Top Down Code Search to Locate An Optimum Code and Reduction in Code Blocking for CDMA Networks

Abstract

In this paper, a top down code search scheme is proposed that identify an optimum OVSF code for assignment at the base station of CDMA wireless networks. An optimum vacant code is the one whose usage produces least code blocking compared to other eligible codes. This scheme provides least code blocking compared to existing schemes without reassignments. In addition, the codes searched during locating the optimum code are significantly less than other existing schemes. The call establishment delay which is a significant factor for real time applications is directly proportional to the number of searches and should be low. The design is explained for single code, and extended to multi code assignment to improve code blocking. The multi code assignment is done using four ways. The first and second multi code schemes uses minimum and maximum rakes for a fixed rate system. The third scheme called scattered multi code scheme divide the incoming call into rate fractions equal to number of rakes available in the system, and each rate fraction is handled in a similar way in which the new call is handled in single code scheme. The rate fractions may be scattered or grouped in the code tree. The fourth multi code scheme, namely grouped multi code scheme allocates codes to all the fractions as close as possible. This maximizes future higher rate vacant codes availability by leaving a complete sub tree vacant when call using multi code ends.

Appendix: Code Searches

1.1 Pure Top Down Code Searches

For a new call with rate $2^{l-1}R$, the codes searched are

$$\begin{aligned} N_{TD} =2(L-l)+1 \end{aligned}$$

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1.2 CFA Code Searches

For a call of rate $2^{l-1}R$, the maximum number of code searched to find vacant code in layer $l$ is $2^{L-l}$. If there are $z$ vacant codes in layer $l,$ for each code, $C_{l,y_i } ,1\le i\le z, 1\le x_i \le 2^{l-1}$, CFA [3] scheme finds number of busy codes under immediate parent of each $C_{l,y_i }$. The total number of code searches for parents of each vacant code in layer l$+$1 are $z\times 2^{l+1}$. If a unique immediate parent code (say$C_{l\,+\,1,\left\lceil {y_i /2} \right\rceil }$) with maximum number of busy codes exists, new call will be assigned to its children and code searching stops. Otherwise, let $z_{1}$ number of parent codes in layer $l+1$ that leads to tie for maximum number of busy children. The number of code searches for layer $l+2$ are $z_1 \times 2^{l+2}$. If a unique result does not exist the procedure is repeated till layer $L$ giving maximum code searches. The total number of code searches for CFA becomes

$$\begin{aligned} N_{CFA} =2^{(L-l)}+z\times 2^{l+1}+z_1 \times 2^{l+2}+\ldots .+z_{L-2} \times 2^{l+L-1} \end{aligned}$$

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1.3 Top Down and Dynamic Code Assignment (DCA)

DCA circumvent code blocking problem by providing zero code blocking at the cost of increased number of code searches which makes it unsuitable for real time applications. The use of TD scheme can significantly reduce code searches in DCA scheme as follows.

1.3.1 Conventional DCA

For new $2^{l-1}R$ call arrival, the maximum number of codes searched to find a vacant code are given by

$$\begin{aligned} NC_{DCA}^1 =2^{L-l} \end{aligned}$$

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If vacant code is available, procedure stops. Otherwise, let $k_{1 }$is the number of blocked codes denoted by $C_{l,x_i }$, where $1\le i\le k_1$ and $1\le x_i \le 2^{L-l}$ in the layer $l$. For each of the blocked codes, the codes in layer $l_{1}, l_1 \in [1,2,\ldots l-1]$ are checked to count number of busy children. The number of codes searched in layer $l_{1}, l_1 \in [l-1,l-2,\ldots ,1]$ are $2^{l-l_1 }$. The total code searches in layer 1 to $l$-l is

$$\begin{aligned} NC_{DCA}^2 =k_1 \times (2+4+\cdots .2^{l-1}). \end{aligned}$$

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Total number of codes searched in DCA becomes

$$\begin{aligned} NC_{DCA}^{\prime } =NC_{DCA}^1 +NC_{DCA}^2 =2^{L-l}+k_1 \times \sum \limits _{i=1}^{l-1} {2^{i}} \end{aligned}$$

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A code with minimum number of children codes is selected, reassignments needs to be carried out for it. Let at least one code in layer $p|p<l$ is busy, the number of codes need to be check for code availability is

$$\begin{aligned} N_{DCA}^{{\prime \prime }} =\sum \limits _{p=1}^{l-1} {a_p } \times 2^{L-p} \end{aligned}$$

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where $a_{p}=0$ if layer $p$ do not have a busy code and $a_{p}=1$ if layer $p$ has a busy code.

So, total number searches becomes

$$\begin{aligned}&N_{DCA} =\sum \limits _{l=1}^L {\lambda _l \times [NC_{DCA}^{\prime } +NC_{DCA}^{{\prime \prime }} ]} \end{aligned}$$

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$$\begin{aligned}&N_{DCA} =\sum \limits _{l=1}^L {\lambda _l \times [NC_{DCA}^{\prime } +NC_{DCA}^{{\prime \prime }} ]} \end{aligned}$$

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1.3.2 DCA Top Down

The number of code searches required to identify suitable blocked code are

$$\begin{aligned} N_{TD-DCA} =2(L-l)+1 \end{aligned}$$

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If suitable code is $C_{l,n_l }$, let there are $p_{l^{\prime }} ,1\le l^{\prime }\le l-1$ busy children of $C_{l,n_l }$ in layer $l^{\prime }$, the total busy children who need reassignments are $\sum \nolimits _{l^{\prime }=1}^{l-1} {p_{l^{\prime }} }$. The maximum number of searches required to identify $\sum \nolimits _{l^{\prime }=1}^{l-1} {p_{l^{\prime }} }$ vacant codes are

$$\begin{aligned} N_{TD-DCA_2 } =\sum \limits _{l^{\prime }=1}^{l-1} {2^{l^{\prime }}} \end{aligned}$$

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The number of code searches required to shift all $p_{l^{\prime }} ,1\le l^{\prime }\le l-1$ busy codes are

$$\begin{aligned} N_{TD-DCA_3 } =\sum \limits _{l^{\prime }=1}^{l-1} {p_{l^{\prime }} \times (2\times (L-l^{\prime })} +1) \end{aligned}$$

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The total code searches in TD DCA are

$$\begin{aligned}&N_{TD-DCA} =N_{TD-DCA_1 } +N_{TD-DCA_2 } +N_{TD-DCA_3 } \end{aligned}$$

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$$\begin{aligned}&N_{TD-DCA} =2(L-l)+1+\sum \limits _{l^{\prime }=1}^{l-1} {(2^{l^{\prime }}+p_{l^{\prime }} \times (2\times (L-l^{\prime })+1))} \end{aligned}$$

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