# An Enhanced Precoder for Multi User Multiple-Input Multiple-Output Downlink Systems
## 1 Introduction  
In the future, wireless communication systems will be able to offer various services, such as virtual reality, big data, etc., and large amounts of data will be able to travel over the network. Therefore, the wireless communication system will probably be able to provide multiple users with high reliability and throughput [1]. However, insufficient bandwidth makes the wireless resources scarce. Therefore, the multiple-input multiple-output (MIMO) system is seen as attractive, due to spectral efficiencies and high throughput [2; 3; 4; 5; 6; 7]. Also, the multi user (MU) MIMO system was invented to provide high capacity for multiple user equipments (UEs) [8; 9]. The MU MIMO system applies a concept of space division multiple access (SDMA) [10]. In a co-channel wireless system, each UE generates inter-user interference (IUI) to other UEs. The challenge is to cancel out IUI disrupting wireless communication. Therefore, the base station (BS) estimates channel state information (CSI) and applies a precoding technique, mitigating IUI. The precoding techniques are divided into nonlinear and linear precoding techniques. Nonlinear techniques [11; 12; 13] that provide high performance are unrealizable due to their high complexity, and linear techniques supply feasible compromises. The block diagonalization (BD) precoder is a typical linear precoder [14]. BD is well known as a precoder to carry out perfect nulling through singular value decomposition (SVD) operations. In the environment where channel correlation is high, BS technique can eliminate IUI through SVD. For this advantage, an improved BD precoder has been proposed in many previous studies. For instance, the author in [15] proposed low complexity for the BD precoder. However, although thereceived signal has a benefit of zero IUI, a BD precoder can not guarantee high bit error rate (BER) performance because the noise component is disregarded. Also, the BD precoder spends most of its spatial resources to achieve perfect nulling, and poor diversity gain is obtained. Therefore, a regularized block diagonalization (RBD) precoder and generalized block diagonalization (GBD) precoder have been proposed in [16; 17]. The RBD precoder has been considered attractive since many probabilities of performance improvement are provided by considering noise power. For this reason, the author in [18] proposed an improved precoder in terms of capacity performance. However, the RBD precoder still consumes transmit antenna resources to mitigate IUI. On the other hand, the GBD precoder offers additional diversity gain, but is not optimized with minimum mean square error (MMSE) criterion. Consequentially, the GBD scheme cannot achieve additional BER performance. In other words, the RBD precoder provides improved BER performance by mitigating the noise effect, but additional diversity gain is not obtained. On the other hand, the GBD precoder offers diversity gain as the number of transmitted data streams is adjusted, but additional gain for BER performance is not guaranteed. Therefore, the scheme that obtains diversity gain and simultaneously mitigates the noise component is required to meet the increased demand of the throughput. Many attempts have been made to increase throughput performance in MU MIMO. In fact, the author in [19] proposed a precoder which obtains improvement throughput by combining the BD with non-orthogonal multiple access (NOMA). However, this precoder uses multiple power domains. Therefore, comparison with a conventional precoder which uses a single power domain is not appropriate. Also, this precoder does not obtain maximum throughput in all signal to noise ratios (SNRs). Thus, a precoder that uses a single power domain and maximizes throughput performance is needed. This paper proposes a modified GBD (MGBD) precoder which provides improved BER gain by satisfying the modified MMSE criteria and additional diversity gain by adopting partial nulling technique.