K-link constant MIMO IFC where inter-link interference is treated as Gaussian noise (Noisy MIMO IFC). Starting from Interference Alignment (IA) constraints [1], analytical conditions that need to be satisfied in order to admit an IA solution for such a MIMO IFC are derived. For a given degrees of freedom allocation, these conditions, along with a recursive algorithm to check its validity in a given K-link MIMO IFC, allow an analytical evaluation of the existence of IA solutions (or lack thereof). Such an attempt has been made recently for several interesting special cases in the published literature, however we address here the most general case of the MIMO IFC and are able to show that, when an IA solution exists, these conditions are satisfied at every step of the proposed recursive algorithm and that an IA solution does not exist when these conditions are not satisfied. When data is transmitted over the wireless communication channel, the transmit signal experiences distortion depending on the channel's fading characteristics. On the one hand, this calls for efficient processing at the receiver to mitigate the detrimental effects of the channel and maximize data throughput. On the other hand, the diversity inherently present in these channels can be leveraged with appropriate transmit processing in order to increase the reliability of the transmission link. Recently, in [1] itwas shown that the channel characteristics can be exploited to maximize the total data throughput in the interference channel where multiple user pairs rely on the same resource to communicate among themselves. In this PhD dissertation, we first propose novel equalizer designs for frequency selective channels. We then present new results on the diversity gain of equalizers in fading channels when appropriate precoding is applied at the transmitter.
Toward the end of the thesis we provide some new insights into interference alignment [1], where the aim is to maximize network throughput in interference channels with joint transmit and receive processing. A summary of the three parts of this dissertation is given below. The first part of the thesis studies receiver designs that maximize the data throughput in the high speed downlink packet access (HSDPA). We propose two-stage equalization for both single antenna (SISO) and multiple antenna (MIMO) frequency selective channels. The first stage consists of chip-level processing and the second stage of processing takes place at the symbol level. In principle, the presence of the aperiodic scrambler at the transmitter renders the symbol level channel time-variant and affects the achievable throughput at the receiver. We analyze the performance of these receivers when the scrambler used at the transmitter is modeled as a randomsequence and compare it with the results of the deterministic treatment of the scrambler. In MIMO HSDPA where the receiver is required to choose the precoding matrix that maximizes its aggregate transport block size,we derive analytical expressions for the choice of the optimumprecodingmatrix that maximizes the sum-capacity of the receiver when it is based on MMSE designs. Finally we extend the current single-user MIMO scenarios in HSDPA to the multiuser case. These extensions require minimal changes to existing standards. When multiple users are to be simultaneously serviced in the downlink, we suggest practical multi-user scheduling strategies that can be employed at the base station so as to maximize the downlink throughput. The second part of the thesis is devoted mainly to theoretical analysis of the diversity order of linear equalization (LE) for transmission in fading channels. It is known that zero-padded block transmission allows LE to achieve fullmultipath diversity present in frequency selective channels. We first show here that, in a dual fashion, LE can achieve full Doppler diversity in time-selective channels when guard bands are inserted in the transmit signal. We then analyze the performance of LE in time-and-frequency (doubly) selective channels. In [2], a two-dimensional generalization of the zeropadding precoder was shown to enable maximum likelihood equalizers (MLE) to achieve the full joint multipath-Doppler diversity offered by doubly selective channels. We show here that the same precoder also allows linear, decision feedback and "hybrid" equalization schemes to achieve the same diversity gains as that of MLE. We also devote our attention to lowcomplexity implementations of these full diversity equalizers. It also appears that a redundancy proportional to channel delay spread is largely enough to allow MLE to collect full channel diversity. We present simulation results that support this observation. We consider the
