We consider the problem of distributed computation of a target function over a multiple-access channel. If the target and channel functions are matched (i.e., compute the same function), significant performance gains can be obtained by jointly designing the computation and communication tasks. However, in most situations there is mismatch between these two functions. In this work, we analyze the impact of this mismatch on the performance gains achievable with joint computation and communication designs over separation-based designs. We show that for most pairs of target and channel functions there is no such gain, and separation of computation and communication is optimal.
There is some work touching on the aspect of structural mismatch between the target and the channel functions. In @cite_13 , an example was given in which the mismatch between a linear target function with integer coefficients and a linear channel function with real coefficients can significantly reduce efficiency. In @cite_7 , it was conjectured that, for computation of finite-field addition over a real-addition channel, there could be a gap between the cut-set bound and the computation rate. In @cite_18 , mismatched computation when the network performs linear finite-field operations was studied. To the best of our knowledge, a systematic study of channel and computation mismatch is initiated in this work.
@cite_18 @cite_13 @cite_7
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Channel reciprocity in time-division duplexing (TDD) massive multiple-input multiple-output (MIMO) systems can be exploited to reduce the overhead required for the acquisition of channel state information (CSI). However, perfect reciprocity is unrealistic in practical systems due to random radio-frequency (RF) circuit mismatches in uplink and downlink channels. This can result in a significant degradation in the performance of linear precoding schemes, which are sensitive to the accuracy of the CSI. In this paper, we model and analyse the impact of RF mismatches on the performance of linear precoding in a TDD multi-user massive MIMO system, by taking the channel estimation error into considerations. We use the truncated Gaussian distribution to model the RF mismatch, and derive closed-form expressions of the output signal-to-interference-plus-noise ratio for maximum ratio transmission and zero forcing precoders. We further investigate the asymptotic performance of the derived expressions, to provide valuable insights into the practical system designs, including useful guidelines for the selection of the effective precoding schemes. Simulation results are presented to demonstrate the validity and accuracy of the proposed analytical results. In this paper we introduce a novel linear precoding technique. The approach used for the design of the precoding matrix is general and the resulting algorithm can address several optimization criteria with an arbitrary number of antennas at the user terminals. We have achieved this by designing the precoding matrices in two steps. In the first step we minimize the overlap of the row spaces spanned by the effective channel matrices of different users using a new cost function. In the next step, we optimize the system performance with respect to specific optimization criteria assuming a set of parallel single- user MIMO channels. By combining the closed form solution with Tomlinson-Harashima precoding we reach the maximum sum-rate capacity when the total number of antennas at the user terminals is less or equal to the number of antennas at the base station. By iterating the closed form solution with appropriate power loading we are able to extract the full diversity in the system and reach the maximum sum-rate capacity in case of high multi-user interference. Joint processing over a group of multi-user MIMO channels in different frequency and time slots yields maximum diversity regardless of the level of multi-user interference. We present a framework to study linear deterministic interference networks over finite fields. Unlike the popular linear deterministic models introduced to study Gaussian networks, we consider networks where the channel coefficients are general scalars over some extension field Fpm (scalar m-th extensionfield models), m×m diagonal matrices over Fp (m-symbol extension ground-field models), and m×m general non-singular matrices (MIMO ground field models). We use the companion matrix representation of the extension field to convert m-th extension scalar models into MIMO ground-field models where the channel matrices have special algebraic structure. For such models, we consider the 2× 2× 2 topology (two-hops two-flow) and the 3-user interference network topology. We derive achievability results and feasibility conditions for certain schemes based on the Precoding-Based Network Alignment (PBNA) approach, where intermediate nodes use random linear network coding (i.e., propagate random linear combinations of their incoming messages) and non-trivial precoding decoding is performed only at the network edges, at the sources and destinations. Furthermore, we apply this approach to the scalar 2×2×2 complex Gaussian IC with fixed channel coefficients, and show two competitive schemes outperforming other known approaches at any SNR, where we combine finite-field linear precoding decoding with lattice coding and the Compute and Forward approach at the signal level. As a side result, we also show significant advantages of vector linear network coding both in terms of feasibility probability (with random coding coefficients) and in terms of coding latency, with respect to standard scalar linear network coding, in PBNA schemes. Consider the multiple-input multiple-output (MIMO) interfering broadcast channel whereby multiple base stations in a cellular network simultaneously transmit signals to a group of users in their own cells while causing interference to each other. The basic problem is to design linear beamformers that can maximize the system throughput. In this paper, we propose a linear transceiver design algorithm for weighted sum-rate maximization that is based on iterative minimization of weighted mean-square error (MSE). The proposed algorithm only needs local channel knowledge and converges to a stationary point of the weighted sum-rate maximization problem. Furthermore, the algorithm and its convergence can be extended to a general class of sum-utility maximization problem. The effectiveness of the proposed algorithm is validated by numerical experiments.