The aim with soft particles is to remove the ugly artifact that appears when the particle quad intersects the scene. There are a lot of different approaches to solve this, some more complicate than others. The simplest formula for soft particles is to just fade the particle if it’s getting to close to the scene. To do this, the scene without particles has to be rendered first and the depth saved in a texture. When drawing the particles, the depth of the particle will be compared to the scene depth. The alpha should be increased by a smooth fade by this depth difference. The formula below in HLSL is the simplest possible for soft particles, and works very well. Scene_depth is the sampled depth (in viewspace) of the scene in the direction of the current pixel. Particle_depth is the depth(in viewspace) of the current particle pixel. Scale is used to control the “softness” of the intersection between particles and scene:
fade = saturate((scene_depth – particle_depth) * scale);
NVIDIA  proposes a method that the following fade should be used instead of the linear one described above, to make the fade even smoother.
float Output = 0.5*pow(saturate(2*(( Input > 0.5) ? 1-Input : Input)), ContrastPower);
Output = ( Input > 0.5) ? 1-Output : Output;
Umenhoffer  proposes a method called spherical billboards to deal with these problems. In this method, the volume is approximated by a sphere. This method also deals with the near clipplane problem that particles will instantly disappear if they get to close to the camera.
There is also an idea  that the alpha channel can be used to represent the density of the particles. Although this method has the drawback that the textures might need to be redone by the artists.
The method by Microsoft  uses a combination of spherical billboards and a texture representation of the volume. But instead of using the alpha channel, they ray march the sphere and sample the density and volume from a 3D noise texture. The result can be seen in the image below.
The video below shows how soft shadows can increase realism in games using large particles. It’s originally an ad for Torque 3D engine.
 Soft Particles by NVIDIA
 Spherical Billboards and their Application to Rendering Explosions
 A Gamasutra article about soft particles
 A DirectX 10 implementation of soft particles by Microsoft, called Volumetric Particles