It looks like crabgrass, but When was this photo taken and what part of the south are you in?

It would also help to know where you live so we can eliminate some types of grass that don't grow in certain places. Be that as it may, you said, I’m about to embark on a backyard renovation. One of the first things that I need to do is to aerate and plants more seeds. You don't need to do any of those things. First of all, unless you live in the PNW, spring is a poor time to renovate a lawn. The best time of year to renovate is at the end of summer. There are two reasons for this. 1) summer heat will kill the newly seeded grass, and 2) crabgrass will dominate the newly seeded grass before you realize it. And lastly, aeration is not needed - there's a better way to soften your soil. By the picture I'm going to guess you live in a mid Atlantic state and have bermuda mixed with weeds. If you have obvious high spots or low spots, now is the time to level those out. Next learn about deep watering. Deep watering has been recommended for literally generations, but for some reason has been ignored in favor of daily light watering. Deep means watering 1 full inch all at one time. The best way to do that consistently is to put out some cat food or tuna cans around the yard and turn on the sprinklers. Time how long it takes to fill all the cans. My oscillator sprinkler takes 8 hours to fill the cans on full sweep. A neighbor's high flow system takes 20 minutes. You have to measure your own system. As to the frequency of watering, this depends on the air temperature more than any other factor with humidity coming in second. But in most cases here is a guide. For daily high temps below 70, deep water once a month. For temps between 70 and 80, water once every 3 weeks. For temps between 80 and 90, water every other week. For temps between 90 and 100, water once a week. For temps from 100 to 105, deep water every 5 days. For temps from 105 to 110, water once every 4 days. Note that you never deep water every day and you never water lightly. If you get a good rainfall, don't water again until the grass tells you it's dry. Simply watering properly will fix many lawn issues. Deep and infrequent watering discourages most weeds which need frequent shallow watering. It also helps to bring up nutrients from deeper in the soil for the plants to use. Mowing. Mow most grasses at the mower's highest setting, because this creates the most grass density and deepest root system. The exceptions are bermuda, centipede, and creeping bentgrass which are most dense when mowed at the mower's lowest setting. Fertilizer. Fertilize for the first time in late may for almost all grasses. The only exception is bermuda which can/should be fertilized after the second mowing in early spring and every month thereafter. Weed control. You have weeds, for sure. Assuming the grass at the perimeter is bermuda, then the weedy grasses look like a fescue or other wild bunch grass. It is harder to get weedy grasses out of grass than it is to get out broadleaf weeds like clover and dandelion. Renovation. If you have bermuda, you should never need to renovate. If you think it needs renovation, it probably needs proper watering. Or, it might need less shade than it's getting. Bermuda needs 5+ hours of unfiltered sunlight every day in the growing season. If you don't have that, then change the grass type or go to a shade loving ground cover. For example bermuda will not grow well next to a fence except the south side. If it is on the north, east, or west side of a fence, it will thin out and look poorly. No amount of renovation will permanently improve bermuda in the shade. If you want to renovate I would suggest strongly to not waste your spring worrying about it. Live with the weeds. The only time to renovate bermuda is in the hottest heat of summer. The best time to renovate fescue, rye, or Kentucky bluegrass is in the late summer. So now what do you want to do? And again, where do you live?

You're out of my normal range in terms of recommendations, but... Your lawn actually looks quite good from the middle distance, so that brings up the question as to your goal here. Making some normal assumptions, we'll start with the normal questions. Do you know what you currently have? I can't ID that from the far shot and I'm lousy at grass ID anyway. What is your watering and feeding regimen? Things will differ depending on whether you currently have a northern or southern lawn, although both tend to prefer deep and infrequent watering. A northern lawn down there will need more frequent watering, I'm thinking--perhaps every 5 days in the hottest part of summer, while a southern lawn shouldn't need to be soaked all that often as TN isn't Texas in terms of heat. But in both cases, you'll want to add about an inch of water all at once if the soil will support that (sandier soils may require modification for less, while heavy silts may hold more water and need watering far less often). What I'm saying here is that the look at a distance is so good that a simple fix in care may be enough for you to "rescue" this lawn (which does not look like it needs rescuing, half the people here would love it if you dug that lawn up and shipped it to them). But if you explain what bothers you, maybe reseeding really is the solution and we can suggest something for you.

For me, identification of grasses usually involves seeing the seed heads, but I'm no expert. They do look different enough to be different species; however, the one on the right could be what the plant looks like when it is about to produce a seed head. Here is an ARTICLE with more info.