Today I came across a nice result on the distribution of eigen values of matrix 
, where the entries of 
are i.i.d. Gaussian distributed. The result says that the 
eigen value 
(in the decreasing order) of has the following distribution, 
for small 
.
Its quite useful for analysing many MIMO techniques, such as MRC, MRT.
The reference is a recent IT Paper: http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=4544985&isnumber=4544949
It turns out that the mysterious “green sheet” is just the WNCG graduation checklist. You can find it at this link.
A student from China recently asked me about how I got interested in relay selection and started obtaining (publishable) results. Since I have some free time on my hands now, I figured I’d share some thoughts on this topic.
I actually don’t think that the way I got interested in relay selection was the ideal strategy in terms of “finding a good research topic.” Instead, I’ll discuss what I think is a better way of “finding a good research topic.” Note that the following is especially relevant for graduate students researching wireless communications (for the obvious reasons).
It’s fairly common for a new graduate student to be overwhelmed by the plethora of potential research topics. When I was starting work on my masters degree, I wanted to do research involving some aspect of wireless networks, since I felt (wrongly, as it turned out) that all of the good point-to-point problems had already been solved. During the summer of 2004, I worked on beamforming for MIMO ad hoc networks, but that ended up being a major dead end. On a related note, I recently perused my research notebook and found that during January 2006, I was interested in cooperative diversity for OFDM networks (my, how things have changed).
This brings up the key question: how should a new graduate student sort through the morass of potential research topics and come up with a good one? I’ll discuss two potential answers.
One approach is to have your advisor answer this question for you, assuming that you have an advisor. In general, you can assume that your advisor has a strong grasp of the current state of research in wireless communications. This knowledge can help him/her determine a topic for you that is 1) interesting, so you won’t be bored stiff for approximately 5 years and 2) worthy of a Ph.D. dissertation, so you will have made a fundamental contribution of some sort by the time you graduate.
The second approach, which I highly recommend, is to take the initiative. To start off, you should do a significant amount of reading. Survey articles in journals such as the IEEE Communications Magazine and the IEEE Signal Processing Magazine can be valuable starting points for the interested yet relatively inexperienced grad student.
A particularly well-written survey article can provide the reader with a good grasp of “what’s been done” on a topic such as “OFDMA power allocation for relay-based networks” and suggest various open problems that are both interesting and important. When reading through these survey articles, one should also scan the list of references to learn about the key papers (and researchers, so you can bookmark their home pages) in a particular area.
It’s then important to read through these key papers to grasp the nuances of the topic that you’re learning about and ask yourself tough questions along the way. For example, do you understand the (technical) paper that you’re reading? Can you justify all of the authors’ assumptions? Can you re-derive every expression (especially the proofs of key theorems) in the paper? I should note that sometimes papers contain typos/gross errors, so you shouldn’t automatically trust everything you read.
If you want to answer these questions in the affirmative, this is a great opportunity for building your technical background. For example, let’s say that the authors are studying a MIMO wireless system and assume that a two-ring scattering model is being employed. If you don’t know what a two-ring scattering model is, you should obtain a copy of a MIMO textbook such as this one by Paulraj et al. and learn more about channel modeling.
Also, let’s say that you’re reading through this famous paper by Gupta and Kumar, and you’re having trouble deriving some (or all, as this paper is actually quite tricky to understand) of the key results. In this case, you might want to strengthen your graph theory background by taking an appropriate class, such as this one at UT-Austin. You might also want to improve your knowledge of random geometry, and you can check your university library for a helpful book such as this one by Bollobas for more coverage of this advanced topic.
As you read through the key technical papers in the area that you’re learning about, you should think of additional open problems and ask yourself more tough questions. For example, you can ponder something like, “the authors’ assumption of a zero-error feedback channel seems a bit restrictive. From my other reading it’s clear that introducing a channel estimation error at the transmitter would better model a practical system. Maybe I can’t obtain an exact expression for the sum capacity given channel estimation errors, since that seems quite complicated, but can I obtain relatively tight bounds?”
Regardless of the approach that you take in terms of finding a good research topic, it’s crucial that you interact with your advisor during this process. Your advisor, who has worked in either the general area that you’re considering or a related area, can help you determine if the open problem you’re considering is either trivial, worthy of multiple dissertations, or actually reasonable for a dissertation. Note that by adopting the second approach I discussed above, your ability to have meaningful dialogue with your advisor during this process is enhanced. In particular, you can evaluate your advisor’s suggestions and converge on a reasonable topic more quickly; this is especially important if your advisor has not worked in the general area that you’re considering.
That’s all I had to say on this subject, at least for now. I welcome comments, especially from my group-mates on this issue of “finding a good research topic.”
Light up Turn on Engage
Laptop and Terminal Euphoria
Linking The Earth
Linking Telephony Everywhere
Luscious Telephony Experience
Limitless Technology for Everyone
Limited Time Enigma
Laugh Track Escapade
Lightning-fast Transfer of Everything
Let’s Turnaround East
Late Troublesome Expensive
Look, Talk, and Enjoy
Live Telecommunication Environment
Leading Telecommunication Excellence
Loads of Traffic for Everyone
Live connection To Everyone
Live communication To Everyone
Lifeline To Everyone
Let’s Take it Easy
Life Time Eternal
Love Thy Enemy
Link Technology Enhancement
Legacy Terminal Equipment
- from LTE / LTE-A TSG RAN mailing list
Some people also say “Long Term Employment” or “Life Time Employment.” :)
But my pick is “Love Thy Enemy.” How about you?
Although there is still a week of finals, the semester is basically finished. This has been my most eventful semester, personally, but how did the WSIL fare? Let’s take a look.
First and foremost, our dear Kaibin Huang just successfully defended his dissertation and is on his way to a post-doc at Hong Kong University of Science and Technology. Not only that, but he was awarded the WNCG Student Leadership award. A WSIL member has won this award two of the past three years.
Along the same lines, Takao Inoue is now a Ph.D. Candidate. He joins Chan-Byoung Chae and Caleb Lo as the next in line to graduate.
We also welcomed the well-known Dr. Marios Kountouris as a post-doctoral researcher.
In addition, we had eight journal papers published:
In addition, our fearless leader Prof. Heath, along with Prof. Andrews, won the WNCG Spring 2008 Bocce Ball tournament.
And finally, a long semester of ups and downs concludes with a nice week in the U.S. Virgin Islands for the IEEE Communication Theory Workshop, with Prof. Heath as General Chair.
Please add more here if I forgot something.
For U.S. PhD-degree holders, don’t use the title “Dr.” in your business cards when you visit Germany. If not, you may face a year behind bars.
Note: this news was not posted on April 1st.
Many of you might know that over the weekend there was a AMD design contest. I was under the impression that such contests are coding heavy and it goes without saying that a potential turnoff for me. Thanks to my roommate, however, my impression changed significantly and I found out that majority of the problems were basically algorithmic puzzles. More importantly it turned out that once you found out the trick involved, the coding required was minimal.
I will give an example shortly. There are offcourse some problems on compiler design and related areas on which we have minimal knowledge. So to form an ideal team for these contests a partner majoring in CE/CS is a must.
Over the weekend me and my roommate (major CE) were able to solve 4 and half problems out of 5. Unfortunately, we were not able to submit our solution to the contest, since my roommate had to fly out of town and due to my “extraordinary” coding skills.
I am writing this post in hope that next year we would see someone from WNCG and especially from WSIL appearing on the LCD TV on the first floor as the winner of such a contest.
Example problem: Let z, l and m be a natural numbers, l less than m. Let p be a prime which appers in the prime factorization of z, e.g. 2 and 3 appear in the prime factorization of 24. The problem is to find out the number of natural numbers between l and m (including l and m) that have p ones in their binary representation.
Draft 3 of IEEE 802.16j has been finished and letter ballot voting has begun. Voting closes March 15th. While Draft 2 officially passed letter ballot, resolutions to comments made with “Disapprove” votes need to be made before moving on in the process. The official announcement is available online, and you can monitor voting progress as well. The document is not available for free to the public, but in due time it will be available for purchase.
The broadcast channel is a communication channel with a single transmitter that transmits independent information to multiple receivers. In information theory, capacity of a communication channel is defined as the maximum rate of information that can be transmitted from the transmitter to the receiver reliably. By reliable transmission we mean that the information can be decoded at the receiver with arbitrarily small probability of error. Let us assume that the broadcast channel has 
receivers, then a rate vector ![${\bf R} = [R_1, R_2, \ldots, R_N]$](http://windowsil.org/latexrender/pictures/bd3bc224c57f6561118b879ecc2a6301.gif "${\bf R} = [R_1, R_2, \ldots, R_N]$")
is said to be achievable on the broadcast channel if information can be transmitted reliably at rate 
from the transmitter to the receiver 
,
, simultaneously. The capacity of broadcast channel is defined as the convex hull of all achievable rate vectors. Finding the capacity of a general broadcast capacity has been a long standing open problem in information theory. In this article we will discuss the multiple input multiple output broadcast channel (MIMO-BC) whose capacity region has been found recently by Weingarten et. al.
The MIMO-BC model is as follows. A transmitter with 
antennas wants to transmit independent information to receivers, where 
receiver is equipped with 
antennas 
. Let 
be the signal transmitted by the transmitter, then the received signal 
received by receiver is given by ![\[{\bf y}_n = H_n{\bf x} + {\bf v}_n,\]](http://windowsil.org/latexrender/pictures/3dc6d0819d1470031d4660b271993574.gif "\[{\bf y}_n = H_n{\bf x} + {\bf v}_n,\]")
where 
is a 
channel matrix and 
is the additive white Gaussian noise (AWGN) with covariance matrix 
.
For MIMO-BC, several transmission strategies have been proposed in literature, for example, superposition coding and dirty paper coding. In superposition coding, if 
is the signal for receiver then 
is transmitted by the transmitter. Dirty paper coding (DPC) is a technique developed by Costa for single input single output (SISO) AWGN channels when there is an interference signal present at the receiver together with AWGN. We assume the interference signal is known non causally at the transmitter. In this setting Costa showed that the capacity is 
which is exactly equal to the capacity of AWGN channel without any interference. Thus, DPC is shown to completely eliminate the effect of interference. Using DPC for the MIMO BC, if the signal for the first receiver is 
, then the signal 
for receiver 
is generated using as the interference signal. Similarly, the signal for the receiver is generated using 
as the interference signals and 
is transmitted from the transmitter. From now on we consider 
in this article for simplicity. With ,the rates 
and 
, simultaneously achievable for receiver 
and , are given by ![\[R_1^{DPC} = \frac{1}{2}\log\frac{\det\left({\bf S}_1+ {\bf S}_2 + {\bf N}_1\right)}{\det\left({\bf S}_2+{\bf N}_1\right)}\]](http://windowsil.org/latexrender/pictures/d231b48745808e6900b2b7cef9bff54d.gif "\[R_1^{DPC} = \frac{1}{2}\log\frac{\det\left({\bf S}_1+ {\bf S}_2 + {\bf N}_1\right)}{\det\left({\bf S}_2+{\bf N}_1\right)}\]")
and ![\[R_2^{DPC} = \frac{1}{2}\log\frac{\det\left({\bf S}_2 + {\bf N}_2\right)} {\det\left({\bf N}_2\right)},\]](http://windowsil.org/latexrender/pictures/439320c9f3e1132578ecfaea9d24fa59.gif "\[R_2^{DPC} = \frac{1}{2}\log\frac{\det\left({\bf S}_2 + {\bf N}_2\right)} {\det\left({\bf N}_2\right)},\]")
where 
is the covariance matrix of . Changing the order of coding, i.e. first generating and depending on generating , ![\[R_1^{DPC} = \frac{1}{2}\log\frac{\det\left({\bf S}_1 + {\bf N}_1\right)}{\det\left({\bf N}_1\right)}\]](http://windowsil.org/latexrender/pictures/3bbf2faa4f6d254df3cf1b10049f875f.gif "\[R_1^{DPC} = \frac{1}{2}\log\frac{\det\left({\bf S}_1 + {\bf N}_1\right)}{\det\left({\bf N}_1\right)}\]")
and ![\[R_2^{DPC} = \frac{1}{2}\log\frac{\det\left({\bf S}_1+ {\bf S}_2 + {\bf N}_2\right)}{\det\left({\bf S}_1+{\bf N}_2\right)}.\]](http://windowsil.org/latexrender/pictures/916d11f440683b3dcc4808c18fb34666.gif "\[R_2^{DPC} = \frac{1}{2}\log\frac{\det\left({\bf S}_1+ {\bf S}_2 + {\bf N}_2\right)}{\det\left({\bf S}_1+{\bf N}_2\right)}.\]")
We denote the convex hull of all rate vectors achievable with DPC as 
.
As shown above, finding the achievable rate region of MIMO-BC is easy using different transmission strategies but proving that they are capacity achieving, i.e. rate more than the rate achieved by a particular transmission strategy is not achievable with reliable transmission constraint, is quite difficult. Weingarten et.al. solved this problem in their paper and showed that rates achieved with DPC are optimal for MIMO-BC.
Here we present the argument for symmetric MIMO Broadcast channels from Weingarten et. al.’s paper, where the number of antennas at the transmitter and each receiver are equal. We also only consider two receivers here for simplicity, the general case follows similarly. As before let the received signal at receiver be 
, where ![\[{\bf y}_n = {\bf H}_n{\bf x}_n + {\bf v}_n, \ n=1,2.\]](http://windowsil.org/latexrender/pictures/8357ddee5a7849d18c5943276714697d.gif "\[{\bf y}_n = {\bf H}_n{\bf x}_n + {\bf v}_n, \ n=1,2.\]")
Since we are assuming 
to be a square matrix, without loss we can multiply the received signal by 
without changing the capacity. Note that is invertible with probability . This is formally defined as aligned MIMO BC (AMIMO-BC) with ![\[{\bf y}_n = {\bf x}_n + {\bf v}_n, \ n=1,2.\]](http://windowsil.org/latexrender/pictures/41d56e0472684582a2f72d21c7a50874.gif "\[{\bf y}_n = {\bf x}_n + {\bf v}_n, \ n=1,2.\]")
Then a transformation of AMIMO-BC is considered, called degraded and aligned MIMO BC (DAMIMO-BC), where ![\[{\bf y}_n = {\bf H}_n{\bf x}_n + {\bf v}^{*}_n, \ n=1,2.\]](http://windowsil.org/latexrender/pictures/1b4465292912001d0491981856889816.gif "\[{\bf y}_n = {\bf H}_n{\bf x}_n + {\bf v}^{*}_n, \ n=1,2.\]")
with 
, 
denotes the covariance matrix. For any two matrices, 
,by 
we mean 
is a negative semidefinite matrix. It is easy to see that DAMIMO-BC is a degraded BC channel, i.e. one receiver receives less noisy signal than the other. For the degraded BC it is known that superposition coding is optimal, however, it is not known whether Gaussian signaling is optimal or not.
For a single input single output degraded BC (SISO-DBC), where the transmitter and each receiver has a single antenna, Bergmans showed that Gaussian signaling is optimal, however, the proof of Bergmans does not extend to the DAMIMO-BC case.
The optimality of Gaussian signalling is shown as follows. Let 
be the set of all achievable rate vectors 
with Gaussian superposition coding for DAMIO-BC and let 
and 
be the input covariance matrices achieving 
and 
. To show that any rate vector which does not belong to 
is not achievable, an enhanced DAMIMO-BC is introduced, which is defined as ![\[{\bf y}_n = {\bf x}_n + {\hat {\bf v}}_n, \ n=1,2.\]](http://windowsil.org/latexrender/pictures/c87dd9d726392c3ff8868b2f862e5a20.gif "\[{\bf y}_n = {\bf x}_n + {\hat {\bf v}}_n, \ n=1,2.\]")
where ![\[cov({\hat {\bf v}}_1) \le cov({\bf v}^{*}_1), cov({\hat {\bf v}}_1) + cov({\hat {\bf v}}_2) \le cov({\bf v}^{*}_1) + cov({\bf v}^{*}_2).\]](http://windowsil.org/latexrender/pictures/db13b5f096f8748b416db46f7bbf44e4.gif "\[cov({\hat {\bf v}}_1) \le cov({\bf v}^{*}_1), cov({\hat {\bf v}}_1) + cov({\hat {\bf v}}_2) \le cov({\bf v}^{*}_1) + cov({\bf v}^{*}_2).\]")
Clearly, any rate vector achievable on DAMIMO-BC is also achievable on the enhanced DAMIMO-BC, thus the capacity region of DAMIMO-BC is contained inside the capacity region of enhanced DAMIMO-BC.
Next, it is shown that for any DAMIMO-BC there exits an enhanced DAMIMO-BC such that the following properties hold
1. Proportionality: There exits 
, such that ![\[\alpha_1\left(B_1 + cov({\hat {\bf v}}_1)\right) = cov({\hat {\bf v}}_{2}).\]](http://windowsil.org/latexrender/pictures/1f40c6624992a5093cb654b9216fcbb0.gif "\[\alpha_1\left(B_1 + cov({\hat {\bf v}}_1)\right) = cov({\hat {\bf v}}_{2}).\]")
2. Rate Preservation: The rate vector 
achievable on enhanced DAMIMO-BC with Gaussian signaling is equal to rate vector 
obtained with Gaussian signaling for DAMIMO-BC.
Then using the proportionality and rate preservation properties, it is shown that any rate vector which does not belong to is not achievable on the enhanced DAMIMO-BC, using Bergmans proof for SISODBC. An important point to note here is that the Bergmans proof works
because of the proportionality property, which is hard to show for DAMIMO-BC. Since the capacity region of DAMIMO-BC is contained inside the capacity region of enhanced DAMIMO-BC, it follows that any rate vector which does not belong to is not achievable and thus Gaussian signaling is optimal.
Coming back to the original AMIMO-BC, to show that DPC is optimal, the authors show that any rate vector which lies outside the region also lies outside the capacity region. Toward that end, it is shown that for any vector 
which lies outside the region there exists an enhanced DAMIMO-BC whose capacity region contains the capacity region of AMIMO-BC, but does not contain . Recall that we found out the capacity region of enhanced DAMIMO-BC and showed that Gaussian signaling is optimal, thus it follows that any rate vector which lies outside the region also lies outside of the capacity region of AMIMO-BC and we conclude that DPC is the optimal transmission strategy.
As a grad student and possibly a system engineer in the near future, I have been thinking about the importance between the two: writing a good paper or filing a good patent? If you are capable of doing both, what is your choice?
Writing a patent is quite different from writing a paper. A good paper should have a clear derivation of a good algorithm that has never been proven before. It should be academically challenging, mathematically tractable & reversible and conceptually innovative. A good example is Teletar’s MIMO capacity paper, Zheng & Tse’s D-MG tradeoff paper and the GLP paper by Dr. Love and Dr. Heath.
A good patent, however, is quite different. A good patent should have broad (as broad as possible) claims which are important in implementing and making real systems / devices. It focuses on new concepts, new methods and new apparatus that have never been claimed before. A good example of it is a series of handover patents by Qualcomm. Qualcomm’s MAHO (mobile assisted handover) patent and so called “501” (soft handover) patents has the following first claims:
——–
[MAHO] 1. A method of mobile assisted handoff in a cellular communication system comprising a plurality of mobile stations and a land system and a plurality of cells, comprising the steps of:
assigning a mobile station a list of cells to measure, wherein said list is divided into two sections, a steady section and an alternating section;
measuring quality level of each assigned cell;
reporting said quality levels to said land system;
transferring a cell from the alternating section of the list to the steady section of the list when said cell has a quality level higher than one of the cells in the steady section, wherein the cell with the lowest quality level in the steady section is transferred to said alternating section; and
changing said cells listed in said alternating section every predetermined period of time.
[link]
[501] 1. In a cellular telephone system in which a mobile system user and another system user communicate user information signals therebetween via at least one of a plurality of geographically separated cell-sites each defining a respective geographic service area, a system for directing communications between said mobile system user and said another system user via said at least one of said plurality of cell-sites as said mobile system user changes cell-site service areas, comprising:
means for, while said mobile system user is in a service area of one cell-site and communicating user information signals with said another system user via said one cell-site, determining a transition of said mobile system user from said one cell-site service area to a service area of another cell-site, and for providing a handoff request identifying said another cell-site;
means responsive to said handoff request for coupling a communication of said user information signals between said mobile system user and said another system user via said another cell-site while said mobile system user and said another system user continue in communication of said user information signals via said one cell-site such that said mobile system user and said another system user concurrently communicate said user information signals through said one cell-site and said another cell-site; and
means responsive to said coupling of communication of said user information signals between said mobile system user and said another system user via said another cell-site for terminating said communication of said user information signals between said mobile system user and said another system user via said one cell-site with said communication of said user information signals continuing between said mobile system user and said another system user via said another cell-site.
[link]
——–
As you see, MAHO and ‘501’ patents contain almost every possible method for the soft handover (SO) and mobile assisted handover (MAHO). It means that if you build a system with handover algorithms at cell edge, you have to design a system without SO and MAHO, to avoid those patents. You can’t either receive two pilot sequences from two base stations simultaneously, or compare the signal strength at the mobile side between the two. Then, what can you do? Will you pay millions of dollars to the legal owner of it, or try not to use both SO and MAHO?
This is the main reason why the WiMAX system uses only hard handover (HO) and why the cell edge performance of that system doesn’t quite good. Another bad new is that even SO and MAHO was flied in 1992 and 1994 respectively (the patent right is valid for 15 years) there are tons of patents which covers another aspect of SO and MAHO. It will be the same in CDMA, LDPC, and probably MIMO.
As explained above, a well-written patent influence on the whole system design. In addition, it presents a huge amount of money to the legal owner (usually a company) and to the inventor (as some form of incentives). For example, Samsung pays about several hundred million dollars to Qualcomm as the CDMA patent right PER YEAR. And when they make a cell phone, they must use Qualcomm’s MSM chip and pay 5.25% - 5.75% of whole retail price as a royalty. Samsung makes at least 100 million cellphones per year.. imagine the amount of money that the CDMA patent makes. Yes, it is quite huge, and a little part of it (which is given to the inventor) is also huge.
The reason that I am writing this article is not to debase the importance of writing a good paper. I think it is one of the most important things to do as a grad student. (Especially the best paper award is a life-long honor. Isn’t it, Kaibin, Ramya, Chan-Byoung?) But it could be better, if you think about filing a patent for your brilliant idea BEFORE you submit it as a paper. (Usually if a thing is already presented and published before, it can’t be the claim of a patent.) You could be a millionaire, or if not so, there is nothing to lose.
I think a good patent may not guarantees a good paper. But a good paper may guarantees a good patent, because the patent can scale down the novel idea in the paper into a practical method and apparatus. One good example is the Alamouti Code. S. Alamouti and V. Tarokh have filed a patent (US 6185258) in Sep. 16, 1997, just before they submit the famous Alamoti code paper.
——–
[Alamoti] 1. An arrangement comprising:
a coder responsive to incoming symbols, forming a set of channel symbols that incorporate redundancy, where the coder employs replications and, at least for some of the channel symbols, forms a negative of an incoming symbol, forms a complex conjugate of an incoming symbol, or forms a negative complex conjugate of an incoming symbol; and
an output stage that applies said channel symbols to at least one transmitter antenna to form at least two distinct channels over a transmission medium.
[link]
——–
As you see in the first claim above, technically any diversity based STBC may infringe their right. It is really terrifying. And it is more terrifying if I can find a patent that has a claim like this: “a device that uses multiple transmit antennas and multiple receive antennas for communication.” It will be all MIMO companies’ nightmare.
