StudentShare
Contact Us
Sign In / Sign Up for FREE
Search
Go to advanced search...
Free

Power Control for Mobile Phones - Essay Example

Cite this document
Summary
This paper addresses the issue of transmission power control in cellular communication devices and is based entirely on the work of Roy D. Yates. Cellular communication devices, more popularly known as mobile phones, have transformed the face of communication in the 21st century. …
Download full paper File format: .doc, available for editing
GRAB THE BEST PAPER97.9% of users find it useful
Power Control for Mobile Phones
Read Text Preview

Extract of sample "Power Control for Mobile Phones"

Section Number Page Number Section I Introduction Section II Interference Constraints 3 Section III Minimum Power Assignment Method 4 Section IV Synchronous Power Control using Minimum Power Assignment Method Theorem 1 Lemma 1 Lemma 2 Theorem 2 5 5 6 7 8 Section V Asynchronous Power Control using Minimum Power Assignment Method Assumptions Theorem 3 Theorem 4 9 9 10 10 Section VI Conclusion 12 Section I: Introduction: Cellular communication devices, more popularly known as mobile phones, have transformed the face of communication in the 21st century. They have now become a necessity rather than a luxury that was enjoyed by the privileged few. As the number of cellular subscribers increases exponentially, there are several issues that have to be addressed to ensure effective and efficient usage of this technology while providing the users with a satisfying communication experience. This paper addresses the issue of transmission power control in cellular communication devices and is based entirely on the work of Roy D. Yates. In cellular communication systems, the power transmitted by a communication device has to be regulated in such a way as to provide an adequate connection to the user, which, in turn, is accomplished by reducing the interference caused by other such communication devices. There are three main bodies of work addressing this concern, firstly, the user can be assigned a fixed base station, secondly, the user can be iteratively assigned to the base station which has the maximum signal to interference ratio and thirdly, a user's signal is a combination of signals from various base stations. This paper aims to concentrate upon the second method mentioned above, i.e. Minimum Power Assignment, which is essentially an iterative method of obtaining the optimum signal strength by dynamically assigning the user to the base station that provides the best signal to interference ratio. In this model, the problem of uplink power control will be reduced to finding a vector (p) of users' transmitter power such that it satisfies the following condition: p>=I (p) Where constraint number j i.e. pj Ij (p) describes the interference that must be surmounted by user j to obtain an acceptable connection. Section II: Interference Constraints: Assumptions and Symbols Used: 1. Number of users = N 2. Number of base stations = M 3. Transmitted power of user j = pj 4. Gain of user j to base k = hkj 5. Receiver noise at base station = 6. Signal to interference Ratio = SIR The general interference constraints that apply to any system state that at a base station (k), a user receives a signal of power (hKjPj). At the same time, the user experiences an interference that can be denoted by ij hkipi + k. Thus, the SIR of a user j at base station (k) and under the power vector (p) can be denoted as pjkj(p) where, hkj kj(p) = ------ ij hkipi + k Section III: Minimum Power Assignment (MPA) Method: The MPA is an iterative procedure and at each step, the user is assigned to the base station at which its SIR is optimized. We can analyze the MPA for two situations: 1. Continuous power adjustment 2. Discrete power adjustment If we denote target SIR for a user by , then, the SIR constraint of a user following the MPA procedure can be denoted as: j pj I j MPA (p) = min k --- kj(p) According to the MPA iteration, i.e. p (t +1) = I MPA( p(t)), the user is assigned to the base station where the power consumed by the mobile device to attain its target SIR i.e. is minimized. This iteration is applicable with the assumption that other users corresponding to the same base station are currently maintaining a fixed transmission power level. We shall now examine the two cases where MPA is applicable in more detail. Section IV: Synchronous Iterative Power Control using Minimum Power Assignment method: Here, we assume that I(p), i.e., the interference to be overcome in order to attain an acceptable connection is a standard interference function, and based on this assumption, we examine the properties of the standard power control algorithm (p(t +1) = I MPA( p(t)) ). This section is based on the analysis of continuous power adjustment performed by Yates, Huang and Hanly. Assuming that we begin synchronous iterative power control with an initial power vector, say (p), after an arbitrary number of iterations say n of the standard power control algorithm, we obtain a new power vector value: In(p). The following are the theorems related to the convergence of the sequence In(p). Theorem 1: If the standard power control algorithm has a fixed point, then, that fixed point is unique Assumptions: p and p' are distinct fixed points Additional Properties of standard deviation function I(p) used: 1. Monotonicity: If p p', then, I(p) I(p') 2. Positivity: I(p)>0 Proof : Step 1: I(p)>0 for all values of power vector p (by the positivity property) Step 2: From step 1 we can conclude that pj >0 (2.1) And p'j >0 (2.2) Step 3: We can assume without loss of generality that there exists a user j such That pj < p'j. (3.1) Step 4: We can conclude from Step 3 that there must also exist a numeric value >1 such that p p' and thus, for some user j, pj pj' Step 5: According to the monotonicity and scalability properties: pj' = I(p') Ij(p) < Ij(p) = pj But, pj' = pj Hence, we find a contradiction which implies that the fixed point must be unique, thus proving the theorem. Lemma 1: If p is a feasible power vector, then, In(p) is a monotonic decreasing sequence of feasible power vectors that converges to a unique fixed point p*. Proof: Step 1: Assume p(0) = p and p(n) = In(p). Feasibility of p implies that p(0) p(1) Step 2: Suppose that p(n-1) P(n) (as a derivation from step 1) Monotonicity implies that I(p(n-1)) I(p(n)) More specifically, p(n) I(p(n)) = p(n+1) Step 3: Thus, p(n) is a decreasing sequence of feasible power vectors. Since the sequence has a lower bound of 0, we can conclude from Theorem 1 that the sequence must converge to a unique fixed point. We shall denote this point by the symbol p*. Interpretation of Lemma 1: Lemma 1 implies that p p* for any feasible power vector. This further implies that p* is the solution of p I(p) and corresponds to the minimum total tranmitted power corresponding to a user under power vector p. This implication is desirable in the case of cellular devices as they mostly work on portable batteries with a fixed amount of stored power and Lemma 1 helps to attain maximum power efficiency for these mobile communication devices. Lemma 2: If I(p) is feasible, then starting from the all zero vector i.e. z, the standard power control algorithm produces a monotonic increasing sequence of power vectors In (z) which converges at p*. Proof: Step 1: Assume that z(n) = In (z). From our initial assumption as stated in lemma 2, it is known that z(0) < p* and that z(1) = I(z) z. Step 2: We can thus suppose that p* z(n) . z(1) z. Step 3: The property of monotonicity implies that: p* = I(p*) I(z(n)) I(z(n-1)) = z(n) i.e. p* z(n+1) z(n) Step 4: Hence, it is found that the sequence corresponding to z(n) is non decreasing, i.e. monotonically increasing and has an upper bound of the value of p*. Theorem 1 also implies that the sequence must converge to p* thus proving lemma2. Theorem 2: If I(p) is feasible, then for any initial power vector p, the standard power control algorithm converges to a unique fixed point p*. Proof: Step 1: Feasibility of I(p) implies the existence of the unique fixed point p*( conclusion from theorem 1). Step 2: We know from lemma 1 and lemma 2 that p*j >0 for all j. Thus, for any initial power vector p, a numeric value can be found such that p* p. Step 3: Extending the result of step 2 and applying the scalability property to it, we can find that p* must be feasible. Step 4: We know that z p p*. The monotonicity property implies that In(z) In(p) In(p*) Step 5: Lemmas 1 and 2 imply that Limn In(p*) = limn In(z) = p* Hence, the theorem stands proven. Section V: Asynchronous Power Control using Minimum Power Assignment: The main issue faced while using the synchronous form of MPA is that users having communication devices with slower processing capabilities may not be able to continuously update the value of the optimal power vector and this may adversely affect the overall power consumption of users under a base station. To counter this problem, an alternative method i.e. asynchronous power control algorithm has been developed. This algorithm utilizes the Totally Asynchronous Model. It allows some users to perform a greater number of power control iterations at a faster rate than other users. Assumptions: 1. Power transmission of user j at time t = pj(t) 2. Power vector at time t = p(t) = (p1(t), , pn(t)) 3. Its assumed that user j may not have access to the most recent values of the components of the power vector at time t. (when user j has out dated information about the received power at a certain base) 4. Most recent time for which pi is known to user j = ij(t). (0 ij(t) t) 5. User j adjusts its transmitter power at time t using the power vector p(j (t)) = (p1(1j (t)), p2(2j (t)), , pn((nj (t))) 6. We also assume a set of times = {0, 1, 2, } at which one or more components pj(t) of p(t) are updated. 7. j is the set of times at which pj(t) is updated Given the above assumptions and the sets 1, 2,, n, the Totally Asynchronous Standard Power Control theorem states that pj(t+1) = Ij(p(j(t)) if t is a subset of T pj(t+1) = pj(t) in other cases Theorem 3 (Asynchronous Convergence Theorem): If there is a sequence of non-empty sets {X(n)} with X(n+1) being a subset of X(n) for all values of n satisfying the following two conditions: 1. Synchronous Convergence Condition: For all n and x X(n), f(x) X(n+1). If {yn} is a sequence such that yn X(n) for all n, then every limit point of {yn} is a fixed point of f. 2. Box Condition: For every n, there exists set Xi(n) X, such that X(n)= X1(n) x X2(n) x .x Xn(n), And the initial solution estimate x(0) belongs to the set X(0), then every limit point of {x(t)} is a fixed point in f. Theorem 4: If I(p) is feasible, then, from any initial power vector p, the asynchronous standard power control algorithm converges to p*. Proof: Step 1: let z denote the all zero vector. Feasibility implies the existence of the fixed point p*. Step 2: Given an initial power vector p, we can choose 1 such that p* p. Step 3: We define X(n) = { p| In(z) p In(p*)} For all n, the set satisfies the box condition. Step 4: Lemma 1 and lemma 2 imply that X(n+1) is a subset of X(n) for all n and limn In(p*) = limn In(z) = p* . Thus, any sequence {p(n)} such that p(n) X(n) for all n must converge to p*. Hence, the theorem stands proven. Section VI: Conclusion: The aim of the minimum power assignment method is to provide users of cellular communication services with an acceptable connection with minimum usage of power on the side of the user so as to elongate battery discharge time, i.e. the amount of time that it takes for the battery of the cellular device to get discharged. The use of the synchronous and asynchronous standard power control algorithms guarantee to find the minimal power level required for establishing an acceptable connection given that the interference from other users that needs to be over come to do so, characterized by the value I(p) is feasible. Asynchronous power control also indicates the robustness of the standard power control algorithm in the face of slower updating of transmission power levels by individual users. The power controlled systems and methods that are described in this report can be implemented by each individual user knowing only its own uplink gains and the total power received at each base station, i.e. a user need not be concerned about the power transmissions of other users corresponding to the same base station, thereby making the algorithm much faster and much less complex. Further development in the field of power control for mobile devices holds the potential to decrease the need for repeated recharging of cellular communication devices and of elongating the standby and talk time simultaneously. Read More
Cite this document
  • APA
  • MLA
  • CHICAGO
(“Power Control for Mobile Phones Essay Example | Topics and Well Written Essays - 2000 words”, n.d.)
Power Control for Mobile Phones Essay Example | Topics and Well Written Essays - 2000 words. Retrieved from https://studentshare.org/technology/1517483-power-control-for-mobile-phones
(Power Control for Mobile Phones Essay Example | Topics and Well Written Essays - 2000 Words)
Power Control for Mobile Phones Essay Example | Topics and Well Written Essays - 2000 Words. https://studentshare.org/technology/1517483-power-control-for-mobile-phones.
“Power Control for Mobile Phones Essay Example | Topics and Well Written Essays - 2000 Words”, n.d. https://studentshare.org/technology/1517483-power-control-for-mobile-phones.
  • Cited: 0 times

CHECK THESE SAMPLES OF Power Control for Mobile Phones

Argument: samart phones

Quotations: “Several previous studies have evaluated the use of mobile phones to support healthcare and public health interventions, notably in the collection and collation of data for healthcare research, and as used in support of medical and healthcare education and clinical practice in the community.... Some studies have highlighted the successful use of mobile phones to support telemedicine and remote healthcare in developing nations, with examples including their use in off-site medical diagnosis and as information support in the treatment of HIV care in difficult to reach rural areas” (Boulos et al....
8 Pages (2000 words) Assignment

Interface of Camera in Mobile

The present invention relates to a mobile communication terminal, and more particularly to a mobile communication terminal having a camera.... Here we want to make such kind of phone which can able to solve various problem with less time economic too, easy to carried,etc … Presently, mobile communication terminals have been equipped with a high-speed data transmitting function as well as a voice communication function....
14 Pages (3500 words) Essay

Business Plan for a new Iphone development company

There is also a convergence of music and games with mobile communication.... There is great demand for the Apple iPhone in the UK market and in fact O2, Apples exclusive UK mobile phone partner reports that, “pre-order demand for new 3G iPhones crashes O2s website within an hour of going live”....
16 Pages (4000 words) Essay

Effects of the iPhone on the Americans

nbsp;  Effects of the iPhone on the AmericansIt is stunning to imagine how life was before the introduction of the Smartphone, the iPhone was not the first smart phone as other manufactures had smart phones however, the consumer adaptability and use placed it above other smart phones.... Their mobile safari was a distinct feature among the smart phones.... System Z on the Go: Accessing z/OS Smart phones,2010 Pp 7).... (2010), System Z on the Go: Accessing z/OS Smart phones....
2 Pages (500 words) Assignment

Internet and Mobile Phones

The essay "Internet and mobile phones" seeks to explore the forms of surveillance facilitated by mobile phones and the Internet and discuss issues of control over personal information and privacy in these contexts.... The internet and cell phones are becoming to get more computerized.... A research conducted by Pew Internet anticipated that the vast majority on the planet will access the Internet through cell phones by 2020.... Much like social networks on the Internet, cell phones give clients an alternate stage to interact with a number of people....
5 Pages (1250 words) Essay

Technology in Business - Smartphones, Blackberry and iPhone

The invention of mobile phones has revolutionized the business world in many ways.... The entry of the mobile phone has made communication easy as it is possible to communicate with a person anytime anywhere in the world if the person possesses a mobile phone.... It also includes Internet browsing and networking capabilities along with 3G facilities and TV on mobile options (iphone, n....
8 Pages (2000 words) Case Study

Successful Products and Strategies of Apple Company

hellip; Apple became the front runner in customer appeal as people waited in line overnight to buy the new phone because of the differentiation that the company introduced in the mobile phone industry.... Unlike any other mobile phone or Smartphone at that time, but like some of the other Apple products were already popular....
7 Pages (1750 words) Case Study

Mobile Apps and Applications: Emerging Technology

Mobile apps and applications are not only a mode of communications worldwide but also a new trend set in order to perform many activities on mobile phones or more preferably say smartphones.... … The paper "mobile Apps and Applications: Emerging Technology" is a good example of a term paper on information technology.... nbsp;mobile apps and applications as an emerging technology are the central ideas of this management report.... This detailed report draws attention to the mobile apps and how this amazing emerging technology has come over a great distance....
10 Pages (2500 words) Term Paper
sponsored ads
We use cookies to create the best experience for you. Keep on browsing if you are OK with that, or find out how to manage cookies.
Contact Us