What is the general formula of BER in SIMO systems.
My system uses BPSK and my channel is AWGN.
I found many formulas but for specific cases and no generic one!.
An example of how i can find BER with Rx=10 is appreciated.
Thanks.
The generic formula can be written as :
p = 1/2 - 1/2*(1+1./power(10,SNRdB/10)).^(-1/2);
theoryBer= 0;
for k=0:1:NumOfRec-1
theoryBer = theoryBer + nchoosek(NumOfRec-1+k,k).*(1-p).^k;
end
Note: Do not forget to specify number of receivers!.
Related
A program to run a Schmid-Leiman transformation using SPSS's Matrix language was published in 2005 by Woolf & Preising in Behavior Research Methods volume 37, pages 48 to 58). It is probably not important for you to know what a Schmid-Leiman transformation is, but I'll explain in comments if you feel it is necessary.
In modifying the program for my own data, I'm getting an error I can't figure out:
Error # 12302 in column 12. Text: ,
Syntax error.
Execution of this command stops.
Error in RIGHT HAND SIDE of COMPUTE command.
The MATRIX statement skipped.
Here is the beginning of the code. The error is showing as coming in Line 6:
* Encoding: UTF-8.
* Schmid-Leiman Solution for 2 level higher-order Factor analysis.
Matrix.
* ENTER YOUR SPECIFICATIONS HERE.
* Enter first-order pattern matrix.
Compute F1={.461, .253, -.058, -.069;
.241, .600, .143, .033;
.582, .047, -.077, -.125;
.327, .297, -.120, -.166;
.176, .448, -.240, -.099;
.680, .069, -.036, -.138;
.415, .228, -.091, -.153;
.
.
.
.390, .205, .002, -.098;
.164, .369, -.170, -.047
}.
As shown above, the text generating the error is shown as a comma (,), but the actual text (following the COMPUTE statement) in column 12 is an open bracket ({). So I have no idea what is going on. Can someone help?
For reference, the original code as proposed by Woolf & Preising (2005) is found here;
The Woolf & Preising article is found here
PS: The sample program given in the link above does run on my copy of SPSS. Here's the beginning of that code:
* Schmid-Leiman Solution for 2 level higher-order Factor analysis.
Matrix.
* ENTER YOUR SPECIFICATIONS HERE.
* Enter first-order pattern matrix.
Compute F1={0.099, 0.5647, -0.1521;
0.0124, 0.9419, -0.1535;
-0.1501, 0.6177, 0.4218;
0.7441, -0.0882, 0.1425;
0.6241, 0.2793, -0.1137;
0.8693, -0.0331, 0.0289;
-0.0154, -0.2706, 0.6262;
-0.0914, 0.0995, 0.7216;
0.1502, 0.0835, 0.398}.
I'm trying to find the last digit of the result of any number raised to any power, using binomial theorem, not modulus or something. Please explain me why last digit of a number's unit number raised to a power is same as the original number raised to the same power using binomial theorem.
Ex. XV^Y = V^Y
Also, I found out that each integer each its cyclicity and I understand that. But I'm confused since:
17^8 = 7^8 = 7^4 since 8 is a multiple of 4.
But why not 7^2 = 7^8 as well? 8 is also a multiple of 2.
It's because of the last digit that you are raising to a power several times and not about the power.
7^1=...7 <=
7^2=...9
7^3=...3
7^4=...1
7^5=...7 <=
7^6=...9
7^7=...3
7^8=...1
7^9=...7 <=
Say you have a number x=t*10+u, where t is the "tens" and u is the units, so e.g. 1234=123*10+4. The binomial theorem states: x^n = sum{k=0,...,n} (t*10)^(n-k)*u^k. As long as (n-k)>0, the summand will be a multiple of 10. You should be able to figure it out from there.
I searched a lot, but I was not able to find any example code, which describes how to use the WEKA HierarchicalClusterer. Using the following C#-code gives me an IllegalArgumentException at "agg.buildClusterer(insts);".
weka.clusterers.HierarchicalClusterer agg = new weka.clusterers.HierarchicalClusterer();
agg.setNumClusters(NumCluster);
/*
Tag[] TAGS_LINK_TYPE = agg.getLinkType().getTags();
agg.setLinkType(new SelectedTag(1, TAGS_LINK_TYPE));
*/
agg.buildClusterer(insts);
for (int i = 0; i < insts.numInstances(); i++)
{
int clusterNumber = agg.clusterInstance(insts.instance(i));
}
The StackTrace says:
at java.util.PriorityQueue..ctor(Int32 initialCapacity, Comparator comparator)
at weka.clusterers.HierarchicalClusterer.doLinkClustering(Int32 , Vector[] , Node[] )
at weka.clusterers.HierarchicalClusterer.buildClusterer(Instances data)
but no Message or InnerException is specified.
The varaible "insts" is an Instances-object, which only holds instances with an equal amount of numerical attributes.
Is anyone able to quickly find my error or please post/link some example code?
Further, is the setting of the LinkType (commented code) correct?
Thanks,
Björn
The HierarchicalClusterer class has a TAGS_LINK_TYPE attribute. So like
agg.setLinkType(new SelectedTag(1, HierarchicalClusterer.TAGS_LINK_TYPE));
will achieve what you are after for setting the linking. Now what on earth does that 1 mean? From the javadocs we see what TAGS_LINK_TYPE contains:
-L Link type (Single, Complete, Average, Mean, Centroid, Ward, Adjusted complete, Neighbor Joining)
[SINGLE|COMPLETE|AVERAGE|MEAN|CENTROID|WARD|ADJCOMLPETE|NEIGHBOR_JOINING]
In general, your code looks ok for the C# case. I see you don't set the distance metric in your example above and maybe you would want to do this? I too use Weka as best I can with C# using IKVM. I have found the dataset allowed for hierarchical clustering is not too large. Maybe your dataset exceeds what WEKA can handled and you would avoid your error if you reduced the size of the dataset?
I have to partition a multiset into two sets who sums are equal. For example, given the multiset:
1 3 5 1 3 -1 2 0
I would output the two sets:
1) 1 3 3
2) 5 -1 2 1 0
both of which sum to 7.
I need to do this using Z3 (smt2 input format) and "Linear Arithmetic Logic", which is defined as:
formula : formula /\ formula | (formula) | atom
atom : sum op sum
op : = | <= | <
sum : term | sum + term
term : identifier | constant | constant identifier
I honestly don't know where to begin with this and any advice at all would be appreciated.
Regards.
Here is an idea:
1- Create a 0-1 integer variable c_i for each element. The idea is c_i is zero if element is in the first set, and 1 if it is in the second set. You can accomplish that by saying that 0 <= c_i and c_i <= 1.
2- The sum of the elements in the first set can be written as 1*(1 - c_1) + 3*(1 - c_2) + ... +
3- The sum of the elements in the second set can be written as 1*c1 + 3*c2 + ...
While SMT-Lib2 is quite expressive, it's not the easiest language to program in. Unless you have a hard requirement that you have to code directly in SMTLib2, I'd recommend looking into other languages that have higher-level bindings to SMT solvers. For instance, both Haskell and Scala have libraries that allow you to script SMT solvers at a much higher level. Here's how to solve your problem using the Haskell, for instance: https://gist.github.com/1701881.
The idea is that these libraries allow you to code at a much higher level, and then perform the necessary translation and querying of the SMT solver for you behind the scenes. (If you really need to get your hands onto the SMTLib encoding of your problem, you can use these libraries as well, as they typically come with the necessary API to dump the SMTLib they generate before querying the solver.)
While these libraries may not offer everything that Z3 gives you access to via SMTLib, they are much easier to use for most practical problems of interest.
I need a well tested Regular Expression (.net style preferred), or some other simple bit of code that will parse a USA/CA phone number into component parts, so:
3035551234122
1-303-555-1234x122
(303)555-1234-122
1 (303) 555 -1234-122
etc...
all parse into:
AreaCode: 303
Exchange: 555
Suffix: 1234
Extension: 122
None of the answers given so far was robust enough for me, so I continued looking for something better, and I found it:
Google's library for dealing with phone numbers
I hope it is also useful for you.
This is the one I use:
^(?:(?:[\+]?(?<CountryCode>[\d]{1,3}(?:[ ]+|[\-.])))?[(]?(?<AreaCode>[\d]{3})[\-/)]?(?:[ ]+)?)?(?<Number>[a-zA-Z2-9][a-zA-Z0-9 \-.]{6,})(?:(?:[ ]+|[xX]|(i:ext[\.]?)){1,2}(?<Ext>[\d]{1,5}))?$
I got it from RegexLib I believe.
This regex works exactly as you want with your examples:
Regex regexObj = new Regex(#"\(?(?<AreaCode>[0-9]{3})\)?[-. ]?(?<Exchange>[0-9]{3})[-. ]*?(?<Suffix>[0-9]{4})[-. x]?(?<Extension>[0-9]{3})");
Match matchResult = regexObj.Match("1 (303) 555 -1234-122");
// Now you have the results in groups
matchResult.Groups["AreaCode"];
matchResult.Groups["Exchange"];
matchResult.Groups["Suffix"];
matchResult.Groups["Extension"];
Strip out anything that's not a digit first. Then all your examples reduce to:
/^1?(\d{3})(\d{3})(\d{4})(\d*)$/
To support all country codes is a little more complicated, but the same general rule applies.
Here is a well-written library used with GeoIP for instance:
http://highway.to/geoip/numberparser.inc
here's a method easier on the eyes provided by the Z Directory (vettrasoft.com),
geared towards American phone numbers:
string_o s2, s1 = "888/872.7676";
z_fix_phone_number (s1, s2);
cout << s2.print(); // prints "+1 (888) 872-7676"
phone_number_o pho = s2;
pho.store_save();
the last line stores the number to database table "phone_number".
column values: country_code = "1", area_code = "888", exchange = "872",
etc.