Additive noise channels with binary-valued inputs and real-valued outputs are considered. The maximum error probability and the minimum channel capacity achieved by any power-constrained noise distribution are obtained. A general framework which applies to a variety of performance measures shows that the least-favorable noise distribution is, in general, a mixture of two lattice probability mass functions. The framework holds for m-ary input constellations on finite-dimensional lattices. >

Worst-case power-constrained noise for binary-input channels

In this letter, the asymptotic information rate of faster-than-Nyquist (FTN) signaling is examined when the data sequence consists of independent and identically distributed (i.i.d.) binary symbols. It is shown that, as the FTN rate tends to infinity, the information rate converges to that of the FTN signaling with i.i.d. Gaussian symbols. This leads to the optimality of the i.i.d. binary FTN signaling in the sense that the channel capacity can be asymptotically achieved by employing a transmit pulse that results in the same power spectral density as the water-filling solution.

{ Asymptotic Optimality of Binary Faster-than-Nyquist Signaling}

The S/N loss due to amplitude quantization is examined in connection with a digital matched filter correlator for a binary coded signal. A minimax binary quantizing concept is described, which adds an optimized noise dither prior to hard clipping. The design philosophy is minimax; i.e., the loss from an ideal analog correlator is minimized in the presence of the worst interference constrained to a specified average power. The resulting worst performance degradation is 4.8 dB, and occurs for constant amplitude interference. The extension of the minimax approach to a multilevel randomized quantizing concept is sketched. With four-level quantization, an upper bound on the performance degradation is 2.3 dB. The effect of finite time estimation of the interference power is determined, with the conclusion that a short-term power averaging can be used with only a small additional loss. Computer simulation results are in accordance with theoretical predictions.

Performance of Digital Matched Filter Correlator With Unknown Interference

Presence of multiple antennas on both sides of a communication channel promises significant improvements in system throughput and power efficiency. In effect, a new class of large multiple-input multiple-output (MIMO) communication systems has recently emerged and attracted both scientific and industrial attention. To analyze these systems in realistic scenarios one has to include such aspects as co-channel interference, multiple access and spatial correlation. In this paper, we study the properties of correlated MIMO multiple-access channels in the presence of external interference. Using the replica method from statistical physics, we derive the ergodic sum-rate of the communication for arbitrary signal constellations when the numbers of antennas at both ends of the channel grow large. Based on these asymptotic expressions, we also address the problem of sum-rate maximization using statistical channel state information and linear precoding. The numerical results demonstrate that when the interfering terminals use discrete constellations, the resulting interference becomes easier to handle compared to Gaussian signals. Thus, it may be possible to accommodate more interfering transmitter-receiver pairs within the same area as compared to the case of Gaussian signals. In addition, we demonstrate numerically for the Gaussian and QPSK signaling schemes that it is possible to design precoder matrices that significantly improve the achievable rates at low-to-mid range of signal-to-noise ratios when compared to isotropic precoding.

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Large-System Analysis of Correlated MIMO Multiple Access Channels with Arbitrary Signaling in the Presence of Interference

Presence of multiple antennas on both sides of a communication channel promises significant improvements in system throughput and power efficiency. In effect, a new class of large multiple-input multiple-output (MIMO) communication systems has recently emerged and attracted both scientific and industrial attention. To analyze these systems in realistic scenarios, one has to include such aspects as co-channel interference, multiple access and spatial correlation. In this paper, we study the properties of correlated MIMO multiple-access channels in the presence of external interference. Using the replica method from statistical physics, we derive the ergodic sum-rate of the communication for arbitrary signal constellations when the numbers of antennas at both ends of the channel grow large. Based on these asymptotic expressions, we also address the problem of sum-rate maximization using statistical channel information and linear precoding. The numerical results demonstrate that when the interfering terminals use discrete constellations, the resulting interference becomes easier to handle compared to Gaussian signals. Thus, it may be possible to accommodate more interfering transmitter-receiver pairs within the same area as compared to the case of Gaussian signals. In addition, we demonstrate numerically for the Gaussian and QPSK signaling schemes that it is possible to design precoder matrices that significantly improve the achievable rates at low-to-mid range of signal-to-noise ratios when compared to isotropic precoding.

For a coherent channel transmitting binary digits, a worst distribution under an average power constraint can be defined. A solution for the very noisy channel is found to be Gaussian, and the minimax demodulator utilizes correlation detection to guarantee an exponential bound on probability of error.

C. Cahn

Papers

Worst interference for coherent binary channel (Corresp.)