How can I write this equation to fit in a single column using IEEEtran?

Question

\documentclass[journal]{IEEEtran}
\usepackage{eqnarray,amsmath}
\usepackage{amssymb}
\usepackage{mathtools}
\begin{document}
\begin{align} \max\limits_{\bm{P}^{(k)}} & R_k(\bm{P}^{(k)})=\sum\limits_{j\in c^{(k)}}\text{log}_2\left(1+\frac{p_j^{(k)}g_{j,j}^{(k)}}{\sigma_N^2+\sum\limits_{j'=1,j'\neq j}^{\vert \mathcal{C}^{(k)}\vert}p_{j'}^{(k)}h_{j',j}^{(k)}+p_{b}^{(k)}h_{b,j}^{(k)}}\right) \nonumber\\ \text{s.t}. &C_{1}:0\le p_{b}^{(k)}\leq P_{b}^{\max}\nonumber\\ &C_{2}:0\leq p_{j}^{(k)}\leq P_{d}^{\max},~~\forall j\in c^{(k)}\nonumber\\ &C_{3}:\text{log}_2(1+\frac{p_b^{(k)}g_{b,n}^{(k)}}{\sigma_N^2+\sum\limits_{j\in c^{(k)}}p_j^{(k)}h_{j,b}^{(k)}})\geq R_{b,min}\label{powerprob}\end{align}
\end{document}

Answer 1

Some suggestions:

• Divide the material into two parts, and place the first part in a multlined environment and the second in an aligned environment. Place this material in a gather enrivonment.

• For the long denominator, use \substack to introduce a line break in the lower limit of summation, and use a \smashoperator directive to "smash" the space around the summation symbol.

• Place the "such that" string in an \intertext directive.

• Optional: To limit the size of the outer parentheses, encase the \smashoperator{...} material in a \smash[]{...} wrapper. In general, doing this might be somewhat problematic. Here, though, there's no problem as the material that comes below is doesn't protrude much to the right.

\documentclass[journal]{IEEEtran}
\usepackage{amssymb,mathtools,bm}
\begin{document}
\begin{gather}\label{powerprob}
\begin{multlined}
\max_{\bm{P}^{(k)}} R_k(\bm{P}^{(k)})\\[-3ex]
=\sum_{j\in c^{(k)}} \log_2 \left( 1+\frac{p_j^{(k)}g_{j,j}^{(k)}}{
\sigma_N^2 +
\smash[b]{\smashoperator{
\sum\limits_{\substack{j'=1,\\j'\neq j\hfill}}^
{\lvert\mathcal{C}^{(k)}\rvert}}}\,
p_{j'}^{(k)}h_{j',j}^{(k)}
+p_{b}^{(k)}h_{b,j}^{(k)}}\right)
\end{multlined} \notag \\
\intertext{such that}
\begin{aligned}[b]
&C_{1}\colon 0\leq p_{b}^{(k)}\leq P_{b}^{\max}  \\[1ex]
&C_{2}\colon 0\leq p_{j}^{(k)}\leq P_{d}^{\max}\quad \forall j\in c^{(k)}  \\[1ex]
&C_{3}\colon \log_2\left(
1+\frac{p_b^{(k)}g_{b,n}^{(k)}}{ \sigma_N^2+\sum_{j\in c^{(k)}} p_j^{(k)}h_{j,b}^{(k)}}
\right)\geq R_{b,\min}
\end{aligned}
\end{gather}
\end{document}

Answer 2

You can use cuted package and use strip envrionment to achieve it:

\documentclass[journal]{IEEEtran}
\usepackage{mathtools,lipsum}
\usepackage{cuted}
%https://tex.stackexchange.com/questions/255086/how-to-put-a-long-equation-spanning-two-columns-while-using-ieeetran
\begin{document}
    \lipsum
    \begin{strip}
        \begin{align}
         \max\limits_{{P}^{(k)}} & R_k({P}^{(k)})=\sum\limits_{j\in c^{(k)}}\text{log}_2\left(1+\frac{p_j^{(k)}g_{j,j}^{(k)}}{\sigma_N^2+\sum\limits_{j'=1,j'\neq j}^{\vert \mathcal{C}^{(k)}\vert}p_{j'}^{(k)}h_{j',j}^{(k)}+p_{b}^{(k)}h_{b,j}^{(k)}}\right) \nonumber\\ \text{s.t}. &C_{1}:0\le p_{b}^{(k)}\leq P_{b}^{\max}\nonumber\\ &C_{2}:0\leq p_{j}^{(k)}\leq P_{d}^{\max},~~\forall j\in c^{(k)}\nonumber\\ &C_{3}:\text{log}_2(1+\frac{p_b^{(k)}g_{b,n}^{(k)}}{\sigma_N^2+\sum\limits_{j\in c^{(k)}}p_j^{(k)}h_{j,b}^{(k)}})\geq R_{b,min}\label{powerprob}
        \end{align}
    \end{strip}
\lipsum
\end{document}

which would give you

PS: I did not know what you mean by \bm, hence, I removed it.