حسرت ہی رہی مجھ پہ وہ احسان کرے گا
دیدار سے ہر درد کا درمان کرے گا
ہے عید کا دن آج وہ نکلے گا سنور کے
وہ عید کے دن حشر کا سامان کرے گا
بے چین مرے دل نہ رقیبوں سے ہوا کر
دشمن ہے تو ہر حال میں نقصان کرے گا
بیمارِ محبت ہے نکل جائے مطب سے
یہ اور مریضوں کو پریشان کرے گا
تائبؔ سے کبھی جان کو تو مانگ کے تو دیکھ
سو بار ترے نام پہ قربان کرے گا
Shaykh Muhammad Nasiruddin Albani is known as the famous scholar of the twentieth century AD. He served in Hadith for almost 60 years. He has also some particularities in the hadith’s research in which he apposed a lot of scholars. The most important of them is that he has said that some Ahadith of Sahih Bukhari and Sahi Muslim are weak. Similarly, in contrast to the previous muhaddiseen, some weak traditions have said correct and some reliable narrators as weak. Apart from this, there are two particularities of him that are very important in the research world. One is that he has explored many of unknown Ahadith and secondly he has divided the books of Hadith into two parts; weak and accurate. Some detail of these particularities is presented in this article.
Due to the ubiquity and exponential growth of cellular devices and data hungry applications, cellular data traffic demand has raised exponentially. To cope with the ever increasing traffic demands conventional cellular networks are shifting to heterogeneous cellular networks (HCNs) where low cost and low power small cell base stations (SBSs) are overlaid with the existing infrastructure of high power macrocell BSs (MBSs). Due to transmit power levels disparity, more users associate with the MBS than the SBS while following the maximum received power association scheme, resulting in an imbalanced load arrangement across the HCN. To balance the load, it is necessary to offload a fraction of users from the overloaded MBSs to low power SBSs. The main goal of this dissertation is to develop tractable frameworks in order to model and analyze different dynamics of load balancing (LB) for HCNs. First, this dissertation develops and analyzes a non-uniform HCN (NuHCN) model where the SBSs are deployed selectively in the available region. In the NuHCN, the available MBS coverage region is divided into sub-regions, such as cell-center region (CCR) and cell-edge region (CER). The MBSs provide service to the users in both the regions; hence, SBSs are assumed to be active in CER and provide service to cell-edge users (CEUs) only. The network performance is further improved by expanding the SBSs’ coverage in CER via cell range expansion (CRE) based cell association. The results demonstrate that the coverage and rate performances can be improved with LB in NuHCNs. In a co-channel HCN, the offloaded users experience severe macro-cell interferix ence (MCI) from the MBSs to which the users were associated prior to offloading. The MCI degrades downlink (DL) signal-to-interference plus noise (SINR) ratio severely. Use of an efficient interference management scheme can overcome this effect. As a second contribution, to accomplish better network performance via LB, a reverse frequency allocation (RFA) scheme is considered both in the uniform and non-uniform HCNs. The results show that better network performance is achieved in NuHCN in conjunction with RFA scheme employment. In the aforementioned contributions, the analyses were performed based on the coupled association (CoA) scheme, where a randomly selected user connects with the same BS in both DL and uplink (UL) directions. In the third contribution of this dissertation, decoupled association (DeA), where the user is associated with two different tier BSs simultaneously, is considered in conjunction with RFA scheme employment. The effects of this diverse bias configurations and RFA employment are studied for the coverage performance while considering both CoA and DeA. The results illustrate that with DeA, user-BS connectivity policy significantly improves the coverage performance.