Measurements of the turbulent density wavenumber spectrum,
δ
n
ˆ
e
(
k
⊥
)
, using the Doppler Back-Scattering (DBS) diagnostic are reported from DIII-D H-mode plasmas with electron cyclotron heating as the only auxiliary heating method. These electron-heated plasmas have low collisionality,
ν
e
∗
<
1
,
T
e
/
T
i
>
1
, and zero injected torque—a regime expected to be relevant for future fusion devices. We probe density fluctuations in the core (ρ ≈ 0.7) over a broad wavenumber range,
0.5
⩽
k
⊥
⩽
16
cm−1 (
0.1
⩽
k
⊥
ρ
s
⩽
5
), to characterize plasma instabilities and compare with theoretical predictions. We present a novel synthetic DBS diagnostic to relate the back-scattered power spectrum,
P
s
(
k
⊥
)
—which is directly measured by DBS—to the underlying electron density fluctuation spectrum,
δ
n
ˆ
e
(
k
⊥
)
. The synthetic DBS
P
s
(
k
⊥
)
spectrum is calculated by combining the SCOTTY beam-tracing code with a model
δ
n
ˆ
e
(
k
⊥
)
predicted either analytically or numerically. In this work we use the quasi-linear code Trapped Gyro-Landau Fluid (TGLF) to approximate the
δ
n
ˆ
e
(
k
⊥
)
spectrum. We find that TGLF, using the experimental profiles, is capable of closely reproducing the DBS measurements. Both the DBS measurements and the TGLF-DBS synthetic diagnostic show a wavenumber spectrum with variable decay. The measurements show weak decay (k
−0.6) for k < 3.5 cm−1, with k
−2.6 at intermediate-k (
3.5
⩽
k
⩽
8.5
cm−1), and rapid decay (k
−9.4) for k > 8.5 cm−1. Scans of physics parameters using TGLF suggest that the normalized
∇
T
e
scale-length,
R
/
L
T
e
, is an important factor for distinguishing microturbulence regimes in these plasmas. A combination of DBS observations and TGLF simulations indicate that fluctuations remain peaked at ITG-scales (low k) while
R
/
L
T
e
-driven TEM/ETG-type modes (intermediate/high k) are marginally sub-dominant.