# Reduced Complexity Detection in MIMO Systems with SC-FDE Modulations and Iterative DFE Receivers  
[PERSON]  
1 IT--Instituto de Telecomunicacoes, Av[PERSON] 1, Torre Norte, piso 10, 1049-001 Lisboa, Portugal;  
[PERSON]ESS] (G.c. ); [EMAIL_ADDRESS] (R.D. ); [EMAIL_ADDRESS] (F.C. ); asilva@av.it (A.S.)  
[PERSON]  
1 IT--Instituto de Telecomunicacoes, Av[PERSON] 1, Torre Norte, piso 10, 1049-001 Lisboa, Portugal;  
[PERSON]ESS] (G.c. ); [EMAIL_ADDRESS] (R.D. ); [EMAIL_ADDRESS] (F.C. ); asilva@av.it (A.S.)  
[PERSON]  
1 IT--Instituto de Telecomunicacoes, Av. [PERSON] 1, Torre Norte, piso 10, 1049-001 Lisboa, Portugal;  
[PERSON]  
1 IT--Universidade Autonoma de Lisboa, [PERSON] 1, Torre Norte, piso 10, 1049-001 Lisboa, Portugal;  
[PERSON]SS] (G.c. ); [PERSON]_ADDRESS] (R.D. ); [EMAIL_ADDRESS] (F.C. ); [EMAIL_ADDRESS] (A.S.)  
[PERSON]  
1 IT--Instituto de Telecomunicacoes, Av. [PERSON] 1, Torre Norte, piso 10, 1049-001 Lisboa, Portugal;  
[PERSON]SS] (G.c. ); [EMAIL_ADDRESS] (R.D. ); [EMAIL_ADDRESS] (F.C. ); asilva@av.it (A.S.)  
[PERSON]  
1 IT--Instituto de Telecomunicacoes, Av. [PERSON] 1, Torre Norte, piso 10, 1049-001 Lisboa, Portugal;  
[PERSON]SS] (G.c. ); [PERSON]_ADDRESS] (R.D. ); [EMAIL_ADDRESS] (F.C. ); [EMAIL_ADDRESS] (A.S.)  
[PERSON]SS] (G.c. ); [EMAIL_ADDRESS] (R.  
It is well known that block transmission techniques, combined with frequency-domain processing, are suitable for broadband wireless systems. These techniques include Orthogonal Frequency Division Multiplexing (OFDM) [6] and Single-Carrier with Frequency Domain Equalization (SC-FDE) [7], which have similar overall signal processing requirements and achievable performance. Due to receiver complexity in SC-FDE and since the envelope fluctuations of single-carrier signals are much lower than the ones in OFDM, SC-FDE and OFDM are preferable for the uplink and downlink transmissions [8], respectively. The performance of SC-FDE can be further improved if linear FDEs are replaced by the powerful Iterative Block Decision Feedback Equalization (IB-DFE) schemes [7]. In fact, the performance of IB-DFE schemes can be close to the Matched Filter Bound (MFB) in many scenarios [7]. For this reason, the IB-DFE concept was already extended to a wide range of scenarios, including Layered Space-Time (LST) schemes [9], Space Division Multiple Access (SDMA) [10], Code Division Multiple Access (CDMA) schemes [11], BS cooperation schemes [5], as well as other MIMO schemes. In this paper, we consider SC-FDE schemes combined with MIMO architectures with \(P\) transmitting and \(R\) receiving antennas, with different overall noise characteristics on the different receiver branches, which can be a result of different noise levels and/or nonlinear effects at the receiver side (e.g., quantization effects [12]). The receivers are based on the IB-DFE and take into account the statistical characteristics of the overall noise at the detection level. The typical MIMO receiver requires the inversion of \(R\times R\) matrices, which might not be efficient when \(R>P\). We present an efficient method for computing the receiver parameters that requires the inversion of \(P\times P\) matrices, which is particularly interesting for the case where \(R\gg P\gg 1\). This method can be applied to any MIMO system combined with IB-DFE-based receivers. Furthermore, in this paper, we present an implementation scheme with low resolution Analog-to-Digital Converters (ADCs). Even though it is possible to cheaply employ ADC solutions, it still can have a significant complexity load, especially for massive MIMO systems. For this reason, a substantial work on massive MIMO with low resolution quantizers is presented in [13; 14; 15]. Moreover, the use of reduced resolution ADCs allows an advantage for BS cooperation systems, which can be considered as distributed MIMO systems where the antennas are placed in different cells [5; 12].