We develop a model for a large array ground receiver system for use in deep space communications, and analyze the resulting array channel capacity. The model includes effects of array geometry, time-dependent spacecraft orbital trajectory, point and extended interference sources, and elevation- dependent noise and atmospheric channel variations. Channel capacity is expressed as a simple quadratic form dependent upon covariance matrices characterizing the source, interference, and additive noise. This formulation facilitates inclusion of array and channel characteristics into the model, as well as comparison of optimal, suboptimal and equivalent single-antenna configurations on achievable throughput. Realistic examples of ground array channel capacity calculations are presented, demonstrating the impact of array geometry, planetary interference sources, and array combining algorithm design upon the achievable data throughput.

The assignment of interference power in the Numerical Results section of the paper entitled “Capacity of Large Array Receivers for Deep-Space Communications in the Presence of Interference” (IEEE Transactions on Communications, February 2008, pp. 194-200) is on a perantenna basis, whereas the received signal power is defined in terms of the entire array. The reason for this normalization is that the signal source is a distant spacecraft, hence appears as a point source to both the individual antenna elements and to the entire array. This means that the signal power remains constant over the entire spacecraft trajectory (ignoring atmospheric attenuation), hence a single value can be assigned for each plot. This however is not the case for interference power collected from nearby extended sources (such as Mars) that are resolved by the array, because the effective shape of the array beam is determined by the projection of the array layout onto the source direction vector, which is a function of time. Therefore, the interference power collected by the array varies over the spacecraft trajectory, but remains constant for the antenna elements that do not resolve the interference: hence it is more convenient to assign interference power on a perantenna basis. In particular, we should emphasize that in the text describing Fig. 2b in the Numerical Results section, the interference power per antenna is set equal to the source power over the array, hence the total interference power collected by the array is N times that of the signal power, where N is the number of antenna elements. Similarly, the summed interference power per antenna in Fig. 3a is nominally one fifth of the signal power. Although not discussed specifically in the text, this same normalization was used to compute the array capacity results of Figs. 4a and 4b.

A modification of the Alamouti code originally proposed for RF wireless applications is described that allows it to be applied in scenarios such as free-space optical communication with direct detection where unipolar modulations like pulse-position modulation and on-off keying are traditionally used to convey the information. The modification of the code and associated decision metric is such as to maintain all of the desirable properties of the original scheme.

The performance and tradeoffs of multipulse position modulation (MPPM) are investigated and compared with that of the traditional (single) pulse position modulation (PPM) scheme typically employed on the optical direct-detection channel. While the primary motivation for the consideration of the problem is to provide performance improvement for deep-space optical communications where narrow high-peak-power transmitted pulses offer significant advantages in terms of detection probabilities and background suppression capabilities at the receiver, the results obtained are sufficiently generic as to apply to other applications.

An optimal adaptive array receiver for use in groundbased optical communications is investigated. Kolmogorov phase screen simulations are used to generate realistic focal-plane distributions of the received optical fields in the presence of turbulence. The array detection concept reduces interference from background radiation by effectively assigning higher confidence levels at each instant of time to those detector elements that contain significant signal energy and suppressing those that do not. A simpler suboptimum structure that replaces the continuous weighting of the optimal receiver by a hard decision over each detector element is also described. It is shown that, for photon counting receivers observing Poisson distributed signals, performance improvements of up to 5 dB can be obtained over conventional single-detector photon counting receivers when observing turbulent optical fields in high background environments.

The use of radial basis function (RBF) networks and least squares algorithms for acquisition and fine tracking of NASA's 70-m-deep space network antennas is described and evaluated. We demonstrate that such a network, trained using the computationally efficient orthogonal least squares algorithm and working in conjunction with an array feed compensation system, can point a 70-m-deep space antenna with root mean square (rms) errors of 0.1-0.5 millidegrees (mdeg) under a wide range of signal-to-noise ratios and antenna elevations. This pointing accuracy is significantly better than the 0.8 mdeg benchmark for communications at Ka-band frequencies (32 GHz). Continuous adaptation strategies for the RBF network were also implemented to compensate for antenna aging, thermal gradients, and other factors leading to time-varying changes in the antenna structure, resulting in dramatic improvements in system performance. The systems described here are currently in testing phases at NASA's Goldstone Deep Space Network (DSN) and were evaluated using Ka-band telemetry from the Cassini spacecraft.

The use of radial basis function networks for fine pointing NASA's 70-meter deep space network antennas is described and evaluated. We demonstrate that such a network, working in conjunction with the array feed compensation system, and trained using the computationally efficient orthogonal least-squares algorithm, can point a 70-meter deep space antenna with RMS errors of less than 0.3 millidegree under good signal-to-noise ratio conditions, achieving significantly higher accuracies than the 0.8 millidegree benchmark for communications at Ka-band frequencies of 32 GHz.

The performance of a real-time digital combining system for use with array feeds has been considered in previous articles. The purpose of the combining operation is to recover signal-to-noise ratio (SNR) losses due to antenna deformations and atmospheric effects. Previously, arbitrary signal powers and noise variances were assumed, but no attempt was made to match the receiver channels to the available signal powers. Here it is shown that for any signal power and noise variance distribution, a "best" channel assignment exists that maximizes the combined SNR in the limit of vanishingly small combining losses. This limit can be approached in practice by observing sufficiently many samples. Specific signal power and noise variance distributions are considered, and it is shown that even relatively "noisy" channels can be used effectively to recover SNR losses resulting from signals diverted out of a "high-quality" channel by antenna deformations.>

A real-time digital signal combining system for use with array feeds is proposed. The combining system attempts to compensate for signal-to-noise ratio (SNR) loss resulting from antenna deformations induced by gravitational and atmospheric effects. The combining weights are obtained directly from the observed residual carrier samples in each channel using a 'sliding-window' implementation of a maximum-likelihood (ML) parameter estimator. It is shown that with averaging times of about 0.1 s, combining loss for a seven-element array can be limited to about 0.1 dB in a realistic operational environment. This result suggests that the real-time combining system proposed is capable of recovering virtually all of the signal power captured by the array feed, even in the presence of severe wind gusts and similar disturbances.>

The structure of a maximum {\em a posteriori} decoder is derived for binary optical fields processed according to Kennedy's near-optimum scheme, but operating in the presence of random optical phase-error and interfering background fields. An exact expression is found for the error probability, and examples to illustrate decoder performance under various operating conditions of interest are provided.