-latency communication (URLLC) links. They provide channel hardening, i.e. reduced channel variations, due to the large number of transmit antennas which exploit spatial diversity by beam-forming. Massive MIMO requires channel state information (CSI) on the base station side. For time-varying vehicular communication channels the CSI acquired during the uplink phase will be outdated for the following downlink phase, leading to reduced spatial channel hardening. We investigate a combination of massive MIMO with general orthogonal precoding (OP) to compensate this effect. OP uses two-dimensional precoding sequences in the time-frequency domain and provides channel hardening by exploiting time-and frequency diversity. We show that the combination of massive MIMO and OP is beneficial for time-varying communication channels. While the spatial channel hardening of massive MIMO decreases, the timefrequency channel hardening of OP increases with larger time-variance of the communication channel. An iterative receiver algorithm for massive MIMO with OP as well as a detailed analysis of the channel hardening effect is presented. We demonstrate a BER reduction by more than one order of magnitude for a velocity of 50 km/h = 16.6 m/s using the orthogonal frequency division multiplexing (OFDM) based 5G new radio (NR) physical layer.INDEX TERMS 5G, massive MIMO, orthogonal precoding, ultra-reliable low-latency communication (URLLC) links. I. INTRODUCTIONUltra-reliable low-latency wireless communication (URLLC) links are an important component for connected autonomous vehicles, industrial wireless control loops, and many other machine-to-machine communication applications [1]. The random fading process in wireless communication channels leads to signal strength fluctuations at the receive antenna and random unpredictable frame errors.Massive multiple-input multiple-output (MIMO) systems reach the capacity of multi-user MIMO systems by linear beam-forming over a large number of transmit antennaThe associate editor coordinating the review of this manuscript and approving it for publication was Jiankang Zhang.

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