An embodiment method for network communications includes receiving, by a network device, a plurality of channel quality indicator (CQI) symbols and one or more acknowledgement (ACK) symbols and selecting a reduced set of candidate CQI symbols by comparing a plurality of candidate CQI symbols with the plurality of CQI symbols. The method further includes generating a plurality of candidate CQI and ACK symbol combinations by combining the reduced set of candidate CQI symbols with candidate ACK symbols. The network device detects the plurality of CQI symbols and the one or more ACK symbols by comparing the plurality of candidate CQI and ACK symbol combinations with the plurality of CQI symbols and the one or more ACK symbols.

Maximum likelihood bit-stream generation and detection techniques are provided using the M-algorithm and Infinite Impulse Response (IIR) filtering. The M-Algorithm is applied to a target input signal X to perform Maximum Likelihood Sequence Estimation on the target input signal X to produce a digital bit stream B, such that after filtering by an IIR filter, the produced digital stream Y produces an error signal satisfying one or more predefined requirements. The predefined requirements comprise, for example, a substantially minimum error. In an exemplary bit detection implementation, the target input signal X comprises an observed analog signal and the produced digital stream Y comprises a digitized output of a receive channel corresponding to a transmitted bit stream. In an exemplary bit stream generation implementation, the target input signal X comprises a desired transmit signal and the produced digital stream Y comprises an estimate of the desired transmit signal.

Software implementations are provided for performing IQ imbalance correction and/or RF equalization. An input signal, x, is processed in software by executing a vector convolution instruction to apply the input signal, x, to a first complex FIR filter that performs one or more of RF equalization and IQ imbalance correction; and executing a vector convolution instruction to apply a conjugate x* of the input signal, x, to a second complex FIR filter that performs the one or more of RF equalization and IQ imbalance correction, wherein the second complex FIR filter is in parallel with the first complex FIR filter. The first and second complex FIR filters have complex coefficients and the input signal comprises a complex signal.

Wireless communication systems employ Multiple Input Multiple Output (MIMO) transmission and reception schemes to increase performance and the data rate of the system. A new approach for an SM-MIMO decoder that operates on the received symbols in parallel is presented. The new approach performs two different QR decompositions of the estimated channel matrix and produces two triangular matrices; one is right triangular and the other is left triangular. The modified systems of equations are processed in parallel. After each M-algorithm process has processed half of the total number of stages, total search space for the globally optimal transmitted symbol vector is reduced significantly. Finally, cumulative distance metrics are computed for the symbol sequences in the reduced search space and a global minimum is determined for the estimated transmitted symbol vector. This approach offers faster processing of the SM-MIMO signals and reduced distance metric computations and search operations.

Quasi-reduced state trellis equalization techniques achieve low-latency inter-symbol interference (ISI) equalization by selecting a subset of accumulated path metrics (APMs) for a leading symbol to propagate over a trellis to candidate states of a trailing symbol. This simplifies the computation of APMs for candidate states of the trailing symbol. Thereafter, APMs for candidate states of the trailing symbol are computed based on the subset of APMs for the leading symbol that were propagated over the trellis. Propagating fewer than all APMs for the leading symbol to the trailing symbol reduces the complexity of APM computation at the trailing symbol.