1) If you are converting 28 volts to 12 volts, you need to stop talking about LDOs. LDO stands for "low drop out", and refers to a regulator which can operate with low voltage across it. "Low voltage" is generally used for less than about 2 volts, although there is no universal standard. Since any regulator you use will have an input-output voltage of 16 volts, this is obviously a non-starter.
2) In principle, at a current of 150 mA, a linear regulator will dissipate 16 x 0.15m or 2.4 watts. For continuous use, your suggested part will die. A dc-dc converter seems the obvious choice in this case.
3) Now we get to the important stuff. The stuff you haven't mentioned. How, exactly, are you going to use this? Note that the data sheet suggests it for use as an optical equivalent of an RWR. In these conditions, it will almost never receive much illumination. But let's say it does. At 12 volts and 150 mA, peak dissipation in the detector array will be 2 watts, and I really doubt that that package can handle that. So, are you going to use it for transient detection, or do you expect continuous use? If it's continuous, you are misusing the part and it will probably fail. At these levels, of course, there is no need for a TIA - does this feed into your previous questions about fast pulses with very wide dynamic range? In principle, you can look at the amplitude of the reference outputs and disconnect the high sensitivity outputs when necessary.
EDIT - In a comment you state that "i use a TIA followed by photo diode , the opamp saturates at input 2.5mA itself". Now, I assume you meant "TIA following each photodiode". Even so, your requirement of 150 mA makes no sense. The high-sensitivity channels will be saturated and putting out 20 mA or so, so you'll need optical attenuation to keep from overdriving your TIAs. 6 outputs times 2.5 mA is 15 mA total.
The preceding, of course, could be wrong, since I could be misinterpreting your setup, operation and requirements. Which is why I asked, "How, exactly, are you going to use this?".
Stop playing coy. Stop trying to parcel out information in dribs and drabs. You are willfully keeping us in the dark, thinking we can help you if we don't know what your problem is, and your limited disclosure makes no sense.
Furthermore, if you look closely at the data sheet, it gives a diode rise time of 5 nsec. This will make the device largely unusable for pulse widths under 10 nsec.