# Precoding for the Sparsely Spread MC-CDMA Downlink with Discrete-Alphabet Inputs

## TL;DR

This paper introduces a power-efficient precoding algorithm for sparse MC-CDMA downlink systems with discrete inputs, reducing complexity while maintaining performance through sparse signatures.

## Contribution

It proposes a novel precoding method leveraging sparse signatures for downlink MC-CDMA, improving power efficiency and reducing computational complexity compared to traditional methods.

## Key findings

- Significance of signature sparsity for reducing precoding complexity.
- Power reduction gains over zero-forcing precoding.
- Sparse MC-CDMA achieves similar throughput with lower complexity.

## Abstract

Sparse signatures have been proposed for the CDMA uplink to reduce multi-user detection complexity, but they have not yet been fully exploited for its downlink counterpart. In this work, we propose a Multi-Carrier CDMA (MC-CDMA) downlink communication, where regular sparse signatures are deployed in the frequency domain. Taking the symbol detection point of view, we formulate a problem appropriate for the downlink with discrete alphabets as inputs. The solution to the problem provides a power-efficient precoding algorithm for the base station, subject to minimum symbol error probability (SEP) requirements at the mobile stations. In the algorithm, signature sparsity is shown to be crucial for reducing precoding complexity. Numerical results confirm system-load-dependent power reduction gain from the proposed precoding over the zero-forcing precoding and the regularized zero-forcing precoding with optimized regularization parameter under the same SEP targets. For a fixed system load, it is also demonstrated that sparse MC-CDMA with a proper choice of sparsity level attains almost the same power efficiency and link throughput as that of dense MC-CDMA yet with reduced precoding complexity, thanks to the sparse signatures.