The Role of the Widely Linear Processing in the Narrowband and Wideband Systems

In this thesis, the role of the Widely-Linear processing in the narrowband and wideband systems has been proposed. With reference to narrowband systems, we analyzed the linear (L) constant modulus (CM) cost function under the general assumptions that improper modulation schemes of practical interest are employed. This study allows one to determine a broad family of undesired minima of the CM cost function, which do not lead to perfect symbol recovery in the absence of noise. Successively, we applied widely linear (WL) approach to the same context, providing the mathematical conditions assuring perfect symbol recovery in the absence of noise. Furthermore, we enlightened that, similarly to the L-CM equalizer, the performances of WL-CM equalizers suffer from the presence of undesired global minima. To overcome this drawback we proposed to resort to a constraint WL-CM equalizer. In the context of wideband systems, with reference to direct-sequence CDMA (DS-CDMA) technique, we developed a performance comparisons among ideal and data-estimated WL- and L-MOE (minimum output energy) receivers. As regard to the ideal implementation, we investigated the relative performances of the WL-MOE and L-MOE receivers in the high-SNR regime. In such a case, we provided a necessary and sufficient condition on the spreading codes, which allows the WL-MOE receiver to achieve perfect multiple access interference (MAI) suppression. As regard the data-estimated versions of the WL-MOE and L-MOE receivers, we derived easily interpretable formulas, which allow one to obtain clear insights about the effects of different parameters on performances. In addition, we have extended the previous analysis accounting for the effects of channel-estimation errors. Specifically, we presented a comprehensive performance comparison between different versions of the data-estimate L- and WL-MOE receivers with blind channel estimation. We derived easily interpretable formula that suggest that when considering finite sample-size implementation, the WL-MOE receiver with channel estimation is able to assure a significant performance gain (for low-to-moderate values of the SNR) with respect to its linear counterpart only when it is built by resorting to a more sophisticated implementation. In such a case, for a given channel length, it allows one to work with an increased number of users which makes it a viable choice in heavily-congested DS-CDMA networks. Finally, in the last part of this thesis, we addressed the problem of deriving mathematical conditions guaranteeing perfect symbol recovery in the absence of noise for either cyclic-prefix (CP) based or zero-padding (ZP) based multicarrier-CDMA (MC-CDMA) downlink transmissions, which employ frequency-domain symbol-spreading. The conditions derived are channel-independent and are expressed in terms of relatively simple system design constraints, regarding the maximum number of allowable users and their spreading sequences. Specifically, it was first shown that, similarly to a ZP-based MC-CDMA downlink, L-zero-forcing (ZF) can be guaranteed for a CP-based MC-CDMA downlink, even when the channel transfer function exhibits nulls on some used subcarriers. On the other hand, when the information-bearing symbols are improper, it was shown that, for both CP- and ZP-based systems, WL-ZF allows one to successfully operate even in overloaded scenarios, by doubling the system capacity, regardless of the channel zero locations. However, such an increased throughput can be achieved as long as appropriate complex-valued spreading codes are used